Agreement of Anterior Segment Parameters Obtained From Swept-Source Fourier-Domain and Time-Domain Anterior Segment Optical Coherence Tomography.

PubMed

Chansangpetch, Sunee; Nguyen, Anwell; Mora, Marta; Badr, Mai; He, Mingguang; Porco, Travis C; Lin, Shan C

2018-03-01

To assess the interdevice agreement between swept-source Fourier-domain and time-domain anterior segment optical coherence tomography (AS-OCT). Fifty-three eyes from 41 subjects underwent CASIA2 and Visante OCT imaging. One hundred eighty-degree axis images were measured with the built-in two-dimensional analysis software for the swept-source Fourier-domain AS-OCT (CASIA2) and a customized program for the time-domain AS-OCT (Visante OCT). In both devices, we examined the angle opening distance (AOD), trabecular iris space area (TISA), angle recess area (ARA), anterior chamber depth (ACD), anterior chamber width (ACW), and lens vault (LV). Bland-Altman plots and intraclass correlation (ICC) were performed. Orthogonal linear regression assessed any proportional bias. ICC showed strong correlation for LV (0.925) and ACD (0.992) and moderate agreement for ACW (0.801). ICC suggested good agreement for all angle parameters (0.771-0.878) except temporal AOD500 (0.743) and ARA750 (nasal 0.481; temporal 0.481). There was a proportional bias in nasal ARA750 (slope 2.44, 95% confidence interval [CI]: 1.95-3.18), temporal ARA750 (slope 2.57, 95% CI: 2.04-3.40), and nasal TISA500 (slope 1.30, 95% CI: 1.12-1.54). Bland-Altman plots demonstrated in all measured parameters a minimal mean difference between the two devices (-0.089 to 0.063); however, evidence of constant bias was found in nasal AOD250, nasal AOD500, nasal AOD750, nasal ARA750, temporal AOD500, temporal AOD750, temporal ARA750, and ACD. Among the parameters with constant biases, CASIA2 tends to give the larger numbers. Both devices had generally good agreement. However, there were proportional and constant biases in most angle parameters. Thus, it is not recommended that values be used interchangeably.

Study of the Effect of Temporal Sampling Frequency on DSCOVR Observations Using the GEOS-5 Nature Run Results. Part II; Cloud Coverage

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Yang, Yuekui

2016-01-01

This is the second part of a study on how temporal sampling frequency affects satellite retrievals in support of the Deep Space Climate Observatory (DSCOVR) mission. Continuing from Part 1, which looked at Earth's radiation budget, this paper presents the effect of sampling frequency on DSCOVR-derived cloud fraction. The output from NASA's Goddard Earth Observing System version 5 (GEOS-5) Nature Run is used as the "truth". The effect of temporal resolution on potential DSCOVR observations is assessed by subsampling the full Nature Run data. A set of metrics, including uncertainty and absolute error in the subsampled time series, correlation between the original and the subsamples, and Fourier analysis have been used for this study. Results show that, for a given sampling frequency, the uncertainties in the annual mean cloud fraction of the sunlit half of the Earth are larger over land than over ocean. Analysis of correlation coefficients between the subsamples and the original time series demonstrates that even though sampling at certain longer time intervals may not increase the uncertainty in the mean, the subsampled time series is further and further away from the "truth" as the sampling interval becomes larger and larger. Fourier analysis shows that the simulated DSCOVR cloud fraction has underlying periodical features at certain time intervals, such as 8, 12, and 24 h. If the data is subsampled at these frequencies, the uncertainties in the mean cloud fraction are higher. These results provide helpful insights for the DSCOVR temporal sampling strategy.

Thermal stabilization of static single-mirror Fourier transform spectrometers

NASA Astrophysics Data System (ADS)

Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.

2017-05-01

Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.

Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms.

PubMed

Trillo, C; Doval, A F; López-Vázquez, J C

2010-07-05

Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method.

Areal and Temporal Analysis of Precipitation Patterns In Slovakia Using Spectral Analysis

NASA Astrophysics Data System (ADS)

Pishvaei, M. R.

Harmonic analysis as an objective method of precipitation seasonality studying is ap- plied to the 1901-2000 monthly precipitation averages at five stations in the low-land part of Slovakia with elevation less than 800 m a.s.l. The significant harmonics of long-term precipitation series have been separately computed for eight 30-year peri- ods, which cover the 20th century and some properties and the variations are com- pared to 100-year monthly precipitation averages. The selected results show that the first and the second harmonics pre-dominantly influence on the annual distribution and climatic seasonal regimes of pre-cipitation that contribute to the precipitation am- plitude/pattern with about 20% and 10%, respectively. These indicate annual and half year variations. The rest harmon-ics often have each less than 5% contribution on the Fourier interpolation course. Maximum in yearly precipitation course, which oc- curs approximately at the begin-ning of July, because of phase changing shifts then to the middle of June. Some probable reasons regarding to Fourier components are discussed. In addition, a tem-poral analysis over precipitation time series belonging to the Hurbanovo Observa-tory as the longest observational series on the territory of Slovakia (with 130-year precipitation records) has been individually performed and possible meteorological factors responsible for the observed patterns are suggested. A comparison of annual precipitation course obtained from daily precipitation totals analysis and polynomial trends with Fourier interpolation has been done too. Daily precipitation data in the latest period are compared for some stations in Slovakia as well. Only selected results are pre-sented in the poster.

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

PubMed

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

Spectral analysis of temporal non-stationary rainfall-runoff processes

NASA Astrophysics Data System (ADS)

Chang, Ching-Min; Yeh, Hund-Der

2018-04-01

This study treats the catchment as a block box system with considering the rainfall input and runoff output being a stochastic process. The temporal rainfall-runoff relationship at the catchment scale is described by a convolution integral on a continuous time scale. Using the Fourier-Stieltjes representation approach, a frequency domain solution to the convolution integral is developed to the spectral analysis of runoff processes generated by temporal non-stationary rainfall events. It is shown that the characteristic time scale of rainfall process increases the runoff discharge variability, while the catchment mean travel time constant plays the role in reducing the variability of runoff discharge. Similar to the behavior of groundwater aquifers, catchments act as a low-pass filter in the frequency domain for the rainfall input signal.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

PubMed

Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda

2017-09-13

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

A method to identify differential expression profiles of time-course gene data with Fourier transformation

PubMed Central

2013-01-01

Background Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. Results This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization. The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. Conclusions Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be potentially used to identify genes which have the same patterns or biological processes, and help facing the present and forthcoming challenges of data analysis in functional genomics. PMID:24134721

Ultrafast and versatile spectroscopy by temporal Fourier transform

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

Analysis of the Localization of Michelson Interferometer Fringes Using Fourier Optics and Temporal Coherence

ERIC Educational Resources Information Center

Narayanamurthy, C. S.

2009-01-01

Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in "Principles of Optics" by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer…

High resolution wavenumber analysis for investigation of arterial pulse wave propagation

NASA Astrophysics Data System (ADS)

Hasegawa, Hideyuki; Sato, Masakazu; Irie, Takasuke

2016-07-01

The propagation of the pulse wave along the artery is relatively fast (several m/s), and a high-temporal resolution is required to measure pulse wave velocity (PWV) in a regional segment of the artery. High-frame-rate ultrasound enables the measurement of the regional PWV. In analyses of wave propagation phenomena, the direction and propagation speed are generally identified in the frequency-wavenumber space using the two-dimensional Fourier transform. However, the wavelength of the pulse wave is very long (1 m at a propagation velocity of 10 m/s and a temporal frequency of 10 Hz) compared with a typical lateral field of view of 40 mm in ultrasound imaging. Therefore, PWV cannot be identified in the frequency-wavenumber space owing to the low resolution of the two-dimensional Fourier transform. In the present study, PWV was visualized in the wavenumber domain using phases of arterial wall acceleration waveforms measured by high-frame-rate ultrasound.

Ultrafast electrical spectrum analyzer based on all-optical Fourier transform and temporal magnification.

PubMed

Duan, Yuhua; Chen, Liao; Zhou, Haidong; Zhou, Xi; Zhang, Chi; Zhang, Xinliang

2017-04-03

Real-time electrical spectrum analysis is of great significance for applications involving radio astronomy and electronic warfare, e.g. the dynamic spectrum monitoring of outer space signal, and the instantaneous capture of frequency from other electronic systems. However, conventional electrical spectrum analyzer (ESA) has limited operation speed and observation bandwidth due to the electronic bottleneck. Therefore, a variety of photonics-assisted methods have been extensively explored due to the bandwidth advantage of the optical domain. Alternatively, we proposed and experimentally demonstrated an ultrafast ESA based on all-optical Fourier transform and temporal magnification in this paper. The radio-frequency (RF) signal under test is temporally multiplexed to the spectrum of an ultrashort pulse, thus the frequency information is converted to the time axis. Moreover, since the bandwidth of this ultrashort pulse is far beyond that of the state-of-the-art photo-detector, a temporal magnification system is applied to stretch the time axis, and capture the RF spectrum with 1-GHz resolution. The observation bandwidth of this ultrafast ESA is over 20 GHz, limited by that of the electro-optic modulator. Since all the signal processing is in the optical domain, the acquisition frame rate can be as high as 50 MHz. This ultrafast ESA scheme can be further improved with better dispersive engineering, and is promising for some ultrafast spectral information acquisition applications.

Predicting Geomorphic and Hydrologic Risks after Wildfire Using Harmonic and Stochastic Analyses

NASA Astrophysics Data System (ADS)

Mikesell, J.; Kinoshita, A. M.; Florsheim, J. L.; Chin, A.; Nourbakhshbeidokhti, S.

2017-12-01

Wildfire is a landscape-scale disturbance that often alters hydrological processes and sediment flux during subsequent storms. Vegetation loss from wildfires induce changes to sediment supply such as channel erosion and sedimentation and streamflow magnitude or flooding. These changes enhance downstream hazards, threatening human populations and physical aquatic habitat over various time scales. Using Williams Canyon, a basin burned by the Waldo Canyon Fire (2012) as a case study, we utilize deterministic and statistical modeling methods (Fourier series and first order Markov chain) to assess pre- and post-fire geomorphic and hydrologic characteristics, including of precipitation, enhanced vegetation index (EVI, a satellite-based proxy of vegetation biomass), streamflow, and sediment flux. Local precipitation, terrestrial Light Detection and Ranging (LiDAR) scanning, and satellite-based products are used for these time series analyses. We present a framework to assess variability of periodic and nonperiodic climatic and multivariate trends to inform development of a post-wildfire risk assessment methodology. To establish the extent to which a wildfire affects hydrologic and geomorphic patterns, a Fourier series was used to fit pre- and post-fire geomorphic and hydrologic characteristics to yearly temporal cycles and subcycles of 6, 4, 3, and 2.4 months. These cycles were analyzed using least-squares estimates of the harmonic coefficients or amplitudes of each sub-cycle's contribution to fit the overall behavior of a Fourier series. The stochastic variances of these characteristics were analyzed by composing first-order Markov models and probabilistic analysis through direct likelihood estimates. Preliminary results highlight an increased dependence of monthly post-fire hydrologic characteristics on 12 and 6-month temporal cycles. This statistical and probabilistic analysis provides a basis to determine the impact of wildfires on the temporal dependence of geomorphic and hydrologic characteristics, which can be incorporated into post-fire mitigation, management, and recovery-based measures to protect and rehabilitate areas subject to influence from wildfires.

A polarized digital shearing speckle pattern interferometry system based on temporal wavelet transformation.

PubMed

Feng, Ziang; Gao, Zhan; Zhang, Xiaoqiong; Wang, Shengjia; Yang, Dong; Yuan, Hao; Qin, Jie

2015-09-01

Digital shearing speckle pattern interferometry (DSSPI) has been recognized as a practical tool in testing strain. The DSSPI system which is based on temporal analysis is attractive because of its ability to measure strain dynamically. In this paper, such a DSSPI system with Wollaston prism has been built. The principles and system arrangement are described and the preliminary experimental result of the displacement-derivative test of an aluminum plate is shown with the wavelet transformation method and the Fourier transformation method. The simulations have been conducted with the finite element method. The comparison of the results shows that quantitative measurement of displacement-derivative has been realized.

Temporal changes in prevalence of scrub typhus rickettsia (Orientia tsutsugamushi) infecting the eggs of Leptotrombidium imphalum (Acari: Trombiculidae).

PubMed

Kollars, T M; Kengluecha, A; Khlaimanee, N; Tanskul, P

2001-01-01

Eggs from seven colony lines of the chigger mite Leptotrombidium imphalum (Vercammen-Grandjean & Langston) were examined for infection with Orientia tsutsugamushi (Hyashi), the etiologic agent of scrub typhus. The polymerase chain reaction (PCR) using primers OtP 56.809 and OtM 56.1221, which amplify a 291 bp region of the P56 gene of O. tsutsugamushi, was used to detect scrub typhus within single eggs. All seven chigger mite lines produced infected eggs with varying rates of infection (Li1 = 8.1%, n = 124; Li2 = 45.6%, n = 90; Li3 = 30.1%, n = 144; Li4 = 31.7%, n = 145; Li5 = 21.3%, n = 136; Li6 = 41.6% n = 77; Li7 = 22.5%, n = 110). The 3 wk with the highest infection rates for each line using Fourier analysis were as follows: Li1 = 2, 7, 14; Li2 = 4, 6, 12; Li3 = 3, 6, 12; Li4 = 4, 6, 12; Li5 = 5, 7, 14; Li7 = 4, 6, 12. Li6 only had nine measurements over time; therefore, Li6 was excluded from individual analysis. Infection rates of scrub typhus in eggs occurred in a 2-wk 2-d cycle, using Fourier analysis of combined data. Not only did infection rates vary among the progeny of females, but temporal variation also occurred.

Ozone Temporal Variability in the Subarctic Region: Comparison of Satellite Measurements with Numerical Simulations

NASA Astrophysics Data System (ADS)

Shved, G. M.; Virolainen, Ya. A.; Timofeyev, Yu. M.; Ermolenko, S. I.; Smyshlyaev, S. P.; Motsakov, M. A.; Kirner, O.

2018-01-01

Fourier and wavelet spectra of time series for the ozone column abundance in the atmospheric 0-25 and 25-60 km layers are analyzed from SBUV satellite observations and from numerical simulations based on the RSHU and EMAC models. The analysis uses datasets for three subarctic locations (St. Petersburg, Harestua, and Kiruna) for 2000-2014. The Fourier and wavelet spectra show periodicities in the range from 10 days to 10 years and from 1 day to 2 years, respectively. The comparison of the spectra shows overall agreement between the observational and modeled datasets. However, the analysis has revealed differences both between the measurements and the models and between the models themselves. The differences primarily concern the Rossby wave period region and the 11-year and semiannual periodicities. Possible reasons are given for the differences between the models and the measurements.

Use of Fourier transforms for asynoptic mapping: Applications to the Upper Atmosphere Research Satellite microwave limb sounder

NASA Technical Reports Server (NTRS)

Elson, Lee S.; Froidevaux, Lucien

1993-01-01

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large-scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

Comparison of fMRI analysis methods for heterogeneous BOLD responses in block design studies

PubMed Central

Bernal-Casas, David; Fang, Zhongnan; Lee, Jin Hyung

2017-01-01

A large number of fMRI studies have shown that the temporal dynamics of evoked BOLD responses can be highly heterogeneous. Failing to model heterogeneous responses in statistical analysis can lead to significant errors in signal detection and characterization and alter the neurobiological interpretation. However, to date it is not clear that, out of a large number of options, which methods are robust against variability in the temporal dynamics of BOLD responses in block-design studies. Here, we used rodent optogenetic fMRI data with heterogeneous BOLD responses and simulations guided by experimental data as a means to investigate different analysis methods’ performance against heterogeneous BOLD responses. Evaluations are carried out within the general linear model (GLM) framework and consist of standard basis sets as well as independent component analysis (ICA). Analyses show that, in the presence of heterogeneous BOLD responses, conventionally used GLM with a canonical basis set leads to considerable errors in the detection and characterization of BOLD responses. Our results suggest that the 3rd and 4th order gamma basis sets, the 7th to 9th order finite impulse response (FIR) basis sets, the 5th to 9th order B-spline basis sets, and the 2nd to 5th order Fourier basis sets are optimal for good balance between detection and characterization, while the 1st order Fourier basis set (coherence analysis) used in our earlier studies show good detection capability. ICA has mostly good detection and characterization capabilities, but detects a large volume of spurious activation with the control fMRI data. PMID:27993672

Laser induced periodic surface structuring on Si by temporal shaped femtosecond pulses.

PubMed

Almeida, G F B; Martins, R J; Otuka, A J G; Siqueira, J P; Mendonca, C R

2015-10-19

We investigated the effect of temporal shaped femtosecond pulses on silicon laser micromachining. By using sinusoidal spectral phases, pulse trains composed of sub-pulses with distinct temporal separations were generated and applied to the silicon surface to produce Laser Induced Periodic Surface Structures (LIPSS). The LIPSS obtained with different sub-pulse separation were analyzed by comparing the intensity of the two-dimensional fast Fourier Transform (2D-FFT) of the AFM images of the ripples (LIPSS). It was observed that LIPSS amplitude is more emphasized for the pulse train with sub-pulses separation of 128 fs, even when compared with the Fourier transform limited pulse. By estimating the carrier density achieved at the end of each pulse train, we have been able to interpret our results with the Sipe-Drude model, that predicts that LIPSS efficacy is higher for a specific induced carrier density. Hence, our results indicate that temporal shaping of the excitation pulse, performed by spectral phase modulation, can be explored in fs-laser microstructuring.

Harmonic regression based multi-temporal cloud filtering algorithm for Landsat 8

NASA Astrophysics Data System (ADS)

Joshi, P.

2015-12-01

Landsat data archive though rich is seen to have missing dates and periods owing to the weather irregularities and inconsistent coverage. The satellite images are further subject to cloud cover effects resulting in erroneous analysis and observations of ground features. In earlier studies the change detection algorithm using statistical control charts on harmonic residuals of multi-temporal Landsat 5 data have been shown to detect few prominent remnant clouds [Brooks, Evan B., et al, 2014]. So, in this work we build on this harmonic regression approach to detect and filter clouds using a multi-temporal series of Landsat 8 images. Firstly, we compute the harmonic coefficients using the fitting models on annual training data. This time series of residuals is further subjected to Shewhart X-bar control charts which signal the deviations of cloud points from the fitted multi-temporal fourier curve. For the process with standard deviation σ we found the second and third order harmonic regression with a x-bar chart control limit [Lσ] ranging between [0.5σ < Lσ < σ] as most efficient in detecting clouds. By implementing second order harmonic regression with successive x-bar chart control limits of L and 0.5 L on the NDVI, NDSI and haze optimized transformation (HOT), and utilizing the seasonal physical properties of these parameters, we have designed a novel multi-temporal algorithm for filtering clouds from Landsat 8 images. The method is applied to Virginia and Alabama in Landsat8 UTM zones 17 and 16 respectively. Our algorithm efficiently filters all types of cloud cover with an overall accuracy greater than 90%. As a result of the multi-temporal operation and the ability to recreate the multi-temporal database of images using only the coefficients of the fourier regression, our algorithm is largely storage and time efficient. The results show a good potential for this multi-temporal approach for cloud detection as a timely and targeted solution for the Landsat 8 research community, catering to the need for innovative processing solutions in the infant stage of the satellite.

Spatio-temporal hierarchy in the dynamics of a minimalist protein model

NASA Astrophysics Data System (ADS)

Matsunaga, Yasuhiro; Baba, Akinori; Li, Chun-Biu; Straub, John E.; Toda, Mikito; Komatsuzaki, Tamiki; Berry, R. Stephen

2013-12-01

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatio-temporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

PubMed

Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

2007-09-01

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

Fluorescence lifetime imaging and Fourier transform infrared spectroscopy of Michelangelo's David.

PubMed

Comelli, Daniela; Valentini, Gianluca; Cubeddu, Rinaldo; Toniolo, Lucia

2005-09-01

We developed a combined procedure for the analysis of works of art based on a portable system for fluorescence imaging integrated with analytical measurements on microsamples. The method allows us to localize and identify organic and inorganic compounds present on the surface of artworks. The fluorescence apparatus measures the temporal and spectral features of the fluorescence emission, excited by ultraviolet (UV) laser pulses. The kinetic of the emission is studied through a fluorescence lifetime imaging system, while an optical multichannel analyzer measures the fluorescence spectra of selected points. The chemical characterization of the compounds present on the artistic surfaces is then performed by means of analytical measurements on microsamples collected with the assistance of the fluorescence maps. The previous concepts have been successfully applied to study the contaminants on the surface of Michelangelo's David. The fluorescence analysis combined with Fourier transform infrared (FT-IR) measurements revealed the presence of beeswax, which permeates most of the statue surface, and calcium oxalate deposits mainly arranged in vertical patterns and related to rain washing.

Independent component analysis for onset detection in piano trills

NASA Astrophysics Data System (ADS)

Brown, Judith C.; Todd, Jeremy G.; Smaragdis, Paris

2002-05-01

The detection of onsets in piano music is difficult due to the presence of many notes simultaneously and their long decay times from pedaling. This is even more difficult for trills where the rapid note changes make it difficult to observe a decrease in amplitude for individual notes in either the temporal wave form or the time dependent Fourier components. Occasionally one note of the trill has a much lower amplitude than the other making an unambiguous determination of its onset virtually impossible. We have analyzed a number of trills from CD's of performances by Horowitz, Ashkenazy, and Goode, choosing the same trill and different performances where possible. The Fourier transform was calculated as a function of time, and the magnitude coefficients served as input for a calculation using the method of independent component analysis. In most cases this gave a more definitive determination of the onset times, as can be demonstrated graphically. For comparison identical calculations have been carried out on recordings of midi generated performances on a Yamaha Disclavier piano.

Comparison of fMRI analysis methods for heterogeneous BOLD responses in block design studies.

PubMed

Liu, Jia; Duffy, Ben A; Bernal-Casas, David; Fang, Zhongnan; Lee, Jin Hyung

2017-02-15

A large number of fMRI studies have shown that the temporal dynamics of evoked BOLD responses can be highly heterogeneous. Failing to model heterogeneous responses in statistical analysis can lead to significant errors in signal detection and characterization and alter the neurobiological interpretation. However, to date it is not clear that, out of a large number of options, which methods are robust against variability in the temporal dynamics of BOLD responses in block-design studies. Here, we used rodent optogenetic fMRI data with heterogeneous BOLD responses and simulations guided by experimental data as a means to investigate different analysis methods' performance against heterogeneous BOLD responses. Evaluations are carried out within the general linear model (GLM) framework and consist of standard basis sets as well as independent component analysis (ICA). Analyses show that, in the presence of heterogeneous BOLD responses, conventionally used GLM with a canonical basis set leads to considerable errors in the detection and characterization of BOLD responses. Our results suggest that the 3rd and 4th order gamma basis sets, the 7th to 9th order finite impulse response (FIR) basis sets, the 5th to 9th order B-spline basis sets, and the 2nd to 5th order Fourier basis sets are optimal for good balance between detection and characterization, while the 1st order Fourier basis set (coherence analysis) used in our earlier studies show good detection capability. ICA has mostly good detection and characterization capabilities, but detects a large volume of spurious activation with the control fMRI data. Copyright © 2016 Elsevier Inc. All rights reserved.

Interpretations of Frequency Domain Analyses of Neural Entrainment: Periodicity, Fundamental Frequency, and Harmonics.

PubMed

Zhou, Hong; Melloni, Lucia; Poeppel, David; Ding, Nai

2016-01-01

Brain activity can follow the rhythms of dynamic sensory stimuli, such as speech and music, a phenomenon called neural entrainment. It has been hypothesized that low-frequency neural entrainment in the neural delta and theta bands provides a potential mechanism to represent and integrate temporal information. Low-frequency neural entrainment is often studied using periodically changing stimuli and is analyzed in the frequency domain using the Fourier analysis. The Fourier analysis decomposes a periodic signal into harmonically related sinusoids. However, it is not intuitive how these harmonically related components are related to the response waveform. Here, we explain the interpretation of response harmonics, with a special focus on very low-frequency neural entrainment near 1 Hz. It is illustrated why neural responses repeating at f Hz do not necessarily generate any neural response at f Hz in the Fourier spectrum. A strong neural response at f Hz indicates that the time scales of the neural response waveform within each cycle match the time scales of the stimulus rhythm. Therefore, neural entrainment at very low frequency implies not only that the neural response repeats at f Hz but also that each period of the neural response is a slow wave matching the time scale of a f Hz sinusoid.

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.

FIBRE AND INTEGRATED OPTICS. OPTICAL PROCESSING OF INFORMATION: Method for optical data processing based on a two-pulse photon echo

NASA Astrophysics Data System (ADS)

Zakharov, S. M.; Manykin, Eduard A.

1995-02-01

The principles of optical processing based on dynamic spatial—temporal properties of two-pulse photon echo signals are considered. The properties of a resonant medium as an on-line filter of temporal and spatial frequencies are discussed. These properties are due to the sensitivity of such a medium to the Fourier spectrum of the second exiting pulse. Degeneracy of quantum resonant systems, demonstrated by the coherent response dependence on the square of the amplitude of the second pulse, can be used for 'simultaneous' correlation processing of optical 'signals'. Various methods for the processing of the Fourier optical image are discussed.

Speckle interferometry with temporal phase evaluation for measuring large-object deformation.

PubMed

Joenathan, C; Franze, B; Haible, P; Tiziani, H J

1998-05-01

We propose a new method for measuring large-object deformations byusing temporal evolution of the speckles in speckleinterferometry. The principle of the method is that by deformingthe object continuously, one obtains fluctuations in the intensity ofthe speckle. A large number of frames of the object motion arecollected to be analyzed later. The phase data for whole-objectdeformation are then retrieved by inverse Fourier transformation of afiltered spectrum obtained by Fourier transformation of thesignal. With this method one is capable of measuring deformationsof more than 100 mum, which is not possible using conventionalelectronic speckle pattern interferometry. We discuss theunderlying principle of the method and the results of theexperiments. Some nondestructive testing results are alsopresented.

Robust phase-shifting interferometry resistant to multiple disturbances

NASA Astrophysics Data System (ADS)

Liu, Qian; Yue, Xiaobin; Li, Lulu; Zhang, Hui; He, Jianguo

2018-04-01

Phase-shifting interferometry (PSI) is sensitive to many disturbances, including the environmental vibration, laser instability, phase-shifting error and camera nonlinearity. A robust PSI (RPSI) based on the temporal spectrum analysis is proposed to suppress the effects of these common disturbances. RPSI retrieves wavefront phase from the temporal Fourier spectrum peak, which is identified by detecting the modulus of spectrum, and a referencing method is presented to improve the phase extracting accuracy. Simulations demonstrate the feasibility and effectiveness of RPSI. Experimental results indicate that RPSI is resistant to common disturbances in implementing PSI and achieves accuracy better than 0.03 rad in the disturbed environment. RPSI relaxes requirements on the hardware, environment and operator, and provides an easy-to-use design of an interferometer.

A non-Fourier approach towards the analysis of heat transfer enhancement with water based nanofluids through a channel

NASA Astrophysics Data System (ADS)

Dil, Taimoor; Khan, M. Sabeel

2018-05-01

In this article, a non-Fourier approach to model the heat transfer phenomenon in nanofluids having application to automotive industry is studied. In this respect, a recently proposed hyperbolic heat flux equation is embedded into the heat energy equation and thereby incorporating the effect of thermal relaxation time. Nanofluids are formed by considering copper oxide (CuO), Titanium dioxide (TiO2) and Aluminum oxide (Al2O3) nano-solid particles in the base fluid. The flow governing system of PDEs along with boundary conditions is transformed into its respective coupled system of nonlinear ODEs using suitable similarity functions. Runge-Kutta-Fehlberg (RK-5) numerical scheme embedded with shooting method is implemented and used to solve the obtained boundary value problem. Numerical simulations are performed and tabulated to analyze the influence of solid volume fraction on local coefficient of skin-friction and Nusselt number. A comparison is made between the results by Fourier and present heat flux model. We conclude that the presented new approach is more general and thus allows predicting the influence of thermal relaxation time on the heat transfer characteristics. Moreover, consideration of present model over the Fourier model helps to predict the actual temporal behavior of solution.

Temporal Characterization of Aircraft Noise Sources

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Sullivan, Brenda M.; Rizzi, Stephen A.

2004-01-01

Current aircraft source noise prediction tools yield time-independent frequency spectra as functions of directivity angle. Realistic evaluation and human assessment of aircraft fly-over noise require the temporal characteristics of the noise signature. The purpose of the current study is to analyze empirical data from broadband jet and tonal fan noise sources and to provide the temporal information required for prediction-based synthesis. Noise sources included a one-tenth-scale engine exhaust nozzle and a one-fifth scale scale turbofan engine. A methodology was developed to characterize the low frequency fluctuations employing the Short Time Fourier Transform in a MATLAB computing environment. It was shown that a trade-off is necessary between frequency and time resolution in the acoustic spectrogram. The procedure requires careful evaluation and selection of the data analysis parameters, including the data sampling frequency, Fourier Transform window size, associated time period and frequency resolution, and time period window overlap. Low frequency fluctuations were applied to the synthesis of broadband noise with the resulting records sounding virtually indistinguishable from the measured data in initial subjective evaluations. Amplitude fluctuations of blade passage frequency (BPF) harmonics were successfully characterized for conditions equivalent to take-off and approach. Data demonstrated that the fifth harmonic of the BPF varied more in frequency than the BPF itself and exhibited larger amplitude fluctuations over the duration of the time record. Frequency fluctuations were found to be not perceptible in the current characterization of tonal components.

Hyper-spectral imaging of aircraft exhaust plumes

NASA Astrophysics Data System (ADS)

Bowen, Spencer; Bradley, Kenneth; Gross, Kevin; Perram, Glen; Marciniak, Michael

2008-10-01

An imaging Fourier-transform spectrometer has been used to determine low spatial resolution temperature and chemical species concentration distributions of aircraft jet engine exhaust plumes. An overview of the imaging Fourier transform spectrometer and the methodology of the project is presented. Results to date are shared and future work is discussed. Exhaust plume data from a Turbine Technologies, LTD, SR-30 turbojet engine at three engine settings was collected using a Telops Field-portable Imaging Radiometric Spectrometer Technology Mid-Wave Extended (FIRST-MWE). Although the plume exhibited high temporal frequency fluctuations, temporal averaging of hyper-spectral data-cubes produced steady-state distributions, which, when co-added and Fourier transformed, produced workable spectra. These spectra were then reduced using a simplified gaseous effluent model to fit forward-modeled spectra obtained from the Line-By-Line Radiative Transfer Model (LBLRTM) and the high-resolution transmission (HITRAN) molecular absorption database to determine approximate temperature and concentration distributions. It is theorized that further development of the physical model will produce better agreement between measured and modeled data.

Ultrafast Bilateral DCE-MRI of the Breast with Conventional Fourier Sampling: Preliminary Evaluation of Semi-quantitative Analysis.

PubMed

Pineda, Federico D; Medved, Milica; Wang, Shiyang; Fan, Xiaobing; Schacht, David V; Sennett, Charlene; Oto, Aytekin; Newstead, Gillian M; Abe, Hiroyuki; Karczmar, Gregory S

2016-09-01

The study aimed to evaluate the feasibility and advantages of a combined high temporal and high spatial resolution protocol for dynamic contrast-enhanced magnetic resonance imaging of the breast. Twenty-three patients with enhancing lesions were imaged at 3T. The acquisition protocol consisted of a series of bilateral, fat-suppressed "ultrafast" acquisitions, with 6.9- to 9.9-second temporal resolution for the first minute following contrast injection, followed by four high spatial resolution acquisitions with 60- to 79.5-second temporal resolution. All images were acquired with standard uniform Fourier sampling. A filtering method was developed to reduce noise and detect significant enhancement in the high temporal resolution images. Time of arrival (TOA) was defined as the time at which each voxel first satisfied all the filter conditions, relative to the time of initial arterial enhancement. Ultrafast images improved visualization of the vasculature feeding and draining lesions. A small percentage of the entire field of view (<6%) enhanced significantly in the 30 seconds following contrast injection. Lesion conspicuity was highest in early ultrafast images, especially in cases with marked parenchymal enhancement. Although the sample size was relatively small, the average TOA for malignant lesions was significantly shorter than the TOA for benign lesions. Significant differences were also measured in other parameters descriptive of early contrast media uptake kinetics (P < 0.05). Ultrafast imaging in the first minute of dynamic contrast-enhanced magnetic resonance imaging of the breast has the potential to add valuable information on early contrast dynamics. Ultrafast imaging could allow radiologists to confidently identify lesions in the presence of marked background parenchymal enhancement. Copyright © 2016 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murphy, Gareth C.; Pessah, Martin E., E-mail: gmurphy@nbi.dk, E-mail: mpessah@nbi.dk

The magnetorotational instability (MRI) is thought to play an important role in enabling accretion in sufficiently ionized astrophysical disks. The rate at which MRI-driven turbulence transports angular momentum is intimately related to both the strength of the amplitudes of the fluctuations on various scales and the degree of anisotropy of the underlying turbulence. This has motivated several studies to characterize the distribution of turbulent power in spectral space. In this paper we investigate the anisotropic nature of MRI-driven turbulence using a pseudo-spectral code and introduce novel ways for providing a robust characterization of the underlying turbulence. We study the growth ofmore » the MRI and the subsequent transition to turbulence via parasitic instabilities, identifying their potential signature in the late linear stage. We show that the general flow properties vary in a quasi-periodic way on timescales comparable to ∼10 inverse angular frequencies, motivating the temporal analysis of its anisotropy. We introduce a 3D tensor invariant analysis to quantify and classify the evolution of the anisotropy of the turbulent flow. This analysis shows a continuous high level of anisotropy, with brief sporadic transitions toward two- and three-component isotropic turbulent flow. This temporal-dependent anisotropy renders standard shell averaging especially when used simultaneously with long temporal averages, inadequate for characterizing MRI-driven turbulence. We propose an alternative way to extract spectral information from the turbulent magnetized flow, whose anisotropic character depends strongly on time. This consists of stacking 1D Fourier spectra along three orthogonal directions that exhibit maximum anisotropy in Fourier space. The resulting averaged spectra show that the power along each of the three independent directions differs by several orders of magnitude over most scales, except the largest ones. Our results suggest that a first-principles theory to describe fully developed MRI-driven turbulence will likely have to consider the anisotropic nature of the flow at a fundamental level.« less

A boostrap algorithm for temporal signal reconstruction in the presence of noise from its fractional Fourier transformed intensity spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Cheng-Yang; /Fermilab

2011-02-01

A bootstrap algorithm for reconstructing the temporal signal from four of its fractional Fourier intensity spectra in the presence of noise is described. An optical arrangement is proposed which realises the bootstrap method for the measurement of ultrashort laser pulses. The measurement of short laser pulses which are less than 1 ps is an ongoing challenge in optical physics. One reason is that no oscilloscope exists today which can directly measure the time structure of these pulses and so it becomes necessary to invent other techniques which indirectly provide the necessary information for temporal pulse reconstruction. One method called FROGmore » (frequency resolved optical gating) has been in use since 19911 and is one of the popular methods for recovering these types of short pulses. The idea behind FROG is the use of multiple time-correlated pulse measurements in the frequency domain for the reconstruction. Multiple data sets are required because only intensity information is recorded and not phase, and thus by collecting multiple data sets, there is enough redundant measurements to yield the original time structure, but not necessarily uniquely (or even up to an arbitrary constant phase offset). The objective of this paper is to describe another method which is simpler than FROG. Instead of collecting many auto-correlated data sets, only two spectral intensity measurements of the temporal signal are needed in the absence of noise. The first can be from the intensity components of its usual Fourier transform and the second from its FrFT (fractional Fourier transform). In the presence of noise, a minimum of four measurements are required with the same FrFT order but with two different apertures. Armed with these two or four measurements, a unique solution up to a constant phase offset can be constructed.« less

Integrated analysis of energy transfers in elastic-wave turbulence.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2017-08-01

In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produce cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.

Qualitative and semiquantitative Fourier transformation using a noncoherent system.

PubMed

Rogers, G L

1979-09-15

A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.

Spatio-Temporal Variability of Water Vapor in the Free Troposphere Investigated by Dial and Ftir Vertical Soundings

NASA Astrophysics Data System (ADS)

Vogelmann, H.; Sussmann, R.; Trickl, T.; Reichert, A.

2016-06-01

We report on the free tropospheric spatio-temporal variability of water vapor investigated by the analysis of a five-year period of water vapor vertical soundings above Mt. Zugspitze (2962 m a.s.l., Germany). Our results are obtained from a combination of measurements of vertically integrated water vapor (IWV), recorded with a solar Fourier Transform InfraRed (FTIR) spectrometer and of water vapor profiles recorded with the nearby differential absorption lidar (DIAL). The special geometrical arrangement of one zenith-viewing and one sun-pointing instrument and the temporal resolution of both optical instruments allow for an investigation of the spatio-temporal variability of IWV on a spatial scale of less than one kilometer and on a time scale of less than one hour. We investigated the short-term variability of both IWV and water vapor profiles from statistical analyses. The latter was also examined by case studies with a clear assignment to certain atmospheric processes as local convection or long-range transport. This study is described in great detail in our recent publication [1].

Disentangling the effects of forage, social rank, and risk on movement autocorrelation of elephants using Fourier and wavelet analyses

PubMed Central

Wittemyer, George; Polansky, Leo; Douglas-Hamilton, Iain; Getz, Wayne M.

2008-01-01

The internal state of an individual—as it relates to thirst, hunger, fear, or reproductive drive—can be inferred by referencing points on its movement path to external environmental and sociological variables. Using time-series approaches to characterize autocorrelative properties of step-length movements collated every 3 h for seven free-ranging African elephants, we examined the influence of social rank, predation risk, and seasonal variation in resource abundance on periodic properties of movement. The frequency domain methods of Fourier and wavelet analyses provide compact summaries of temporal autocorrelation and show both strong diurnal and seasonal based periodicities in the step-length time series. This autocorrelation is weaker during the wet season, indicating random movements are more common when ecological conditions are good. Periodograms of socially dominant individuals are consistent across seasons, whereas subordinate individuals show distinct differences diverging from that of dominants during the dry season. We link temporally localized statistical properties of movement to landscape features and find that diurnal movement correlation is more common within protected wildlife areas, and multiday movement correlations found among lower ranked individuals are typically outside of protected areas where predation risks are greatest. A frequency-related spatial analysis of movement-step lengths reveal that rest cycles related to the spatial distribution of critical resources (i.e., forage and water) are responsible for creating the observed patterns. Our approach generates unique information regarding the spatial-temporal interplay between environmental and individual characteristics, providing an original approach for understanding the movement ecology of individual animals and the spatial organization of animal populations. PMID:19060207

Nonlinear oscillations of inviscid free drops

NASA Technical Reports Server (NTRS)

Patzek, T. W.; Benner, R. E., Jr.; Basaran, O. A.; Scriven, L. E.

1991-01-01

The present analysis of free liquid drops' inviscid oscillations proceeds through solution of Bernoulli's equation to obtain the free surface shape and of Laplace's equation for the velocity potential field. Results thus obtained encompass drop-shape sequences, pressure distributions, particle paths, and the temporal evolution of kinetic and surface energies; accuracy is verified by the near-constant drop volume and total energy, as well as the diminutiveness of mass and momentum fluxes across drop surfaces. Further insight into the nature of oscillations is provided by Fourier power spectrum analyses of mode interactions and frequency shifts.

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

USGS Publications Warehouse

Zhang, R.R.; Ma, S.; Safak, E.; Hartzell, S.

2003-01-01

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.

Automated Bayesian model development for frequency detection in biological time series.

PubMed

Granqvist, Emma; Oldroyd, Giles E D; Morris, Richard J

2011-06-24

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

Background A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. Results In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Conclusions Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure. PMID:21702910

Temporal variability and climatology of hydrodynamic, water property and water quality parameters in the West Johor Strait of Singapore.

PubMed

Behera, Manasa Ranjan; Chun, Cui; Palani, Sundarambal; Tkalich, Pavel

2013-12-15

The study presents a baseline variability and climatology study of measured hydrodynamic, water properties and some water quality parameters of West Johor Strait, Singapore at hourly-to-seasonal scales to uncover their dependency and correlation to one or more drivers. The considered parameters include, but not limited by sea surface elevation, current magnitude and direction, solar radiation and air temperature, water temperature, salinity, chlorophyll-a and turbidity. FFT (Fast Fourier Transform) analysis is carried out for the parameters to delineate relative effect of tidal and weather drivers. The group and individual correlations between the parameters are obtained by principal component analysis (PCA) and cross-correlation (CC) technique, respectively. The CC technique also identifies the dependency and time lag between driving natural forces and dependent water property and water quality parameters. The temporal variability and climatology of the driving forces and the dependent parameters are established at the hourly, daily, fortnightly and seasonal scales. Copyright © 2013 Elsevier Ltd. All rights reserved.

Fast Fourier transformation results from gamma-ray burst profiles

NASA Technical Reports Server (NTRS)

Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.

1992-01-01

Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.

Femtosecond optical packet generation by a direct space-to-time pulse shaper.

PubMed

Leaird, D E; Weiner, A M

1999-06-15

We demonstrate femtosecond operation of a direct space-to-time pulse shaper in which there is direct mapping (no Fourier transform) between the spatial position of the masking function and the temporal position in the output waveform. We use this apparatus to generate trains of 20 pulses as an ultrafast optical data packet over an approximately 40-ps temporal window.

Shallow Water Reverberation Measurement and Prediction

DTIC Science & Technology

1994-06-01

tool . The temporal signal processing consisted of a short-time Fourier transform spectral estimation method applied to data from a single hydrophone...The three-dimensional Hamiltonian Acoustic Ray-tracing Program for the Ocean (HARPO) was used as the primary propagation modeling tool . The temporal...summarizes the work completed and discusses lessons learned . Advice regarding future work to refine the present study will be provided. 6 our poiut source

Acousto-Optic Processing of 2-D Signals Using Temporal and Spatial Integration.

DTIC Science & Technology

1983-05-31

Documents includes data on: Architectures; Coherence Properties of Pulsed Laser Diodes; Acousto - optic device data; Dynamic Range Issues; Image correlation; Synthetic aperture radar; 2-D Fourier transform; and Moments.

Experimental geometry for simultaneous beam characterization and sample imaging allowing for pink beam Fourier transform holography or coherent diffractive imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flewett, Samuel; Eisebitt, Stefan

2011-02-20

One consequence of the self-amplified stimulated emission process used to generate x rays in free electron lasers (FELs) is the intrinsic shot-to-shot variance in the wavelength and temporal coherence. In order to optimize the results from diffractive imaging experiments at FEL sources, it will be advantageous to acquire a means of collecting coherence and spectral information simultaneously with the diffraction pattern from the sample we wish to study. We present a holographic mask geometry, including a grating structure, which can be used to extract both temporal and spatial coherence information alongside the sample scatter from each individual FEL shot andmore » also allows for the real space reconstruction of the sample using either Fourier transform holography or iterative phase retrieval.« less

Modulation-frequency encoded multi-color fluorescent DNA analysis in an optofluidic chip.

PubMed

Dongre, Chaitanya; van Weerd, Jasper; Besselink, Geert A J; Vazquez, Rebeca Martinez; Osellame, Roberto; Cerullo, Giulio; van Weeghel, Rob; van den Vlekkert, Hans H; Hoekstra, Hugo J W M; Pollnau, Markus

2011-02-21

We introduce a principle of parallel optical processing to an optofluidic lab-on-a-chip. During electrophoretic separation, the ultra-low limit of detection achieved with our set-up allows us to record fluorescence from covalently end-labeled DNA molecules. Different sets of exclusively color-labeled DNA fragments-otherwise rendered indistinguishable by spatio-temporal coincidence-are traced back to their origin by modulation-frequency-encoded multi-wavelength laser excitation, fluorescence detection with a single ultrasensitive, albeit color-blind photomultiplier, and Fourier analysis decoding. As a proof of principle, fragments obtained by multiplex ligation-dependent probe amplification from independent human genomic segments, associated with genetic predispositions to breast cancer and anemia, are simultaneously analyzed.

Regional distribution of ventilation assessed by Kr-81m scintigraphy employing temporal Fourier transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slosman, D.; Susskind, H.; Cinotti, L.

1986-01-01

Temporal Fourier analysis was applied to Kr-81m ventilation scintigraphy to determine the amplitude (AMP1) and phase (PHA1) of the first harmonic of a single composite respiratory cycle and to compare regional patterns in subjects with obstructive pulmonary disease (COPD) and nonobstructed subjects. Six nonobstructed subjects, three subjects with small airway disease, six subjects with COPD, and one subject with restrictive disease were investigated. The mean value of the functional PHA1 image (PHA1m) correlated negatively with 1-second forced expiratory volume (FEV1) (r = -0.801, P less than .001), with %FEV1/FVC (r = -0.636, P less than .01) and maximum midexpiratory flowmore » rate (FEF25-75%) (r = -0.723, P less than .002), and correlated positively with residual volume (r = 0.640, P less than .01). PHA1m values for the six subjects with COPD were significantly higher (t = 2.359, P less than .05) than for the ten nonobstructed subjects. Display of phase and amplitude functional images permits a visual evaluation of the regional distribution of ventilation to be made. Regional abnormalities of air flow were detected in obstructed subjects, and the presence of airway obstruction could be predicted. Dynamic ventilation imaging, therefore, appears to be a potentially useful noninvasive technique to assess lung impairment on a localized level.« less

Broadband Doppler-limited two-photon and stepwise excitation spectroscopy with laser frequency combs

NASA Astrophysics Data System (ADS)

Hipke, Arthur; Meek, Samuel A.; Ideguchi, Takuro; Hänsch, Theodor W.; Picqué, Nathalie

2014-07-01

Multiplex two-photon excitation spectroscopy is demonstrated at Doppler-limited resolution. We describe first Fourier-transform two-photon spectroscopy of an atomic sample with two mode-locked laser oscillators in a dual-comb technique. Each transition is uniquely identified by the modulation imparted by the interfering comb excitations. The temporal modulation of the spontaneous two-photon fluorescence is monitored with a single photodetector, and the spectrum of all excited transitions is revealed by a Fourier transform.

a 2d Model of Ultrasonic Testing for Cracks Near a Nonplanar Surface

NASA Astrophysics Data System (ADS)

Westlund, Jonathan; Boström, Anders

2010-02-01

2D P-SV elastic wave scattering by a crack near a non-planar surface is investigated. The wave scattering problem is solved in the frequency domain using a combination of the boundary element method (BEM) for the back surface displacement and a Fourier series expansion of the crack opening displacement (COD). The model accounts for the action of the transmitting and receiving ultrasonic contact probes, and the time traces are obtained by applying an inverse temporal Fourier transform.

Characterization and Simulation of Transient Vibrations Using Band Limited Temporal Moments

DOE PAGES

Smallwood, David O.

1994-01-01

A method is described to characterize shocks (transient time histories) in terms of the Fourier energy spectrum and the temporal moments of the shock passed through a contiguous set of band pass filters. The product model is then used to generate of a random process as simulations that in the mean will have the same energy and moments as the characterization of the transient event.

Femtosecond direct space-to-time pulse shaping in an integrated-optic configuration.

PubMed

Leaird, D E; Weiner, A M

2004-07-01

We demonstrate femtosecond operation of an integrated-optic direct space-to-time pulse shaper for which there is a direct mapping (no Fourier transform) between the spatial position of the masking function and the temporal position in the output waveform. The apparatus is used to generate trains of more than 30 pulses as an ultrafast optical data packet over approximately an 80-ps temporal window.

Temporal self-splitting of optical pulses

NASA Astrophysics Data System (ADS)

Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan

2018-05-01

We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.

Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

PubMed

Mei, Liang; Svanberg, Sune

2015-03-20

This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions

NASA Astrophysics Data System (ADS)

Pathak, Pallabi; Sharma, Sumita K.; Nakamura, Y.; Bailung, H.

2017-12-01

The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations.

Can weekly noise levels of urban road traffic, as predominant noise source, estimate annual ones?

PubMed

Prieto Gajardo, Carlos; Barrigón Morillas, Juan Miguel; Rey Gozalo, Guillermo; Vílchez-Gómez, Rosendo

2016-11-01

The effects of noise pollution on human quality of life and health were recognised by the World Health Organisation a long time ago. There is a crucial dilemma for the study of urban noise when one is looking for proven methodologies that can allow, on the one hand, an increase in the quality of predictions, and on the other hand, saving resources in the spatial and temporal sampling. The temporal structure of urban noise is studied in this work from a different point of view. This methodology, based on Fourier analysis, is applied to several measurements of urban noise, mainly from road traffic and one-week long, carried out in two cities located on different continents and with different sociological life styles (Cáceres, Spain and Talca, Chile). Its capacity to predict annual noise levels from weekly measurements is studied. The relation between this methodology and the categorisation method is also analysed.

Parametric spectro-temporal analyzer (PASTA) for real-time optical spectrum observation

NASA Astrophysics Data System (ADS)

Zhang, Chi; Xu, Jianbing; Chui, P. C.; Wong, Kenneth K. Y.

2013-06-01

Real-time optical spectrum analysis is an essential tool in observing ultrafast phenomena, such as the dynamic monitoring of spectrum evolution. However, conventional method such as optical spectrum analyzers disperse the spectrum in space and allocate it in time sequence by mechanical rotation of a grating, so are incapable of operating at high speed. A more recent method all-optically stretches the spectrum in time domain, but is limited by the allowable input condition. In view of these constraints, here we present a real-time spectrum analyzer called parametric spectro-temporal analyzer (PASTA), which is based on the time-lens focusing mechanism. It achieves a frame rate as high as 100 MHz and accommodates various input conditions. As a proof of concept and also for the first time, we verify its applications in observing the dynamic spectrum of a Fourier domain mode-locked laser, and the spectrum evolution of a laser cavity during its stabilizing process.

All-optical framing photography based on hyperspectral imaging method

NASA Astrophysics Data System (ADS)

Liu, Shouxian; Li, Yu; Li, Zeren; Chen, Guanghua; Peng, Qixian; Lei, Jiangbo; Liu, Jun; Yuan, Shuyun

2017-02-01

We propose and experimentally demonstrate a new all optical-framing photography that uses hyperspectral imaging methods to record a chirped pulse's temporal-spatial information. This proposed method consists of three parts: (1) a chirped laser pulse encodes temporal phenomena onto wavelengths; (2) a lenslet array generates a series of integral pupil images;(3) a dispersive device disperses the integral images at void space of image sensor. Compared with Ultrafast All-Optical Framing Technology(Daniel Frayer,2013,2014) and Sequentially Time All-Optical Mapping Photography( Nakagawa 2014, 2015), our method is convenient to adjust the temporal resolution and to flexibly increase the numbers of frames. Theoretically, the temporal resolution of our scheme is limited by the amount of dispersion that is added to a Fourier transform limited femtosecond laser pulse. Correspondingly, the optimal number of frames is decided by the ratio of the observational time window to the temporal resolution, and the effective pixels of each frame are mostly limited by the dimensions M×N of the lenslet array. For example, if a 40fs Fourier transform limited femtosecond pulse is stretched to 10ps, a CCD camera with 2048×3072 pixels can record 15 framing images with temporal resolution of 650fs and image size of 100×100 pixels. As spectrometer structure, our recording part has another advantage that not only amplitude images but also frequency domain interferograms can be imaged. Therefore, it is comparatively easy to capture fast dynamics in the refractive index change of materials. A further dynamic experiment is being conducted.

A New Method for Nonlinear and Nonstationary Time Series Analysis and Its Application to the Earthquake and Building Response Records

NASA Technical Reports Server (NTRS)

Huang, Norden E.

1999-01-01

A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum, Example of application of this method to earthquake and building response will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

High-speed Fourier ptychographic microscopy based on programmable annular illuminations.

PubMed

Sun, Jiasong; Zuo, Chao; Zhang, Jialin; Fan, Yao; Chen, Qian

2018-05-16

High-throughput quantitative phase imaging (QPI) is essential to cellular phenotypes characterization as it allows high-content cell analysis and avoids adverse effects of staining reagents on cellular viability and cell signaling. Among different approaches, Fourier ptychographic microscopy (FPM) is probably the most promising technique to realize high-throughput QPI by synthesizing a wide-field, high-resolution complex image from multiple angle-variably illuminated, low-resolution images. However, the large dataset requirement in conventional FPM significantly limits its imaging speed, resulting in low temporal throughput. Moreover, the underlying theoretical mechanism as well as optimum illumination scheme for high-accuracy phase imaging in FPM remains unclear. Herein, we report a high-speed FPM technique based on programmable annular illuminations (AIFPM). The optical-transfer-function (OTF) analysis of FPM reveals that the low-frequency phase information can only be correctly recovered if the LEDs are precisely located at the edge of the objective numerical aperture (NA) in the frequency space. By using only 4 low-resolution images corresponding to 4 tilted illuminations matching a 10×, 0.4 NA objective, we present the high-speed imaging results of in vitro Hela cells mitosis and apoptosis at a frame rate of 25 Hz with a full-pitch resolution of 655 nm at a wavelength of 525 nm (effective NA = 0.8) across a wide field-of-view (FOV) of 1.77 mm 2 , corresponding to a space-bandwidth-time product of 411 megapixels per second. Our work reveals an important capability of FPM towards high-speed high-throughput imaging of in vitro live cells, achieving video-rate QPI performance across a wide range of scales, both spatial and temporal.

Advance in ERG Analysis: From Peak Time and Amplitude to Frequency, Power, and Energy

PubMed Central

Lina, Jean-Marc; Lachapelle, Pierre

2014-01-01

Purpose. To compare time domain (TD: peak time and amplitude) analysis of the human photopic electroretinogram (ERG) with measures obtained in the frequency domain (Fourier analysis: FA) and in the time-frequency domain (continuous (CWT) and discrete (DWT) wavelet transforms). Methods. Normal ERGs (n = 40) were analyzed using traditional peak time and amplitude measurements of the a- and b-waves in the TD and descriptors extracted from FA, CWT, and DWT. Selected descriptors were also compared in their ability to monitor the long-term consequences of disease process. Results. Each method extracted relevant information but had distinct limitations (i.e., temporal and frequency resolutions). The DWT offered the best compromise by allowing us to extract more relevant descriptors of the ERG signal at the cost of lesser temporal and frequency resolutions. Follow-ups of disease progression were more prolonged with the DWT (max 29 years compared to 13 with TD). Conclusions. Standardized time domain analysis of retinal function should be complemented with advanced DWT descriptors of the ERG. This method should allow more sensitive/specific quantifications of ERG responses, facilitate follow-up of disease progression, and identify diagnostically significant changes of ERG waveforms that are not resolved when the analysis is only limited to time domain measurements. PMID:25061605

Fourier-Domain Shift Matching: A Robust Time-of-Flight Approach for Shear Wave Speed Estimation.

PubMed

Rosen, David; Jiang, Jingfeng

2018-05-01

Our primary objective of this work was to design and test a new time-of-flight (TOF) method that allows measurements of shear wave speed (SWS) following impulsive excitation in soft tissues. Particularly, under the assumption of the local plane shear wave, this work named the Fourier-domain shift matching (FDSM) method, estimates SWS by aligning a series of shear waveforms either temporally or spatially using a solution space deduced by characteristic curves of the well-known 1-D wave equation. The proposed SWS estimation method was tested using computer-simulated data, and tissue-mimicking phantom and ex vivo tissue experiments. Its performance was then compared with three other known TOF methods: lateral time-to-peak (TTP) method with robust random sampling consensus (RANSAC) fitting method, Radon sum transformation method, and a modified cross correlation method. Hereafter, these three TOF methods are referred to as the TTP-RANSAC, Radon sum, and X-corr methods, respectively. In addition to an adapted form of the 2-D Fourier transform (2-D FT)-based method in which the (group) SWS was approximated by averaging phase SWS values was considered for comparison. Based on data evaluated, we found that the overall performance of the above-mentioned temporal implementation of the proposed FDSM method was most similar to the established Radon sum method (correlation = 0.99, scale factor = 1.03, and mean difference = 0.07 m/s), and the 2-D FT (correlation = 0.98, scale factor = 1.00, and mean difference = 0.10 m/s) at high signal quality. However, results obtained from the 2-D FT method diverged (correlation = 0.201) from these of the proposed temporal implementation in the presence of diminished signal quality, whereas the agreement between the Radon sum approach and the proposed temporal implementation largely remained the same (correlation = 0.98).

The Fourier analysis of biological transients.

PubMed

Harris, C M

1998-08-31

With modern computing technology the digital implementation of the Fourier transform is widely available, mostly in the form of the fast Fourier transform (FFT). Although the FFT has become almost synonymous with the Fourier transform, it is a fast numerical technique for computing the discrete Fourier transform (DFT) of a finite sequence of sampled data. The DFT is not directly equivalent to the continuous Fourier transform of the underlying biological signal, which becomes important when analyzing biological transients. Although this distinction is well known by some, for many it leads to confusion in how to interpret the FFT of biological data, and in how to precondition data so as to yield a more accurate Fourier transform using the FFT. We review here the fundamentals of Fourier analysis with emphasis on the analysis of transient signals. As an example of a transient, we consider the human saccade to illustrate the pitfalls and advantages of various Fourier analyses.

Fast periodic stimulation (FPS): a highly effective approach in fMRI brain mapping.

PubMed

Gao, Xiaoqing; Gentile, Francesco; Rossion, Bruno

2018-06-01

Defining the neural basis of perceptual categorization in a rapidly changing natural environment with low-temporal resolution methods such as functional magnetic resonance imaging (fMRI) is challenging. Here, we present a novel fast periodic stimulation (FPS)-fMRI approach to define face-selective brain regions with natural images. Human observers are presented with a dynamic stream of widely variable natural object images alternating at a fast rate (6 images/s). Every 9 s, a short burst of variable face images contrasting with object images in pairs induces an objective face-selective neural response at 0.111 Hz. A model-free Fourier analysis achieves a twofold increase in signal-to-noise ratio compared to a conventional block-design approach with identical stimuli and scanning duration, allowing to derive a comprehensive map of face-selective areas in the ventral occipito-temporal cortex, including the anterior temporal lobe (ATL), in all individual brains. Critically, periodicity of the desired category contrast and random variability among widely diverse images effectively eliminates the contribution of low-level visual cues, and lead to the highest values (80-90%) of test-retest reliability in the spatial activation map yet reported in imaging higher level visual functions. FPS-fMRI opens a new avenue for understanding brain function with low-temporal resolution methods.

Wavelength-encoded tomography based on optical temporal Fourier transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk

We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -μm (ideally 36 μm) resolution is achieved based on a 7.5-nm bandwidth swept-pump,more » using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.« less

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.

2016-04-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.

ZWD time series analysis derived from NRT data processing. A regional study of PW in Greece.

NASA Astrophysics Data System (ADS)

Pikridas, Christos; Balidakis, Kyriakos; Katsougiannopoulos, Symeon

2015-04-01

ZWD (Zenith Wet/non-hydrostatic Delay) estimates are routinely derived Near Real Time from the new established Analysis Center in the Department of Geodesy and Surveying of Aristotle University of Thessaloniki (DGS/AUT-AC), in the framework of E-GVAP (EUMETNET GNSS water vapour project) since October 2014. This process takes place on an hourly basis and yields, among else, station coordinates and tropospheric parameter estimates for a network of 90+ permanent GNSS (Global Navigation Satellite System) stations. These are distributed at the wider part of Hellenic region. In this study, temporal and spatial variability of ZWD estimates were examined, as well as their relation with coordinate series extracted from both float and fixed solution of the initial phase ambiguities. For this investigation, Bernese GNSS Software v5.2 was used for the acquisition of the 6 month dataset from the aforementioned network. For time series analysis we employed techniques such as the Generalized Lomb-Scargle periodogram and Burg's maximum entropy method due to inefficiencies of the Discrete Fourier Transform application in the test dataset. Through the analysis, interesting results for further geophysical interpretation were drawn. In addition, the spatial and temporal distributions of Precipitable Water vapour (PW) obtained from both ZWD estimates and ERA-Interim reanalysis grids were investigated.

Fourier analysis and signal processing by use of the Moebius inversion formula

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.

1990-01-01

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

Single-shot spectro-temporal characterization of XUV pulses from a seeded free-electron laser

PubMed Central

De Ninno, Giovanni; Gauthier, David; Mahieu, Benoît; Ribič, Primož Rebernik; Allaria, Enrico; Cinquegrana, Paolo; Danailov, Miltcho Bojanov; Demidovich, Alexander; Ferrari, Eugenio; Giannessi, Luca; Penco, Giuseppe; Sigalotti, Paolo; Stupar, Matija

2015-01-01

Intense ultrashort X-ray pulses produced by modern free-electron lasers (FELs) allow one to probe biological systems, inorganic materials and molecular reaction dynamics with nanoscale spatial and femtoscale temporal resolution. These experiments require the knowledge, and possibly the control, of the spectro-temporal content of individual pulses. FELs relying on seeding have the potential to produce spatially and temporally fully coherent pulses. Here we propose and implement an interferometric method, which allows us to carry out the first complete single-shot spectro-temporal characterization of the pulses, generated by an FEL in the extreme ultraviolet spectral range. Moreover, we provide the first direct evidence of the temporal coherence of a seeded FEL working in the extreme ultraviolet spectral range and show the way to control the light generation process to produce Fourier-limited pulses. Experiments are carried out at the FERMI FEL in Trieste. PMID:26290320

Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements

NASA Technical Reports Server (NTRS)

Lait, Leslie R.; Stanford, John L.

1988-01-01

A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.

Fourier-interpolation superresolution optical fluctuation imaging (fSOFi) (Conference Presentation)

NASA Astrophysics Data System (ADS)

Enderlein, Joerg; Stein, Simon C.; Huss, Anja; Hähnel, Dirk; Gregor, Ingo

2016-02-01

Stochastic Optical Fluctuation Imaging (SOFI) is a superresolution fluorescence microscopy technique which allows to enhance the spatial resolution of an image by evaluating the temporal fluctuations of blinking fluorescent emitters. SOFI is not based on the identification and localization of single molecules such as in the widely used Photoactivation Localization Microsopy (PALM) or Stochastic Optical Reconstruction Microscopy (STORM), but computes a superresolved image via temporal cumulants from a recorded movie. A technical challenge hereby is that, when directly applying the SOFI algorithm to a movie of raw images, the pixel size of the final SOFI image is the same as that of the original images, which becomes problematic when the final SOFI resolution is much smaller than this value. In the past, sophisticated cross-correlation schemes have been used for tackling this problem. Here, we present an alternative, exact, straightforward, and simple solution using an interpolation scheme based on Fourier transforms. We exemplify the method on simulated and experimental data.

Periodic Recurrence Patterns In X-Ray Solar Flare Appearances

NASA Astrophysics Data System (ADS)

Gyenge, N.; Erdélyi, R.

2018-06-01

The temporal recurrence of micro-flare events is studied for a time interval before and after of major solar flares. Our sample is based on the X-ray flare observations by the Geostationary Operational Environmental Satellite (GOES) and Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The analyzed data contain 1330/301 M-class and X-class GOES/RHESSI energetic solar flares and 4062/4119 GOES/RHESSI micro-flares covering the period elapse since 2002. The temporal analysis of recurrence, by Fast Fourier Transform, of the micro-flares, shows multiple significant periods. Based on the GOES and RHESSI data, the temporal analysis also demonstrates that multiple periods manifest simultaneously in both statistical samples without any significant shift over time. In the GOES sample, the detected significant periods are: 11.33, 5.61, 3.75, 2.80, and 2.24 minutes. The RHESSI data show similar significant periods at 8.54, 5.28, 3.66, 2.88, and 2.19 minutes. The periods are interpreted as signatures of standing oscillations, with the longest period (P 1) being the fundamental and others being higher harmonic modes. The period ratio of the fundamental and higher harmonics (P 1/P N ) is also analyzed. The standing modes may be signatures of global oscillations of the entire solar atmosphere encompassing magnetized plasma from the photosphere to the corona in active regions.

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

Temporal Coherence: A Model for Non-Stationarity in Natural and Simulated Wind Records

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rinker, Jennifer M.; Gavin, Henri P.; Clifton, Andrew

We present a novel methodology for characterizing and simulating non-stationary stochastic wind records. In this new method, non-stationarity is characterized and modelled via temporal coherence, which is quantified in the discrete frequency domain by probability distributions of the differences in phase between adjacent Fourier components. Temporal coherence can also be used to quantify non-stationary characteristics in wind data. Three case studies are presented that analyze the non-stationarity of turbulent wind data obtained at the National Wind Technology Center near Boulder, Colorado, USA. The first study compares the temporal and spectral characteristics of a stationary wind record and a non-stationary windmore » record in order to highlight their differences in temporal coherence. The second study examines the distribution of one of the proposed temporal coherence parameters and uses it to quantify the prevalence of nonstationarity in the dataset. The third study examines how temporal coherence varies with a range of atmospheric parameters to determine what conditions produce more non-stationarity.« less

[Spatio-temporal analysis of the biophysical and ecological conditions of Triatoma dimidiata (Hemiptera: Reduviidae: Triatominae) in the northeast region of Colombia].

PubMed

Badel-Mogollón, Jaime; Rodríguez-Figueroa, Laura; Parra-Henao, Gabriel

2017-03-29

Due to the lack of information regarding biophysical and spatio-temporal conditions (hydrometheorologic and vegetal coverage density) in areas with Triatoma dimidiata in the Colombian departments of Santander and Boyacá, there is a need to elucidate the association patterns of these variables to determine the distribution and control of this species. To make a spatio-temporal analysis of biophysical variables related to the distribution of T. dimidiate observed in the northeast region of Colombia. We used the Intergovernmental Panel on Climate Change Special Report on Emissions Scenarios (IPCC SRES) data bases registering vector presence and hydrometheorologic data. We studied the variables of environmental temperature, relative humidity, rainfall and vegetal coverage density at regional and local levels, and we conducted spatial geostatistic, descriptive statistical and Fourier temporal series analyses. Temperatures two meters above the ground and on covered surface ranged from 14,5°C to 18,8°C in the areas with the higher density of T. dimidiata. The environmental temperature fluctuated between 30 and 32°C. Vegetal coverage density and rainfall showed patterns of annual and biannual peaks. Relative humidity values fluctuated from 66,8 to 85,1%. Surface temperature and soil coverage were the variables that better explained the life cycle of T. dimidiata in the area. High relative humidity promoted the seek of shelters and an increase of the geographic distribution in the annual and biannual peaks of regional rainfall. The ecologic and anthropic conditions suggest that T. dimidiata is a highly resilient species.

Harmonic regression of Landsat time series for modeling attributes from national forest inventory data

NASA Astrophysics Data System (ADS)

Wilson, Barry T.; Knight, Joseph F.; McRoberts, Ronald E.

2018-03-01

Imagery from the Landsat Program has been used frequently as a source of auxiliary data for modeling land cover, as well as a variety of attributes associated with tree cover. With ready access to all scenes in the archive since 2008 due to the USGS Landsat Data Policy, new approaches to deriving such auxiliary data from dense Landsat time series are required. Several methods have previously been developed for use with finer temporal resolution imagery (e.g. AVHRR and MODIS), including image compositing and harmonic regression using Fourier series. The manuscript presents a study, using Minnesota, USA during the years 2009-2013 as the study area and timeframe. The study examined the relative predictive power of land cover models, in particular those related to tree cover, using predictor variables based solely on composite imagery versus those using estimated harmonic regression coefficients. The study used two common non-parametric modeling approaches (i.e. k-nearest neighbors and random forests) for fitting classification and regression models of multiple attributes measured on USFS Forest Inventory and Analysis plots using all available Landsat imagery for the study area and timeframe. The estimated Fourier coefficients developed by harmonic regression of tasseled cap transformation time series data were shown to be correlated with land cover, including tree cover. Regression models using estimated Fourier coefficients as predictor variables showed a two- to threefold increase in explained variance for a small set of continuous response variables, relative to comparable models using monthly image composites. Similarly, the overall accuracies of classification models using the estimated Fourier coefficients were approximately 10-20 percentage points higher than the models using the image composites, with corresponding individual class accuracies between six and 45 percentage points higher.

Exploiting visual search theory to infer social interactions

NASA Astrophysics Data System (ADS)

Rota, Paolo; Dang-Nguyen, Duc-Tien; Conci, Nicola; Sebe, Nicu

2013-03-01

In this paper we propose a new method to infer human social interactions using typical techniques adopted in literature for visual search and information retrieval. The main piece of information we use to discriminate among different types of interactions is provided by proxemics cues acquired by a tracker, and used to distinguish between intentional and casual interactions. The proxemics information has been acquired through the analysis of two different metrics: on the one hand we observe the current distance between subjects, and on the other hand we measure the O-space synergy between subjects. The obtained values are taken at every time step over a temporal sliding window, and processed in the Discrete Fourier Transform (DFT) domain. The features are eventually merged into an unique array, and clustered using the K-means algorithm. The clusters are reorganized using a second larger temporal window into a Bag Of Words framework, so as to build the feature vector that will feed the SVM classifier.

Efficiency index: a new parameter to define breathing patterns during dynamic Xe-127 ventilation studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slosman, D.; Susskind, H.; Bossuyt, A.

1986-03-01

Ventilation imaging can be improved by gating scintigraphic data with the respiratory cycle using temporal Fourier analysis (TFA) to quantify the temporal behavior of the ventilation. Sixteen consecutive images, representing equal-time increments of an average respiratory cycle, were produced by TFA in the posterior view on a pixel-by-pixel basis. An Efficiency Index (EFF), defined as the ratio of the summation of all the differences between maximum and minimum counts for each pixel to that for the entire lung during the respiratory cycle, was derived to describe the pattern of ventilation. The gated ventilation studies were carried out with Xe-127 inmore » 12 subjects: normal lung function (4), small airway disease (2), COPD (5), and restrictive disease (1). EFF for the first three harmonics correlated linearly with FEV1 (r = 0.701, p< 0.01). This approach is suggested as a very sensitive method to quantify the extent and regional distribution of airway obstruction.« less

Flow disturbance due to presence of the vane anemometer

NASA Astrophysics Data System (ADS)

Bujalski, M.; Gawor, M.; Sobczyk, J.

2014-08-01

This paper presents the results of the preliminary experimental investigations of the disturbance of velocity field resulting from placing a vane anemometer in the analyzed air flow. Experiments were conducted in a wind tunnel with a closed loop. For the measurement process, Particle Image Velocimetry (PIV) method was used to visualize the flow structure and evaluate the instantaneous, two-dimensional velocity vector fields. Regions of inflow on the vane anemometer as well as flow behind it were examined. Ensemble averaged velocity distribution and root-mean-square (RMS) velocity fluctuations were determined. The results below are presented in the form of contour-velocity maps and profile plots. In order to investigate velocity fluctuations in the wake of vane anemometer with high temporal resolution hot-wire anemometry (HWA) technique was used. Frequency analysis by means of Fast Fourier Transform was carried out. The obtained results give evidence to a significant spatially and temporally complex flow disturbance in the vicinity of analyzed instrument.

A 2D MTF approach to evaluate and guide dynamic imaging developments.

PubMed

Chao, Tzu-Cheng; Chung, Hsiao-Wen; Hoge, W Scott; Madore, Bruno

2010-02-01

As the number and complexity of partially sampled dynamic imaging methods continue to increase, reliable strategies to evaluate performance may prove most useful. In the present work, an analytical framework to evaluate given reconstruction methods is presented. A perturbation algorithm allows the proposed evaluation scheme to perform robustly without requiring knowledge about the inner workings of the method being evaluated. A main output of the evaluation process consists of a two-dimensional modulation transfer function, an easy-to-interpret visual rendering of a method's ability to capture all combinations of spatial and temporal frequencies. Approaches to evaluate noise properties and artifact content at all spatial and temporal frequencies are also proposed. One fully sampled phantom and three fully sampled cardiac cine datasets were subsampled (R = 4 and 8) and reconstructed with the different methods tested here. A hybrid method, which combines the main advantageous features observed in our assessments, was proposed and tested in a cardiac cine application, with acceleration factors of 3.5 and 6.3 (skip factors of 4 and 8, respectively). This approach combines features from methods such as k-t sensitivity encoding, unaliasing by Fourier encoding the overlaps in the temporal dimension-sensitivity encoding, generalized autocalibrating partially parallel acquisition, sensitivity profiles from an array of coils for encoding and reconstruction in parallel, self, hybrid referencing with unaliasing by Fourier encoding the overlaps in the temporal dimension and generalized autocalibrating partially parallel acquisition, and generalized autocalibrating partially parallel acquisition-enhanced sensitivity maps for sensitivity encoding reconstructions.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

Broadband interferometric characterization of divergence and spatial chirp.

PubMed

Meier, Amanda K; Iliev, Marin; Squier, Jeff A; Durfee, Charles G

2015-09-01

We demonstrate a spectral interferometric method to characterize lateral and angular spatial chirp to optimize intensity localization in spatio-temporally focused ultrafast beams. Interference between two spatially sheared beams in an interferometer will lead to straight fringes if the wavefronts are curved. To produce reference fringes, we delay one arm relative to another in order to measure fringe rotation in the spatially resolved spectral interferogram. With Fourier analysis, we can obtain frequency-resolved divergence. In another arrangement, we spatially flip one beam relative to the other, which allows the frequency-dependent beamlet direction (angular spatial chirp) to be measured. Blocking one beam shows the spatial variation of the beamlet position with frequency (i.e., the lateral spatial chirp).

Mathematics of pulsed vocalizations with application to killer whale biphonation.

PubMed

Brown, Judith C

2008-05-01

Formulas for the spectra of pulsed vocalizations for both the continuous and discrete cases are rigorously derived from basic formulas for Fourier analysis, a topic discussed qualitatively in Watkins' classic paper on "the harmonic interval" ["The harmonic interval: Fact or artifact in spectral analysis of pulse trains," in Marine Bioacoustics 2, edited by W. N. Tavogla (Pergamon, New York, 1967), pp. 15-43]. These formulas are summarized in a table for easy reference, along with most of the corresponding graphs. The case of a "pulse tone" is shown to involve multiplication of two temporal wave forms, corresponding to convolution in the frequency domain. This operation is discussed in detail and shown to be equivalent to a simpler approach using a trigonometric formula giving sum and difference frequencies. The presence of a dc component in the temporal wave form, which implies physically that there is a net positive pressure at the source, is discussed, and examples of the corresponding spectra are calculated and shown graphically. These have application to biphonation (two source signals) observed for some killer whale calls and implications for a source mechanism. A MATLAB program for synthesis of a similar signal is discussed and made available online.

A PRESTO-SENSE sequence with alternating partial-Fourier encoding for rapid susceptibility-weighted 3D MRI time series.

PubMed

Klarhöfer, Markus; Dilharreguy, Bixente; van Gelderen, Peter; Moonen, Chrit T W

2003-10-01

A 3D sequence for dynamic susceptibility imaging is proposed which combines echo-shifting principles (such as PRESTO), sensitivity encoding (SENSE), and partial-Fourier acquisition. The method uses a moderate SENSE factor of 2 and takes advantage of an alternating partial k-space acquisition in the "slow" phase encode direction allowing an iterative reconstruction using high-resolution phase estimates. Offering an isotropic spatial resolution of 4 x 4 x 4 mm(3), the novel sequence covers the whole brain including parts of the cerebellum in 0.5 sec. Its temporal signal stability is comparable to that of a full-Fourier, full-FOV EPI sequence having the same dynamic scan time but much less brain coverage. Initial functional MRI experiments showed consistent activation in the motor cortex with an average signal change slightly less than that of EPI. Copyright 2003 Wiley-Liss, Inc.

Fourier-Legendre spectral methods for incompressible channel flow

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1984-01-01

An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

Discerning comb and Fourier mean frequency from an fs laser based on the principle of non-interaction of waves

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar; Prasad, Narasimha

2012-02-01

The key objective of this article is to underscore that as engineers, we need to pay close attention in repeatedly validating and re-validating the underlying physical processes behind a working theory that models a phenomenon we are using to create tools and technologies. We use the test case, the prevailing mode-lock theory, to illustrate our views by identifying existing contradictions and showing approach towards their resolution by identifying the relevant physical processes. The current theory tells us that the Fourier summation of all the allowed cavity modes directly produces the train of pulses. It effectively assumes that electromagnetic (EM) waves are capable of re-organizing their spatial and temporal energy distribution to generate a train of temporal pulses while preserving the spatial mode energy distribution. The implication is that EM waves interact with each other by themselves. Even though the theory is working, we have three logical problems. First, in the real world, in the linear domain, waves never interact with each other. On careful analysis of all types of interference experiments, we will recognize that only in the presence of some interacting material medium can we observe the physical superposition EFFECT. In other words, detectors carryout the superposition effect we call interference phenomenon, through the summation of their multiple simultaneous linear stimulations and then absorbing energy proportional to the square modulus of the sum total stimulation. Second, a Fourier monochromatic wave, existing in all space and time, is a non-causal hypothesis. Just because our theories are working does not mean that we have understood the real physical interaction processes in nature. We need to build our theories based upon space and time finite EM wave packet containing a finite amount of energy, which is a causal approach. Third, in spite of staggering successes of Quantum Mechanics, we do not yet have a self consistent model for space and time finite model of a photon. QM only predicts that EM energy emission (spontaneous and stimulated) takes place only in a discrete amount at a time from atoms and molecules. It does not give us recipe about how to visualize a propagating photon as it expands diffractively. However, Huygens-Fresnel's classical diffraction integral gives us a rigorous model, which is the cornerstone of modeling evolution of laser cavity modes, CW or pulsed. In this paper, we highlight the contradictions that arise out of the prevailing mode-lock theory and resolve them by using causal models, already underscored above. For example, there are now a wide range of very successful technological applications of the frequency comb extracted out of fs lasers. If the Fourier summation were the correct physical process, then all the cavity modes would have been summed (converted) into a single mean frequency around the gain line center for perfectly mode-locked systems. Further, sending such fs pulses through an optical spectrometer would have always displayed a transform limited fringe, centering on the mean Fourier frequency, rather than generating the comb frequencies, albeit instrumentally broadened. Output pulse train from a phase locked laser is functionally produced due to the oscillatory time-gating behavior of the intra-cavity phase-locking devices. So, we need to pay more attention to the fast temporal behavior of the materials we use for achieving very fast time-gating, since this material imposes phase locking on the cavity modes to enhance its own high-contrast time-gating behavior.

A solar radio dynamic spectrograph with flexible temporal-spectral resolution

NASA Astrophysics Data System (ADS)

Du, Qing-Fu; Chen, Lei; Zhao, Yue-Chang; Li, Xin; Zhou, Yan; Zhang, Jun-Rui; Yan, Fa-Bao; Feng, Shi-Wei; Li, Chuan-Yang; Chen, Yao

2017-09-01

Observation and research on solar radio emission have unique scientific values in solar and space physics and related space weather forecasting applications, since the observed spectral structures may carry important information about energetic electrons and underlying physical mechanisms. In this study, we present the design of a novel dynamic spectrograph that has been installed at the Chashan Solar Radio Observatory operated by the Laboratory for Radio Technologies, Institute of Space Sciences at Shandong University. The spectrograph is characterized by real-time storage of digitized radio intensity data in the time domain and its capability to perform off-line spectral analysis of the radio spectra. The analog signals received via antennas and amplified with a low-noise amplifier are converted into digital data at a speed reaching up to 32 k data points per millisecond. The digital data are then saved into a high-speed electronic disk for further off-line spectral analysis. Using different word lengths (1-32 k) and time cadences (5 ms-10 s) for off-line fast Fourier transform analysis, we can obtain the dynamic spectrum of a radio burst with different (user-defined) temporal (5 ms-10 s) and spectral (3 kHz˜320 kHz) resolutions. This enables great flexibility and convenience in data analysis of solar radio bursts, especially when some specific fine spectral structures are under study.

Dual-domain point diffraction interferometer

DOEpatents

Naulleau, Patrick P.; Goldberg, Kenneth Alan

2000-01-01

A hybrid spatial/temporal-domain point diffraction interferometer (referred to as the dual-domain PS/PDI) that is capable of suppressing the scattered-reference-light noise that hinders the conventional PS/PDI is provided. The dual-domain PS/PDI combines the separate noise-suppression capabilities of the widely-used phase-shifting and Fourier-transform fringe pattern analysis methods. The dual-domain PS/PDI relies on both a more restrictive implementation of the image plane PS/PDI mask and a new analysis method to be applied to the interferograms generated and recorded by the modified PS/PDI. The more restrictive PS/PDI mask guarantees the elimination of spatial-frequency crosstalk between the signal and the scattered-light noise arising from scattered-reference-light interfering with the test beam. The new dual-domain analysis method is then used to eliminate scattered-light noise arising from both the scattered-reference-light interfering with the test beam and the scattered-reference-light interfering with the "true" pinhole-diffracted reference light. The dual-domain analysis method has also been demonstrated to provide performance enhancement when using the non-optimized standard PS/PDI design. The dual-domain PS/PDI is essentially a three-tiered filtering system composed of lowpass spatial-filtering the test-beam electric field using the more restrictive PS/PDI mask, bandpass spatial-filtering the individual interferogram irradiance frames making up the phase-shifting series, and bandpass temporal-filtering the phase-shifting series as a whole.

Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969-2007.

PubMed

Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo

2015-08-01

Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis

ERIC Educational Resources Information Center

LoPresto, Michael C.

2013-01-01

What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.

The application of an optical Fourier spectrum analyzer on detecting defects in mass-produced satellite photographs

NASA Technical Reports Server (NTRS)

Athale, R.; Lee, S. H.

1976-01-01

Various defects in mass-produced pictures transmitted to earth from a satellite are investigated. It is found that the following defects are readily detectable via Fourier spectrum analysis: (1) bit slip, (2) breakup causing loss of image, and (3) disabled track at the top of the imagery. The scratches made on the film during mass production, which are difficult to detect by visual observation, also show themselves readily in Fourier spectrum analysis. A relation is established between the number of scratches, their width and depth and the intensity of their Fourier spectra. Other defects that are found to be equally suitable for Fourier spectrum analysis or visual (image analysis) detection are synchronous loss without blurring of image, and density variation in gray scale. However, the Fourier spectrum analysis is found to be unsuitable for detection of such defects as pin holes, annotation error, synchronous loss with blurring of images, and missing image in the beginning of the work order. The design of an automated, real time system, which will reject defective films, is treated.

HydroClimATe: hydrologic and climatic analysis toolkit

USGS Publications Warehouse

Dickinson, Jesse; Hanson, Randall T.; Predmore, Steven K.

2014-01-01

The potential consequences of climate variability and climate change have been identified as major issues for the sustainability and availability of the worldwide water resources. Unlike global climate change, climate variability represents deviations from the long-term state of the climate over periods of a few years to several decades. Currently, rich hydrologic time-series data are available, but the combination of data preparation and statistical methods developed by the U.S. Geological Survey as part of the Groundwater Resources Program is relatively unavailable to hydrologists and engineers who could benefit from estimates of climate variability and its effects on periodic recharge and water-resource availability. This report documents HydroClimATe, a computer program for assessing the relations between variable climatic and hydrologic time-series data. HydroClimATe was developed for a Windows operating system. The software includes statistical tools for (1) time-series preprocessing, (2) spectral analysis, (3) spatial and temporal analysis, (4) correlation analysis, and (5) projections. The time-series preprocessing tools include spline fitting, standardization using a normal or gamma distribution, and transformation by a cumulative departure. The spectral analysis tools include discrete Fourier transform, maximum entropy method, and singular spectrum analysis. The spatial and temporal analysis tool is empirical orthogonal function analysis. The correlation analysis tools are linear regression and lag correlation. The projection tools include autoregressive time-series modeling and generation of many realizations. These tools are demonstrated in four examples that use stream-flow discharge data, groundwater-level records, gridded time series of precipitation data, and the Multivariate ENSO Index.

Delay differential analysis of time series.

PubMed

Lainscsek, Claudia; Sejnowski, Terrence J

2015-03-01

Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis.

Fourier Spectroscopy: A Simple Analysis Technique

ERIC Educational Resources Information Center

Oelfke, William C.

1975-01-01

Presents a simple method of analysis in which the student can integrate, point by point, any interferogram to obtain its Fourier transform. The manual technique requires no special equipment and is based on relationships that most undergraduate physics students can derive from the Fourier integral equations. (Author/MLH)

Wireless Intrusion Detection

DTIC Science & Technology

2007-03-01

32 4.4 Algorithm Pseudo - Code ...................................................................................34 4.5 WIND Interface With a...difference estimates of xc temporal derivatives, or by using a polynomial fit to the previous values of xc. 34 4.4 ALGORITHM PSEUDO - CODE Pseudo ...Phase Shift Keying DQPSK Differential Quadrature Phase Shift Keying EVM Error Vector Magnitude FFT Fast Fourier Transform FPGA Field Programmable

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

NASA Astrophysics Data System (ADS)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

On the Spectrum of Periodic Signals

ERIC Educational Resources Information Center

Al-Smadi, Adnan

2004-01-01

In theory, there are many methods for the representation of signals. In practice, however, Fourier analysis involving the resolution of signals into sinusoidal components is used widely. There are several methods for Fourier analysis available for representation of signals. If the signal is periodic, then the Fourier series is used to represent…

Measurement of drug and macromolecule diffusion across atherosclerotic rabbit aorta ex vivo by attenuated total reflection-Fourier transform infrared imaging

NASA Astrophysics Data System (ADS)

Palombo, Francesca; Danoux, Charlène B.; Weinberg, Peter D.; Kazarian, Sergei G.

2009-07-01

Diffusion of two model drugs-benzyl nicotinate and ibuprofen-and the plasma macromolecule albumin across atherosclerotic rabbit aorta was studied ex vivo by attenuated total reflection-Fourier transform infrared (ATR-FTIR) imaging. Solutions of these molecules were applied to the endothelial surface of histological sections of the aortic wall that were sandwiched between two impermeable surfaces. An array of spectra, each corresponding to a specific location in the section, was obtained at various times during solute diffusion into the wall and revealed the distribution of the solutes within the tissue. Benzyl nicotinate in Ringer's solution showed higher affinity for atherosclerotic plaque than for apparently healthy tissue. Transmural concentration profiles for albumin demonstrated its permeation across the section and were consistent with a relatively low distribution volume for the macromolecule in the middle of the wall. The ability of albumin to act as a drug carrier for ibuprofen, otherwise undetected within the tissue, was demonstrated by multivariate subtraction image analysis. In conclusion, ATR-FTIR imaging can be used to study transport processes in tissue samples with high spatial and temporal resolution and without the need to label the solutes under study.

Comparison of temporal and spectral scattering methods using acoustically large breast models derived from magnetic resonance images.

PubMed

Hesford, Andrew J; Tillett, Jason C; Astheimer, Jeffrey P; Waag, Robert C

2014-08-01

Accurate and efficient modeling of ultrasound propagation through realistic tissue models is important to many aspects of clinical ultrasound imaging. Simplified problems with known solutions are often used to study and validate numerical methods. Greater confidence in a time-domain k-space method and a frequency-domain fast multipole method is established in this paper by analyzing results for realistic models of the human breast. Models of breast tissue were produced by segmenting magnetic resonance images of ex vivo specimens into seven distinct tissue types. After confirming with histologic analysis by pathologists that the model structures mimicked in vivo breast, the tissue types were mapped to variations in sound speed and acoustic absorption. Calculations of acoustic scattering by the resulting model were performed on massively parallel supercomputer clusters using parallel implementations of the k-space method and the fast multipole method. The efficient use of these resources was confirmed by parallel efficiency and scalability studies using large-scale, realistic tissue models. Comparisons between the temporal and spectral results were performed in representative planes by Fourier transforming the temporal results. An RMS field error less than 3% throughout the model volume confirms the accuracy of the methods for modeling ultrasound propagation through human breast.

Fourier transform spectrometer controller for partitioned architectures

NASA Astrophysics Data System (ADS)

Tamas-Selicean, D.; Keymeulen, D.; Berisford, D.; Carlson, R.; Hand, K.; Pop, P.; Wadsworth, W.; Levy, R.

The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Researchers at ESA and NASA advocated for the use of partitioned architecture to reduce this complexity. Partitioned architectures rely on platform mechanisms to provide robust temporal and spatial separation between applications. Such architectures have been successfully implemented in several industries, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture.

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

NASA Technical Reports Server (NTRS)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Validating data analysis of broadband laser ranging

NASA Astrophysics Data System (ADS)

Rhodes, M.; Catenacci, J.; Howard, M.; La Lone, B.; Kostinski, N.; Perry, D.; Bennett, C.; Patterson, J.

2018-03-01

Broadband laser ranging combines spectral interferometry and a dispersive Fourier transform to achieve high-repetition-rate measurements of the position of a moving surface. Telecommunications fiber is a convenient tool for generating the large linear dispersions required for a dispersive Fourier transform, but standard fiber also has higher-order dispersion that distorts the Fourier transform. Imperfections in the dispersive Fourier transform significantly complicate the ranging signal and must be dealt with to make high-precision measurements. We describe in detail an analysis process for interpreting ranging data when standard telecommunications fiber is used to perform an imperfect dispersive Fourier transform. This analysis process is experimentally validated over a 27-cm scan of static positions, showing an accuracy of 50 μm and a root-mean-square precision of 4.7 μm.

Comparative analysis of imaging configurations and objectives for Fourier microscopy.

PubMed

Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid

2015-11-01

Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.

A Fourier analysis for a fast simulation algorithm. [for switching converters

NASA Technical Reports Server (NTRS)

King, Roger J.

1988-01-01

This paper presents a derivation of compact expressions for the Fourier series analysis of the steady-state solution of a typical switching converter. The modeling procedure for the simulation and the steady-state solution is described, and some desirable traits for its matrix exponential subroutine are discussed. The Fourier analysis algorithm was tested on a phase-controlled parallel-loaded resonant converter, providing an experimental confirmation.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Evaluation of Hydrologic and Meteorological Impacts on Dengue Fever Incidences in Southern Taiwan using Time- Frequency Method

NASA Astrophysics Data System (ADS)

Tsai, Christina; Yeh, Ting-Gu

2017-04-01

Extreme weather events are occurring more frequently as a result of climate change. Recently dengue fever has become a serious issue in southern Taiwan. It may have characteristic temporal scales that can be identified. Some researchers have hypothesized that dengue fever incidences are related to climate change. This study applies time-frequency analysis to time series data concerning dengue fever and hydrologic and meteorological variables. Results of three time-frequency analytical methods - the Hilbert Huang transform (HHT), the Wavelet Transform (WT) and the Short Time Fourier Transform (STFT) are compared and discussed. A more effective time-frequency analysis method will be identified to analyze relevant time series data. The most influential time scales of hydrologic and meteorological variables that are associated with dengue fever are determined. Finally, the linkage between hydrologic/meteorological factors and dengue fever incidences can be established.

The Fourier decomposition method for nonlinear and non-stationary time series analysis.

PubMed

Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

2017-03-01

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

The Fourier decomposition method for nonlinear and non-stationary time series analysis

PubMed Central

Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

2017-01-01

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of ‘Fourier intrinsic band functions’ (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms. PMID:28413352

Development of an Imaging Fourier Transform Spectrometer

DTIC Science & Technology

1986-05-01

during multiple tests or concurrently applying many identical instrument systems to a single test. These difficult, expensive, and time-consuming...processes would introduce AEDC-TR-86-17 uncertainties due to nonstationary sources and instrument instability associated with multiple firings or... multiple instruments. For even moderate spatial, spectral, and temporal resolution, none of the previously mentioned approaches is reasonable. The

The combined use of order tracking techniques for enhanced Fourier analysis of order components

NASA Astrophysics Data System (ADS)

Wang, K. S.; Heyns, P. S.

2011-04-01

Order tracking is one of the most important vibration analysis techniques for diagnosing faults in rotating machinery. It can be performed in many different ways, each of these with distinct advantages and disadvantages. However, in the end the analyst will often use Fourier analysis to transform the data from a time series to frequency or order spectra. It is therefore surprising that the study of the Fourier analysis of order-tracked systems seems to have been largely ignored in the literature. This paper considers the frequently used Vold-Kalman filter-based order tracking and computed order tracking techniques. The main pros and cons of each technique for Fourier analysis are discussed and the sequential use of Vold-Kalman filtering and computed order tracking is proposed as a novel idea to enhance the results of Fourier analysis for determining the order components. The advantages of the combined use of these order tracking techniques are demonstrated numerically on an SDOF rotor simulation model. Finally, the approach is also demonstrated on experimental data from a real rotating machine.

High-range resolution spectral analysis of precipitation through range imaging of the Chung-Li VHF radar

NASA Astrophysics Data System (ADS)

Tsai, Shih-Chiao; Chen, Jenn-Shyong; Chu, Yen-Hsyang; Su, Ching-Lun; Chen, Jui-Hsiang

2018-01-01

Multi-frequency range imaging (RIM) has been operated in the Chung-Li very high-frequency (VHF) radar, located on the campus of National Central University, Taiwan, since 2008. RIM processes the echo signals with a group of closely spaced transmitting frequencies through appropriate inversion methods to obtain high-resolution distribution of echo power in the range direction. This is beneficial to the investigation of the small-scale structure embedded in dynamic atmosphere. Five transmitting frequencies were employed in the radar experiment for observation of the precipitating atmosphere during the period between 21 and 23 August 2013. Using the Capon and Fourier methods, the radar echoes were synthesized to retrieve the temporal signals at a smaller range step than the original range resolution defined by the pulse width, and such retrieved temporal signals were then processed in the Doppler frequency domain to identify the atmosphere and precipitation echoes. An analysis called conditional averaging was further executed for echo power, Doppler velocity, and spectral width to verify the potential capabilities of the retrieval processing in resolving small-scale precipitation and atmosphere structures. Point-by-point correction of range delay combined with compensation of range-weighting function effect has been performed during the retrieval of temporal signals to improve the continuity of power spectra at gate boundaries, making the small-scale structures in the power spectra more natural and reasonable. We examined stratiform and convective precipitation and demonstrated their different structured characteristics by means of the Capon-processed results. The new element in this study is the implementation of RIM on spectral analysis, especially for precipitation echoes.

Analysis on the time and frequency domains of the acceleration in front crawl stroke.

PubMed

Gil, Joaquín Madera; Moreno, Luis-Millán González; Mahiques, Juan Benavent; Muñoz, Víctor Tella

2012-05-01

The swimming involves accelerations and decelerations in the swimmer's body. Thus, the main objective of this study is to make a temporal and frequency analysis of the acceleration in front crawl swimming, regarding the gender and the performance. The sample was composed by 31 male swimmers (15 of high-level and 16 of low-level) and 20 female swimmers (11 of high-level and 9 of low-level). The acceleration was registered from the third complete cycle during eight seconds in a 25 meters maximum velocity test. A position transducer (200Hz) was used to collect the data, and it was synchronized to an aquatic camera (25Hz). The acceleration in the temporal (root mean square, minimum and maximum of the acceleration) and frequency (power peak, power peak frequency and spectral area) domains was calculated with Fourier analysis, as well as the velocity and the spectrums distribution in function to present one or more main peaks (type 1 and type 2). A one-way ANOVA was used to establish differences between gender and performance. Results show differences between genders in all the temporal domain variables (p<0.05) and only the Spectral Area (SA) in the frequency domain (p<0.05). Between gender and performance, only the Root Mean Square (RMS) showed differences in the performance of the male swimmers (p<0.05) and in the higher level swimmers, the Maximum (Max) and the Power Peak (PP) of the acceleration showed differences between both genders (p<0.05). These results confirms the importance of knowing the RMS to determine the efficiency of the swimmers regarding gender and performance level.

Extracting temporal and spatial information from remotely sensed data for mapping wildlife habitat: Tucson

USGS Publications Warehouse

Wallace, Cynthia S.A.; Advised by Marsh, Stuart E.

2002-01-01

The research accomplished in this dissertation used both mathematical and statistical techniques to extract and evaluate measures of landscape temporal dynamics and spatial structure from remotely sensed data for the purpose of mapping wildlife habitat. By coupling the landscape measures gleaned from the remotely sensed data with various sets of animal sightings and population data, effective models of habitat preference were created.Measures of temporal dynamics of vegetation greenness as measured by National Oceanographic and Atmospheric Administration’s Advanced Very High Resolution Radiometer (AVHRR) satellite were used to effectively characterize and map season specific habitat of the Sonoran pronghorn antelope, as well as produce preliminary models of potential yellow-billed cuckoo habitat in Arizona. Various measures that capture different aspects of the temporal dynamics of the landscape were derived from AVHRR Normalized Difference Vegetation Index composite data using three main classes of calculations: basic statistics, standardized principal components analysis, and Fourier analysis. Pronghorn habitat models based on the AVHRR measures correspond visually and statistically to GIS-based models produced using data that represent detailed knowledge of ground-condition.Measures of temporal dynamics also revealed statistically significant correlations with annual estimates of elk population in selected Arizona Game Management Units, suggesting elk respond to regional environmental changes that can be measured using satellite data. Such relationships, once verified and established, can be used to help indirectly monitor the population.Measures of landscape spatial structure derived from IKONOS high spatial resolution (1-m) satellite data using geostatistics effectively map details of Sonoran pronghorn antelope habitat. Local estimates of the nugget, sill, and range variogram parameters calculated within 25 x 25-meter image windows describe the spatial autocorrelation of the image, permitting classification of all pixels into coherent units whose signature graphs exhibit a classic variogram shape. The variogram parameters captured in these signatures have been shown in previous studies to discriminate between different species-specific vegetation associations.The synoptic view of the landscape provided by satellite data can inform resource management efforts. The ability to characterize the spatial structure and temporal dynamics of habitat using repeatable remote sensing data allows closer monitoring of the relationship between a species and its landscape.

Max CAPR: high-resolution 3D contrast-enhanced MR angiography with acquisition times under 5 seconds.

PubMed

Haider, Clifton R; Borisch, Eric A; Glockner, James F; Mostardi, Petrice M; Rossman, Phillip J; Young, Phillip M; Riederer, Stephen J

2010-10-01

High temporal and spatial resolution is desired in imaging of vascular abnormalities having short arterial-to-venous transit times. Methods that exploit temporal correlation to reduce the observed frame time demonstrate temporal blurring, obfuscating bolus dynamics. Previously, a Cartesian acquisition with projection reconstruction-like (CAPR) sampling method has been demonstrated for three-dimensional contrast-enhanced angiographic imaging of the lower legs using two-dimensional sensitivity-encoding acceleration and partial Fourier acceleration, providing 1mm isotropic resolution of the calves, with 4.9-sec frame time and 17.6-sec temporal footprint. In this work, the CAPR acquisition is further undersampled to provide a net acceleration approaching 40 by eliminating all view sharing. The tradeoff of frame time and temporal footprint in view sharing is presented and characterized in phantom experiments. It is shown that the resultant 4.9-sec acquisition time, three-dimensional images sets have sufficient spatial and temporal resolution to clearly portray arterial and venous phases of contrast passage. It is further hypothesized that these short temporal footprint sequences provide diagnostic quality images. This is tested and shown in a series of nine contrast-enhanced MR angiography patient studies performed with the new method.

Robust and transferable quantification of NMR spectral quality using IROC analysis

NASA Astrophysics Data System (ADS)

Zambrello, Matthew A.; Maciejewski, Mark W.; Schuyler, Adam D.; Weatherby, Gerard; Hoch, Jeffrey C.

2017-12-01

Non-Fourier methods are increasingly utilized in NMR spectroscopy because of their ability to handle nonuniformly-sampled data. However, non-Fourier methods present unique challenges due to their nonlinearity, which can produce nonrandom noise and render conventional metrics for spectral quality such as signal-to-noise ratio unreliable. The lack of robust and transferable metrics (i.e. applicable to methods exhibiting different nonlinearities) has hampered comparison of non-Fourier methods and nonuniform sampling schemes, preventing the identification of best practices. We describe a novel method, in situ receiver operating characteristic analysis (IROC), for characterizing spectral quality based on the Receiver Operating Characteristic curve. IROC utilizes synthetic signals added to empirical data as "ground truth", and provides several robust scalar-valued metrics for spectral quality. This approach avoids problems posed by nonlinear spectral estimates, and provides a versatile quantitative means of characterizing many aspects of spectral quality. We demonstrate applications to parameter optimization in Fourier and non-Fourier spectral estimation, critical comparison of different methods for spectrum analysis, and optimization of nonuniform sampling schemes. The approach will accelerate the discovery of optimal approaches to nonuniform sampling experiment design and non-Fourier spectrum analysis for multidimensional NMR.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

Linear theory on temporal instability of megahertz faraday waves for monodisperse microdroplet ejection.

PubMed

Tsai, Shirley C; Tsai, Chen S

2013-08-01

A linear theory on temporal instability of megahertz Faraday waves for monodisperse microdroplet ejection based on mass conservation and linearized Navier-Stokes equations is presented using the most recently observed micrometer- sized droplet ejection from a millimeter-sized spherical water ball as a specific example. The theory is verified in the experiments utilizing silicon-based multiple-Fourier horn ultrasonic nozzles at megahertz frequency to facilitate temporal instability of the Faraday waves. Specifically, the linear theory not only correctly predicted the Faraday wave frequency and onset threshold of Faraday instability, the effect of viscosity, the dynamics of droplet ejection, but also established the first theoretical formula for the size of the ejected droplets, namely, the droplet diameter equals four-tenths of the Faraday wavelength involved. The high rate of increase in Faraday wave amplitude at megahertz drive frequency subsequent to onset threshold, together with enhanced excitation displacement on the nozzle end face, facilitated by the megahertz multiple Fourier horns in resonance, led to high-rate ejection of micrometer- sized monodisperse droplets (>10(7) droplets/s) at low electrical drive power (<;1 W) with short initiation time (<;0.05 s). This is in stark contrast to the Rayleigh-Plateau instability of a liquid jet, which ejects one droplet at a time. The measured diameters of the droplets ranging from 2.2 to 4.6 μm at 2 to 1 MHz drive frequency fall within the optimum particle size range for pulmonary drug delivery.

First results of ground-based LWIR hyperspectral imaging remote gas detection

NASA Astrophysics Data System (ADS)

Zheng, Wei-jian; Lei, Zheng-gang; Yu, Chun-chao; Wang, Hai-yang; Fu, Yan-peng; Liao, Ning-fang; Su, Jun-hong

2014-11-01

The new progress of ground-based long-wave infrared remote sensing is presented. The LWIR hyperspectral imaging by using the windowing spatial and temporal modulation Fourier spectroscopy, and the results of outdoor ether gas detection, verify the features of LWIR hyperspectral imaging remote sensing and technical approach. It provides a new technical means for ground-based gas remote sensing.

The τq-Fourier transform: Covariance and uniqueness

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-05-01

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “τq-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the τq-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the τq-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.

Off-axis illumination direct-to-digital holography

DOEpatents

Thomas, Clarence E.; Price, Jeffery R.; Voelkl, Edgar; Hanson, Gregory R.

2004-06-08

Systems and methods are described for off-axis illumination direct-to-digital holography. A method of recording an off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis, includes: reflecting a reference beam from a reference mirror at a non-normal angle; reflecting an object beam from an object at an angle with respect to an optical axis defined by a focusing lens; focusing the reference beam and the object beam at a focal plane of a digital recorder to form the off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; digitally recording the off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; Fourier analyzing the recorded off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes by transforming axes of the recorded off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes in Fourier space to sit on top of a heterodyne carrier frequency defined as an angle between the reference beam and the object beam; applying a digital filter to cut off signals around an original origin; and then performing an inverse Fourier transform.

Insights into Fourier Synthesis and Analysis: Part 2--A Simplified Mathematics.

ERIC Educational Resources Information Center

Moore, Guy S. M.

1988-01-01

Introduced is an analysis of a waveform into its Fourier components. Topics included are simplified analysis of a square waveform, a triangular waveform, half-wave rectified alternating current (AC), and impulses. Provides the mathematical expression and simplified analysis diagram of each waveform. (YP)

Spatially-Heterodyned Holography

DOEpatents

Thomas, Clarence E [Knoxville, TN; Hanson, Gregory R [Clinton, TN

2006-02-21

A method of recording a spatially low-frequency heterodyne hologram, including spatially heterodyne fringes for Fourier analysis, includes: splitting a laser beam into a reference beam and an object beam; interacting the object beam with an object; focusing the reference beam and the object beam at a focal plane of a digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis; digital recording the spatially low-frequency heterodyne hologram; Fourier transforming axes of the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam; cutting off signals around an origin; and performing an inverse Fourier transform.

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.

1969-01-01

Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.

Fourier Analysis and Structure Determination: Part I: Fourier Transforms.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

PubMed

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2¹⁰ times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

k-space image correlation to probe the intracellular dynamics of gold nanoparticles

NASA Astrophysics Data System (ADS)

Bouzin, M.; Sironi, L.; Chirico, G.; D'Alfonso, L.; Inverso, D.; Pallavicini, P.; Collini, M.

2016-04-01

The collective action of dynein, kinesin and myosin molecular motors is responsible for the intracellular active transport of cargoes, vesicles and organelles along the semi-flexible oriented filaments of the cytoskeleton. The overall mobility of the cargoes upon binding and unbinding to motor proteins can be modeled as an intermittency between Brownian diffusion in the cell cytoplasm and active ballistic excursions along actin filaments or microtubules. Such an intermittent intracellular active transport, exhibited by star-shaped gold nanoparticles (GNSs, Gold Nanostars) upon internalization in HeLa cancer cells, is investigated here by combining live-cell time-lapse confocal reflectance microscopy and the spatio-temporal correlation, in the reciprocal Fourier space, of the acquired image sequences. At first, the analytical theoretical framework for the investigation of a two-state intermittent dynamics is presented for Fourier-space Image Correlation Spectroscopy (kICS). Then simulated kICS correlation functions are employed to evaluate the influence of, and sensitivity to, all the kinetic and dynamic parameters the model involves (the transition rates between the diffusive and the active transport states, the diffusion coefficient and drift velocity of the imaged particles). The optimal procedure for the analysis of the experimental data is outlined and finally exploited to derive whole-cell maps for the parameters underlying the GNSs super-diffusive dynamics. Applied here to the GNSs subcellular trafficking, the proposed kICS analysis can be adopted for the characterization of the intracellular (super-) diffusive dynamics of any fluorescent or scattering biological macromolecule.

Evaluation and statistical judgement of neural responses to sinusoidal stimulation in cases with superimposed drift and noise.

PubMed

Jastreboff, P W

1979-06-01

Time histograms of neural responses evoked by sinuosidal stimulation often contain a slow drifting and an irregular noise which disturb Fourier analysis of these responses. Section 2 of this paper evaluates the extent to which a linear drift influences the Fourier analysis, and develops a combined Fourier and linear regression analysis for detecting and correcting for such a linear drift. Usefulness of this correcting method is demonstrated for the time histograms of actual eye movements and Purkinje cell discharges evoked by sinusoidal rotation of rabbits in the horizontal plane. In Sect. 3, the analysis of variance is adopted for estimating the probability of the random occurrence of the response curve extracted by Fourier analysis from noise. This method proved to be useful for avoiding false judgements as to whether the response curve was meaningful, particularly when the response was small relative to the contaminating noise.

Fourier-based linear systems description of free-breathing pulmonary magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Capaldi, D. P. I.; Svenningsen, S.; Cunningham, I. A.; Parraga, G.

2015-03-01

Fourier-decomposition of free-breathing pulmonary magnetic resonance imaging (FDMRI) was recently piloted as a way to provide rapid quantitative pulmonary maps of ventilation and perfusion without the use of exogenous contrast agents. This method exploits fast pulmonary MRI acquisition of free-breathing proton (1H) pulmonary images and non-rigid registration to compensate for changes in position and shape of the thorax associated with breathing. In this way, ventilation imaging using conventional MRI systems can be undertaken but there has been no systematic evaluation of fundamental image quality measurements based on linear systems theory. We investigated the performance of free-breathing pulmonary ventilation imaging using a Fourier-based linear system description of each operation required to generate FDMRI ventilation maps. Twelve subjects with chronic obstructive pulmonary disease (COPD) or bronchiectasis underwent pulmonary function tests and MRI. Non-rigid registration was used to co-register the temporal series of pulmonary images. Pulmonary voxel intensities were aligned along a time axis and discrete Fourier transforms were performed on the periodic signal intensity pattern to generate frequency spectra. We determined the signal-to-noise ratio (SNR) of the FDMRI ventilation maps using a conventional approach (SNRC) and using the Fourier-based description (SNRF). Mean SNR was 4.7 ± 1.3 for subjects with bronchiectasis and 3.4 ± 1.8, for COPD subjects (p>.05). SNRF was significantly different than SNRC (p<.01). SNRF was approximately 50% of SNRC suggesting that the linear system model well-estimates the current approach.

Window and Overlap Processing Effects on Power Estimates from Spectra

NASA Astrophysics Data System (ADS)

Trethewey, M. W.

2000-03-01

Fast Fourier transform (FFT) spectral processing is based on the assumption of stationary ergodic data. In engineering practice, the assumption is often violated and non-stationary data processed. Data windows are commonly used to reduce leakage by decreasing the signal amplitudes near the boundaries of the discrete samples. With certain combinations of non-stationary signals and windows, the temporal weighting may attenuate important signal characteristics to adversely affect any subsequent processing. In other words, the window artificially reduces a significant section of the time signal. Consequently, spectra and overall power estimated from the affected samples are unreliable. FFT processing can be particularly problematic when the signal consists of randomly occurring transients superimposed on a more continuous signal. Overlap processing is commonly used in this situation to improve the estimates. However, the results again depend on the temporal character of the signal in relation to the window weighting. A worst-case scenario, a short-duration half sine pulse, is used to illustrate the relationship between overlap percentage and resulting power estimates. The power estimates are shown to depend on the temporal behaviour of the square of overlapped window segments. An analysis shows that power estimates may be obtained to within 0.27 dB for the following windows and overlap combinations: rectangular (0% overlap), Hanning (62.5% overlap), Hamming (60.35% overlap) and flat-top (82.25% overlap).

Tagging cortical networks in emotion: a topographical analysis

PubMed Central

Keil, Andreas; Costa, Vincent; Smith, J. Carson; Sabatinelli, Dean; McGinnis, E. Menton; Bradley, Margaret M.; Lang, Peter J.

2013-01-01

Viewing emotional pictures is associated with heightened perception and attention, indexed by a relative increase in visual cortical activity. Visual cortical modulation by emotion is hypothesized to reflect re-entrant connectivity originating in higher-order cortical and/or limbic structures. The present study used dense-array electroencephalography and individual brain anatomy to investigate functional coupling between the visual cortex and other cortical areas during affective picture viewing. Participants viewed pleasant, neutral, and unpleasant pictures that flickered at a rate of 10 Hz to evoke steady-state visual evoked potentials (ssVEPs) in the EEG. The spectral power of ssVEPs was quantified using Fourier transform, and cortical sources were estimated using beamformer spatial filters based on individual structural magnetic resonance images. In addition to lower-tier visual cortex, a network of occipito-temporal and parietal (bilateral precuneus, inferior parietal lobules) structures showed enhanced ssVEP power when participants viewed emotional (either pleasant or unpleasant), compared to neutral pictures. Functional coupling during emotional processing was enhanced between the bilateral occipital poles and a network of temporal (left middle/inferior temporal gyrus), parietal (bilateral parietal lobules), and frontal (left middle/inferior frontal gyrus) structures. These results converge with findings from hemodynamic analyses of emotional picture viewing and suggest that viewing emotionally engaging stimuli is associated with the formation of functional links between visual cortex and the cortical regions underlying attention modulation and preparation for action. PMID:21954087

Using the auxiliary camera for system calibration of 3D measurement by digital speckle

NASA Astrophysics Data System (ADS)

Xue, Junpeng; Su, Xianyu; Zhang, Qican

2014-06-01

The study of 3D shape measurement by digital speckle temporal sequence correlation have drawn a lot of attention by its own advantages, however, the measurement mainly for depth z-coordinate, horizontal physical coordinate (x, y) are usually marked as image pixel coordinate. In this paper, a new approach for the system calibration is proposed. With an auxiliary camera, we made up the temporary binocular vision system, which are used for the calibration of horizontal coordinates (mm) while the temporal sequence reference-speckle-sets are calibrated. First, the binocular vision system has been calibrated using the traditional method. Then, the digital speckles are projected on the reference plane, which is moved by equal distance in the direction of depth, temporal sequence speckle images are acquired with camera as reference sets. When the reference plane is in the first position and final position, crossed fringe pattern are projected to the plane respectively. The control points of pixel coordinates are extracted by Fourier analysis from the images, and the physical coordinates are calculated by the binocular vision. The physical coordinates corresponding to each pixel of the images are calculated by interpolation algorithm. Finally, the x and y corresponding to arbitrary depth value z are obtained by the geometric formula. Experiments prove that our method can fast and flexibly measure the 3D shape of an object as point cloud.

Fractional-order Fourier analysis for ultrashort pulse characterization.

PubMed

Brunel, Marc; Coetmellec, Sébastien; Lelek, Mickael; Louradour, Frédéric

2007-06-01

We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.

An Efficient Adaptive Window Size Selection Method for Improving Spectrogram Visualization.

PubMed

Nisar, Shibli; Khan, Omar Usman; Tariq, Muhammad

2016-01-01

Short Time Fourier Transform (STFT) is an important technique for the time-frequency analysis of a time varying signal. The basic approach behind it involves the application of a Fast Fourier Transform (FFT) to a signal multiplied with an appropriate window function with fixed resolution. The selection of an appropriate window size is difficult when no background information about the input signal is known. In this paper, a novel empirical model is proposed that adaptively adjusts the window size for a narrow band-signal using spectrum sensing technique. For wide-band signals, where a fixed time-frequency resolution is undesirable, the approach adapts the constant Q transform (CQT). Unlike the STFT, the CQT provides a varying time-frequency resolution. This results in a high spectral resolution at low frequencies and high temporal resolution at high frequencies. In this paper, a simple but effective switching framework is provided between both STFT and CQT. The proposed method also allows for the dynamic construction of a filter bank according to user-defined parameters. This helps in reducing redundant entries in the filter bank. Results obtained from the proposed method not only improve the spectrogram visualization but also reduce the computation cost and achieves 87.71% of the appropriate window length selection.

Inverse source problems in elastodynamics

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao

2018-04-01

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.

[Using 2-DCOS to identify the molecular spectrum peaks for the isomer in the multi-component mixture gases Fourier transform infrared analysis].

PubMed

Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua

2014-10-01

The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.

Beyond Fourier

NASA Astrophysics Data System (ADS)

Hoch, Jeffrey C.

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

Spatiotemporal behaviour of isodiffracting hollow Gaussian pulsed beams

NASA Astrophysics Data System (ADS)

Xu, Yanbing; Lü, Baida

2007-05-01

A model of isodiffracting hollow Gaussian pulsed beams (HGPBs) is presented. Based on the Fourier transform method, an analytical formula for the HGPBs propagating in free space is derived, which enables us to study the spatiotemporal behaviour of the ultrashort pulsed beams. Some interesting phenomena of ultrashort pulsed beams, such as the symmetrical temporal profiles, the dark rings, etc, are discussed in detail and illustrated numerically.

A Dynamic Compressive Gammachirp Auditory Filterbank

PubMed Central

Irino, Toshio; Patterson, Roy D.

2008-01-01

It is now common to use knowledge about human auditory processing in the development of audio signal processors. Until recently, however, such systems were limited by their linearity. The auditory filter system is known to be level-dependent as evidenced by psychophysical data on masking, compression, and two-tone suppression. However, there were no analysis/synthesis schemes with nonlinear filterbanks. This paper describe18300060s such a scheme based on the compressive gammachirp (cGC) auditory filter. It was developed to extend the gammatone filter concept to accommodate the changes in psychophysical filter shape that are observed to occur with changes in stimulus level in simultaneous, tone-in-noise masking. In models of simultaneous noise masking, the temporal dynamics of the filtering can be ignored. Analysis/synthesis systems, however, are intended for use with speech sounds where the glottal cycle can be long with respect to auditory time constants, and so they require specification of the temporal dynamics of auditory filter. In this paper, we describe a fast-acting level control circuit for the cGC filter and show how psychophysical data involving two-tone suppression and compression can be used to estimate the parameter values for this dynamic version of the cGC filter (referred to as the “dcGC” filter). One important advantage of analysis/synthesis systems with a dcGC filterbank is that they can inherit previously refined signal processing algorithms developed with conventional short-time Fourier transforms (STFTs) and linear filterbanks. PMID:19330044

Estimation of multiple accelerated motions using chirp-Fourier transform and clustering.

PubMed

Alexiadis, Dimitrios S; Sergiadis, George D

2007-01-01

Motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed, which, however, cannot handle both time-varying and multiple motions. Extending previously published ideas, we present an efficient method for estimating multiple, linearly time-varying motions. It is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals. From this viewpoint, one can exploit established signal processing tools such as the chirp-Fourier transform. It is shown that accelerated motion results in energy concentration along planes in the 4-D space: spatial frequencies-temporal frequency-chirp rate. Using fuzzy c-planes clustering, we estimate the plane/motion parameters. The effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted.

Mapping agroecological zones and time lag in vegetation growth by means of Fourier analysis of time series of NDVI images

NASA Technical Reports Server (NTRS)

Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.

1993-01-01

Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.

A BASIC program for the removal of noise from reaction traces using Fourier filtering.

PubMed

Brittain, T

1989-04-01

Software for the removal of noise from reaction curves using the principle of Fourier filtering has been written in BASIC to execute on a PC. The program inputs reaction traces which are subjected to a rotation-inversion process, to produce functions suitable for Fourier analysis. Fourier transformation into the frequency domain is followed by multiplication of the transform by a rectangular filter function, to remove the noise frequencies. Inverse transformation then yields a noise-reduced reaction trace suitable for further analysis. The program is interactive at each stage and could easily be modified to remove noise from a range of input data types.

Temporal radiographic texture analysis in the detection of periprosthetic osteolysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilkie, Joel R.; Giger, Maryellen L.; Chinander, Michael R.

2008-01-15

Periprosthetic osteolysis is one of the most serious long-term problems in total hip arthroplasty. It has been primarily attributed to the body's inflammatory response to submicron polyethylene particles worn from the hip implant, and it leads to bone loss and structural deterioration in the surrounding bone. It was previously demonstrated that radiographic texture analysis (RTA) has the ability to distinguish between osteolysis and normal cases at the time of clinical detection of the disease; however, that analysis did not take into account the changes in texture over time. The goal of this preliminary analysis, however, is to assess the abilitymore » of temporal radiographic texture analysis (tRTA) to distinguish between patients who develop osteolysis and normal cases. Two tRTA methods were used in the study: the RTA feature change from baseline at various follow-up intervals and the slope of the best-fit line to the RTA data series. These tRTA methods included Fourier-based and fractal-based features calculated from digitized images of 202 total hip replacement cases, including 70 that developed osteolysis. Results show that separation between the osteolysis and normal groups increased over time for the feature difference method, as the disease progressed, with area under the curve (AUC) values from receiver operating characteristic analysis of 0.65 to 0.72 at 15 years postsurgery. Separation for the slope method was also evident, with AUC values ranging from 0.65 to 0.76 for the task of distinguishing between osteolysis and normal cases. The results suggest that tRTA methods have the ability to measure changes in trabecular structure, and may be useful in the early detection of periprosthetic osteolysis.« less

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

PubMed

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

Multi-frequency data analysis in AFM by wavelet transform

NASA Astrophysics Data System (ADS)

Pukhova, V.; Ferrini, G.

2017-10-01

Interacting cantilevers in AFM experiments generate non-stationary, multi-frequency signals consisting of numerous excited flexural and torsional modes and their harmonics. The analysis of such signals is challenging, requiring special methodological approaches and a powerful mathematical apparatus. The most common approach to the signal analysis is to apply Fourier transform analysis. However, FT gives accurate spectra for stationary signals, and for signals changing their spectral content over time, FT provides only an averaged spectrum. Hence, for non-stationary and rapidly varying signals, such as those from interacting cantilevers, a method that shows the spectral evolution in time is needed. One of the most powerful techniques, allowing detailed time-frequency representation of signals, is the wavelet transform. It is a method of analysis that allows representation of energy associated to the signal at a particular frequency and time, providing correlation between the spectral and temporal features of the signal, unlike FT. This is particularly important in AFM experiments because signals nonlinearities contains valuable information about tip-sample interactions and consequently surfaces properties. The present work is aimed to show the advantages of wavelet transform in comparison with FT using as an example the force curve analysis in dynamic force spectroscopy.

Vicinal fluorine-fluorine coupling constants: Fourier analysis.

PubMed

San Fabián, J; Westra Hoekzema, A J A

2004-10-01

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn> or =3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation. (c) 2004 American Institute of Physics

Vicinal fluorine-fluorine coupling constants: Fourier analysis

NASA Astrophysics Data System (ADS)

San Fabián, J.; Westra Hoekzema, A. J. A.

2004-10-01

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn⩾3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation.

Apparatus for direct-to-digital spatially-heterodyned holography

DOEpatents

Thomas, Clarence E.; Hanson, Gregory R.

2006-12-12

An apparatus operable to record a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis includes: a laser; a beamsplitter optically coupled to the laser; an object optically coupled to the beamsplitter; a focusing lens optically coupled to both the beamsplitter and the object; a digital recorder optically coupled to the focusing lens; and a computer that performs a Fourier transform, applies a digital filter, and performs an inverse Fourier transform. A reference beam and an object beam are focused by the focusing lens at a focal plane of the digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis which is recorded by the digital recorder, and the computer transforms the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes and shifts axes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam and cuts off signals around an original origin before performing the inverse Fourier transform.

Comparative measurement of collagen bundle orientation by Fourier analysis and semiquantitative evaluation: reliability and agreement in Masson's trichrome, Picrosirius red and confocal microscopy techniques.

PubMed

Marcos-Garcés, V; Harvat, M; Molina Aguilar, P; Ferrández Izquierdo, A; Ruiz-Saurí, A

2017-08-01

Measurement of collagen bundle orientation in histopathological samples is a widely used and useful technique in many research and clinical scenarios. Fourier analysis is the preferred method for performing this measurement, but the most appropriate staining and microscopy technique remains unclear. Some authors advocate the use of Haematoxylin-Eosin (H&E) and confocal microscopy, but there are no studies comparing this technique with other classical collagen stainings. In our study, 46 human skin samples were collected, processed for histological analysis and stained with Masson's trichrome, Picrosirius red and H&E. Five microphotographs of the reticular dermis were taken with a 200× magnification with light microscopy, polarized microscopy and confocal microscopy, respectively. Two independent observers measured collagen bundle orientation with semiautomated Fourier analysis with the Image-Pro Plus 7.0 software and three independent observers performed a semiquantitative evaluation of the same parameter. The average orientation for each case was calculated with the values of the five pictures. We analyzed the interrater reliability, the consistency between Fourier analysis and average semiquantitative evaluation and the consistency between measurements in Masson's trichrome, Picrosirius red and H&E-confocal. Statistical analysis for reliability and agreement was performed with the SPSS 22.0 software and consisted of intraclass correlation coefficient (ICC), Bland-Altman plots and limits of agreement and coefficient of variation. Interrater reliability was almost perfect (ICC > 0.8) with all three histological and microscopy techniques and always superior in Fourier analysis than in average semiquantitative evaluation. Measurements were consistent between Fourier analysis by one observer and average semiquantitative evaluation by three observers, with an almost perfect agreement with Masson's trichrome and Picrosirius red techniques (ICC > 0.8) and a strong agreement with H&E-confocal (0.7 < ICC < 0.8). Comparison of measurements between the three techniques for the same observer showed an almost perfect agreement (ICC > 0.8), better with Fourier analysis than with semiquantitative evaluation (single and average). These results in nonpathological skin samples were also confirmed in a preliminary analysis in eight scleroderma skin samples. Our results show that Masson's trichrome and Picrosirius red are consistent with H&E-confocal for measuring collagen bundle orientation in histological samples and could thus be used indistinctly for this purpose. Fourier analysis is superior to average semiquantitative evaluation and should keep being used as the preferred method. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Spectral ballistic imaging: a novel technique for viewing through turbid or obstructing media.

PubMed

Granot, Er'el; Sternklar, Shmuel

2003-08-01

We propose a new method for viewing through turbid or obstructing media. The medium is illuminated with a modulated cw laser and the amplitude and phase of the transmitted (or reflected) signal is measured. This process takes place for a set of wavelengths in a certain wide band. In this way we acquire the Fourier transform of the temporal output. With this information we can reconstruct the temporal shape of the transmitted signal by computing the inverse transform. The proposed method benefits from the advantages of the first-light technique: high resolution, simple algorithms, insensitivity to boundary condition, etc., without suffering from its main deficiencies: complex and expensive equipment.

Ocular-following responses to white noise stimuli in humans reveal a novel nonlinearity that results from temporal sampling

PubMed Central

Sheliga, Boris M.; Quaia, Christian; FitzGibbon, Edmond J.; Cumming, Bruce G.

2016-01-01

White noise stimuli are frequently used to study the visual processing of broadband images in the laboratory. A common goal is to describe how responses are derived from Fourier components in the image. We investigated this issue by recording the ocular-following responses (OFRs) to white noise stimuli in human subjects. For a given speed we compared OFRs to unfiltered white noise with those to noise filtered with band-pass filters and notch filters. Removing components with low spatial frequency (SF) reduced OFR magnitudes, and the SF associated with the greatest reduction matched the SF that produced the maximal response when presented alone. This reduction declined rapidly with SF, compatible with a winner-take-all operation. Removing higher SF components increased OFR magnitudes. For higher speeds this effect became larger and propagated toward lower SFs. All of these effects were quantitatively well described by a model that combined two factors: (a) an excitatory drive that reflected the OFRs to individual Fourier components and (b) a suppression by higher SF channels where the temporal sampling of the display led to flicker. This nonlinear interaction has an important practical implication: Even with high refresh rates (150 Hz), the temporal sampling introduced by visual displays has a significant impact on visual processing. For instance, we show that this distorts speed tuning curves, shifting the peak to lower speeds. Careful attention to spectral content, in the light of this nonlinearity, is necessary to minimize the resulting artifact when using white noise patterns undergoing apparent motion. PMID:26762277

A multi-pixel InSAR time series analysis method: Simultaneous estimation of atmospheric noise, orbital errors and deformation

NASA Astrophysics Data System (ADS)

Jolivet, R.; Simons, M.

2016-12-01

InSAR time series analysis allows reconstruction of ground deformation with meter-scale spatial resolution and high temporal sampling. For instance, the ESA Sentinel-1 Constellation is capable of providing 6-day temporal sampling, thereby opening a new window on the spatio-temporal behavior of tectonic processes. However, due to computational limitations, most time series methods rely on a pixel-by-pixel approach. This limitation is a concern because (1) accounting for orbital errors requires referencing all interferograms to a common set of pixels before reconstruction of the time series and (2) spatially correlated atmospheric noise due to tropospheric turbulence is ignored. Decomposing interferograms into statistically independent wavelets will mitigate issues of correlated noise, but prior estimation of orbital uncertainties will still be required. Here, we explore a method that considers all pixels simultaneously when solving for the spatio-temporal evolution of interferometric phase Our method is based on a massively parallel implementation of a conjugate direction solver. We consider an interferogram as the sum of the phase difference between 2 SAR acquisitions and the corresponding orbital errors. In addition, we fit the temporal evolution with a physically parameterized function while accounting for spatially correlated noise in the data covariance. We assume noise is isotropic for any given InSAR pair with a covariance described by an exponential function that decays with increasing separation distance between pixels. We regularize our solution in space using a similar exponential function as model covariance. Given the problem size, we avoid matrix multiplications of the full covariances by computing convolutions in the Fourier domain. We first solve the unregularized least squares problem using the LSQR algorithm to approach the final solution, then run our conjugate direction solver to account for data and model covariances. We present synthetic tests showing the efficiency of our method. We then reconstruct a 20-year continuous time series covering Northern Chile. Without input from any additional GNSS data, we recover the secular deformation rate, seasonal oscillations and the deformation fields from the 2005 Mw 7.8 Tarapaca and 2007 Mw 7.7 Tocopilla earthquakes.

Organised Motion in a Tall Spruce Canopy: Temporal Scales, Structure Spacing and Terrain Effects

NASA Astrophysics Data System (ADS)

Thomas, Christoph; Foken, Thomas

2007-01-01

This study investigates the organised motion near the canopy-atmosphere interface of a moderately dense spruce forest in heterogeneous, complex terrain. Wind direction is used to assess differences in topography and surface properties. Observations were obtained at several heights above and within the canopy using sonic anemometers and fast-response gas analysers over the course of several weeks. Analysed variables include the three-dimensional wind vector, the sonic temperature, and the concentration of carbon dioxide. Wavelet analysis was used to extract the organised motion from time series and to derive its temporal scales. Spectral Fourier analysis was deployed to compute power spectra and phase spectra. Profiles of temporal scales of ramp-like coherent structures in the vertical and longitudinal wind components showed a reversed variation with height and were of similar size within the canopy. Temporal scales of scalar fields were comparable to those of the longitudinal wind component suggesting that the lateral scalar transport dominates. The existence of a 1 power law in the longitudinal power spectra was confirmed for a few cases only, with a majority showing a clear 5/3 decay. The variation of effective scales of organised motion in the longitudinal velocity and temperature were found to vary with atmospheric stability, suggesting that both Kelvin-Helmholtz instabilities and attached eddies dominate the flow with increasing convectional forcing. The canopy mixing-layer analogy was observed to be applicable for ramp-like coherent structures in the vertical wind component for selected wind directions only. Departures from the prediction of m = Λ w L {/s -1} = 8 10 (where Λ w is the streamwise spacing of coherent structures in the vertical wind w and L s is a canopy shear length scale) were caused by smaller shear length scales associated with large-scale changes in the terrain as well as the vertical structure of the canopy. The occurrence of linear gravity waves was related to a rise in local topography and can therefore be referred to as mountain-type gravity waves. Temporal scales of wave motion and ramp-like coherent structures were observed to be comparable.

Beyond Fourier.

PubMed

Hoch, Jeffrey C

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.

The New Physical Optics Notebook: Tutorials in Fourier Optics.

ERIC Educational Resources Information Center

Reynolds, George O.; And Others

This is a textbook of Fourier optics for the classroom or self-study. Major topics included in the 38 chapters are: Huygens' principle and Fourier transforms; image formation; optical coherence theory; coherent imaging; image analysis; coherent noise; interferometry; holography; communication theory techniques; analog optical computing; phase…

Quantitative design of emergency monitoring network for river chemical spills based on discrete entropy theory.

PubMed

Shi, Bin; Jiang, Jiping; Sivakumar, Bellie; Zheng, Yi; Wang, Peng

2018-05-01

Field monitoring strategy is critical for disaster preparedness and watershed emergency environmental management. However, development of such is also highly challenging. Despite the efforts and progress thus far, no definitive guidelines or solutions are available worldwide for quantitatively designing a monitoring network in response to river chemical spill incidents, except general rules based on administrative divisions or arbitrary interpolation on routine monitoring sections. To address this gap, a novel framework for spatial-temporal network design was proposed in this study. The framework combines contaminant transport modelling with discrete entropy theory and spectral analysis. The water quality model was applied to forecast the spatio-temporal distribution of contaminant after spills and then corresponding information transfer indexes (ITIs) and Fourier approximation periodic functions were estimated as critical measures for setting sampling locations and times. The results indicate that the framework can produce scientific preparedness plans of emergency monitoring based on scenario analysis of spill risks as well as rapid design as soon as the incident happened but not prepared. The framework was applied to a hypothetical spill case based on tracer experiment and a real nitrobenzene spill incident case to demonstrate its suitability and effectiveness. The newly-designed temporal-spatial monitoring network captured major pollution information at relatively low costs. It showed obvious benefits for follow-up early-warning and treatment as well as for aftermath recovery and assessment. The underlying drivers of ITIs as well as the limitations and uncertainty of the approach were analyzed based on the case studies. Comparison with existing monitoring network design approaches, management implications, and generalized applicability were also discussed. Copyright © 2018 Elsevier Ltd. All rights reserved.

Full Waveform Modeling of Transient Electromagnetic Response Based on Temporal Interpolation and Convolution Method

NASA Astrophysics Data System (ADS)

Qi, Youzheng; Huang, Ling; Wu, Xin; Zhu, Wanhua; Fang, Guangyou; Yu, Gang

2017-07-01

Quantitative modeling of the transient electromagnetic (TEM) response requires consideration of the full transmitter waveform, i.e., not only the specific current waveform in a half cycle but also the bipolar repetition. In this paper, we present a novel temporal interpolation and convolution (TIC) method to facilitate the accurate TEM modeling. We first calculate the temporal basis response on a logarithmic scale using the fast digital-filter-based methods. Then, we introduce a function named hamlogsinc in the framework of discrete signal processing theory to reconstruct the basis function and to make the convolution with the positive half of the waveform. Finally, a superposition procedure is used to take account of the effect of previous bipolar waveforms. Comparisons with the established fast Fourier transform method demonstrate that our TIC method can get the same accuracy with a shorter computing time.

A Quantitative Approach to Scar Analysis

PubMed Central

Khorasani, Hooman; Zheng, Zhong; Nguyen, Calvin; Zara, Janette; Zhang, Xinli; Wang, Joyce; Ting, Kang; Soo, Chia

2011-01-01

Analysis of collagen architecture is essential to wound healing research. However, to date no consistent methodologies exist for quantitatively assessing dermal collagen architecture in scars. In this study, we developed a standardized approach for quantitative analysis of scar collagen morphology by confocal microscopy using fractal dimension and lacunarity analysis. Full-thickness wounds were created on adult mice, closed by primary intention, and harvested at 14 days after wounding for morphometrics and standard Fourier transform-based scar analysis as well as fractal dimension and lacunarity analysis. In addition, transmission electron microscopy was used to evaluate collagen ultrastructure. We demonstrated that fractal dimension and lacunarity analysis were superior to Fourier transform analysis in discriminating scar versus unwounded tissue in a wild-type mouse model. To fully test the robustness of this scar analysis approach, a fibromodulin-null mouse model that heals with increased scar was also used. Fractal dimension and lacunarity analysis effectively discriminated unwounded fibromodulin-null versus wild-type skin as well as healing fibromodulin-null versus wild-type wounds, whereas Fourier transform analysis failed to do so. Furthermore, fractal dimension and lacunarity data also correlated well with transmission electron microscopy collagen ultrastructure analysis, adding to their validity. These results demonstrate that fractal dimension and lacunarity are more sensitive than Fourier transform analysis for quantification of scar morphology. PMID:21281794

Inviscid linear stability analysis of two fluid columns of different densities subject to gravity

NASA Astrophysics Data System (ADS)

Prathama, Aditya; Pantano, Carlos

2017-11-01

We investigate the inviscid linear stability of vertical interface between two fluid columns of different densities under the influence of gravity. In this flow arrangement, the two free streams are continuously accelerating, in contrast to the canonical Kelvin-Helmholtz or Rayleigh-Taylor instabilities whose base flows are stationary (or weakly time dependent). In these classical cases, the temporal evolution of the interface can be expressed as Fourier or Laplace solutions in time. This is not possible in our case; instead, we employ the initial value problem method to solve the equations analytically. The results, expressed in terms of the well-known parabolic cylinder function, indicate that the instability grows as the exponential of a quadratic function of time. The analysis shows that in this accelerating Kelvin-Helmholtz configuration, the interface is unconditionally unstable at all wave modes, despite the presence of surface tension. Department of Energy, National Nuclear Security Administration (Award No. DE-NA0002382) and the California Institute of Technology.

Discrimination among populations of sockeye salmon fry with Fourier analysis of otolith banding patterns formed during incubation

USGS Publications Warehouse

Finn, James E.; Burger, Carl V.; Holland-Bartels, Leslie E.

1997-01-01

We used otolith banding patterns formed during incubation to discriminate among hatchery- and wild-incubated fry of sockeye salmon Oncorhynchus nerka from Tustumena Lake, Alaska. Fourier analysis of otolith luminance profiles was used to describe banding patterns: the amplitudes of individual Fourier harmonics were discriminant variables. Correct classification of otoliths to either hatchery or wild origin was 83.1% (cross-validation) and 72.7% (test data) with the use of quadratic discriminant function analysts on 10 Fourier amplitudes. Overall classification rates among the six test groups (one hatchery and five wild groups) were 46.5% (cross-validation) and 39.3% (test data) with the use of linear discriminant function analysis on 16 Fourier amplitudes. Although classification rates for wild-incubated fry from any one site never exceeded 67% (cross-validation) or 60% (test data), location-specific information was evident for all groups because the probability of classifying an individual to its true incubation location was significantly greater than chance. Results indicate phenotypic differences in otolith microstructure among incubation sites separated by less than 10 km. Analysis of otolith luminance profiles is a potentially useful technique for discriminating among and between various populations of hatchery and wild fish.

Combined Characterization of the Time Response of Impression Materials via Traditional and FTIR Measurements

PubMed Central

Derchi, Giacomo; Manca, Enrico; Shayganpour, Amirreza; Barone, Antonio; Diaspro, Alberto; Salerno, Marco

2015-01-01

We investigated the temporal response of four dental impression materials, namely three siloxanes (Imprint 4, Flexitime, Aquasil) and one polyether (Impregum). The null hypothesis was that the nominal working times are confirmed by instrumental laboratory tests. We also aimed to identify alternative techniques with strong physical-chemical background for the assessment of temporal response. Traditional characterization was carried out by shark fin test device and durometer at both ambient and body temperature. Additionally, Fourier-transform infrared spectroscopy was performed at room temperature. From shark fin height and Shore hardness versus time the working time and the setting time of the materials were evaluated, respectively. These were in reasonable agreement with the nominal values, except for Impregum, which showed longer working time. Spectroscopy confirmed the different character of the two types of materials, and provided for Imprint 4 and Aquasil an independent evaluation of both evolution times, consistent with the results of the other techniques. Shark fin test and durometer measurements showed deviations in setting time, low sensitivity to temperature for Flexitime, and longer working time at higher temperature for Impregum. Deviations of working time appear in operating conditions from what specified by the manufacturers. Fourier-transform infrared spectroscopy can provide insight in the correlation between material properties and their composition and structure.

Turbulence excited frequency domain damping measurement and truncation effects

NASA Technical Reports Server (NTRS)

Soovere, J.

1976-01-01

Existing frequency domain modal frequency and damping analysis methods are discussed. The effects of truncation in the Laplace and Fourier transform data analysis methods are described. Methods for eliminating truncation errors from measured damping are presented. Implications of truncation effects in fast Fourier transform analysis are discussed. Limited comparison with test data is presented.

An Investigation into the Use of Spatially-Filtered Fourier Transforms to Classify Mammary Lesions.

DTIC Science & Technology

difference in Fourier space between lesioned breast tissue which would enable accurate computer classification of benign and malignant lesions. Low...separate benign and malignant breast tissue. However, no success was achieved when using two-dimensional Fourier transform and power spectrum analysis. (Author)

An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

Tomography: Three Dimensional Image Construction. Applications of Analysis to Medical Radiology. [and] Genetic Counseling. Applications of Probability to Medicine. [and] The Design of Honeycombs. Applications of Differential Equations to Biology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 318, 456, 502.

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Asymmetry of perceived key movement in chorale sequences: converging evidence from a probe-tone analysis.

PubMed

Cuddy, L L; Thompson, W F

1992-01-01

In a probe-tone experiment, two groups of listeners--one trained, the other untrained, in traditional music theory--rated the goodness of fit of each of the 12 notes of the chromatic scale to four-voice harmonic sequences. Sequences were 12 simplified excerpts from Bach chorales, 4 nonmodulating, and 8 modulating. Modulations occurred either one or two steps in either the clockwise or the counterclockwise direction on the cycle of fifths. A consistent pattern of probe-tone ratings was obtained for each sequence, with no significant differences between listener groups. Two methods of analysis (Fourier analysis and regression analysis) revealed a directional asymmetry in the perceived key movement conveyed by modulating sequences. For a given modulation distance, modulations in the counterclockwise direction effected a clearer shift in tonal organization toward the final key than did clockwise modulations. The nature of the directional asymmetry was consistent with results reported for identification and rating of key change in the sequences (Thompson & Cuddy, 1989a). Further, according to the multiple-regression analysis, probe-tone ratings did not merely reflect the distribution of tones in the sequence. Rather, ratings were sensitive to the temporal structure of the tonal organization in the sequence.

Performance of the Wavelet Decomposition on Massively Parallel Architectures

NASA Technical Reports Server (NTRS)

El-Ghazawi, Tarek A.; LeMoigne, Jacqueline; Zukor, Dorothy (Technical Monitor)

2001-01-01

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

Temporal diagnostic analysis of the SWAT model to detect dominant periods of poor model performance

NASA Astrophysics Data System (ADS)

Guse, Björn; Reusser, Dominik E.; Fohrer, Nicola

2013-04-01

Hydrological models generally include thresholds and non-linearities, such as snow-rain-temperature thresholds, non-linear reservoirs, infiltration thresholds and the like. When relating observed variables to modelling results, formal methods often calculate performance metrics over long periods, reporting model performance with only few numbers. Such approaches are not well suited to compare dominating processes between reality and model and to better understand when thresholds and non-linearities are driving model results. We present a combination of two temporally resolved model diagnostic tools to answer when a model is performing (not so) well and what the dominant processes are during these periods. We look at the temporal dynamics of parameter sensitivities and model performance to answer this question. For this, the eco-hydrological SWAT model is applied in the Treene lowland catchment in Northern Germany. As a first step, temporal dynamics of parameter sensitivities are analyzed using the Fourier Amplitude Sensitivity test (FAST). The sensitivities of the eight model parameters investigated show strong temporal variations. High sensitivities were detected for two groundwater (GW_DELAY, ALPHA_BF) and one evaporation parameters (ESCO) most of the time. The periods of high parameter sensitivity can be related to different phases of the hydrograph with dominances of the groundwater parameters in the recession phases and of ESCO in baseflow and resaturation periods. Surface runoff parameters show high parameter sensitivities in phases of a precipitation event in combination with high soil water contents. The dominant parameters give indication for the controlling processes during a given period for the hydrological catchment. The second step included the temporal analysis of model performance. For each time step, model performance was characterized with a "finger print" consisting of a large set of performance measures. These finger prints were clustered into four reoccurring patterns of typical model performance, which can be related to different phases of the hydrograph. Overall, the baseflow cluster has the lowest performance. By combining the periods with poor model performance with the dominant model components during these phases, the groundwater module was detected as the model part with the highest potential for model improvements. The detection of dominant processes in periods of poor model performance enhances the understanding of the SWAT model. Based on this, concepts how to improve the SWAT model structure for the application in German lowland catchment are derived.

Absolute Measurement of Tilts via Fourier Analysis of Interferograms

NASA Technical Reports Server (NTRS)

Toland, Ronald W.

2004-01-01

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the inteferogram to serve as a 'carrier signal' for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

Absolute Measurement of Tilts via Fourier Analysis of Interferograms

NASA Technical Reports Server (NTRS)

Toland, Ronald W.

2004-01-01

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the interferogram to serve as a carrier signal for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

First measurements of continuous δ18O-CO2 with a Fourier Transform InfraRed spectrometer in Heidelberg, Germany

NASA Astrophysics Data System (ADS)

Vardag, S. N.; Hammer, S.; Sabasch, M.; Griffith, D. W. T.; Levin, I.

2014-07-01

The continuous in-situ measurement of δ18O in atmospheric CO2 opens a new door to differentiating between CO2 source and sink components with high temporal resolution. Continuous 13C-CO2 measurement systems have been commercially available already for some time, but until now, only few instruments have been able to provide a continuous measurement of the oxygen isotope ratio in CO2. Besides precise 13C/12C observations, the Fourier Transform InfraRed (FTIR) spectrometer also measures the 18O/16O ratio of CO2, but the precision and accuracy of the measurements has not been evaluated yet. Here we present a first analysis of δ18O-CO2 (and δ13C-CO2) measurements with the FTIR in Heidelberg. We find that our spectrometer measures 18O in CO2 with a reproducibility of better than 0.3‰ at a temporal resolution of less than 10 min, as determined from surveillance gas measurements over a period of ten months. An Allan deviation test shows that the δ18O repeatability reaches 0.15‰ for half-hourly means. The compatibility of our spectroscopic measurements was determined by comparing FTIR measurements of calibration gases and ambient air to mass-spectrometric measurements of flask samples, filled with the cylinder gases or episodically collected over a diurnal cycle (event). We found that direct cylinder gas measurements agree to 0.01 ± 0.04‰ (mean and standard deviation) for δ13C-CO2 and 0.01 ± 0.11‰ for δ18O. Two weekly episodes of recent ambient air measurements, one in winter and one in summer, are discussed in view of the question, which potential insights and new challenges combined highly resolved δ18O-CO2 and δ13C-CO2 records may provide in terms of better understanding regional scale continental carbon exchange processes.

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

NASA Astrophysics Data System (ADS)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

Temporal resolution of orientation-defined texture segregation: a VEP study.

PubMed

Lachapelle, Julie; McKerral, Michelle; Jauffret, Colin; Bach, Michael

2008-09-01

Orientation is one of the visual dimensions that subserve figure-ground discrimination. A spatial gradient in orientation leads to "texture segregation", which is thought to be concurrent parallel processing across the visual field, without scanning. In the visual-evoked potential (VEP) a component can be isolated which is related to texture segregation ("tsVEP"). Our objective was to evaluate the temporal frequency dependence of the tsVEP to compare processing speed of low-level features (e.g., orientation, using the VEP, here denoted llVEP) with texture segregation because of a recent literature controversy in that regard. Visual-evoked potentials (VEPs) were recorded in seven normal adults. Oriented line segments of 0.1 degrees x 0.8 degrees at 100% contrast were presented in four different arrangements: either oriented in parallel for two homogeneous stimuli (from which were obtained the low-level VEP (llVEP)) or with a 90 degrees orientation gradient for two textured ones (from which were obtained the texture VEP). The orientation texture condition was presented at eight different temporal frequencies ranging from 7.5 to 45 Hz. Fourier analysis was used to isolate low-level components at the pattern-change frequency and texture-segregation components at half that frequency. For all subjects, there was lower high-cutoff frequency for tsVEP than for llVEPs, on average 12 Hz vs. 17 Hz (P = 0.017). The results suggest that the processing of feature gradients to extract texture segregation requires additional processing time, resulting in a lower fusion frequency.

Periodic trim solutions with hp-version finite elements in time

NASA Technical Reports Server (NTRS)

Peters, David A.; Hou, Lin-Jun

1990-01-01

Finite elements in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time finite elements in which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.

Automated classification of LV regional wall motion based on spatio-temporal profiles from cardiac cine magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Mantilla, Juan; Garreau, Mireille; Bellanger, Jean-Jacques; Paredes, José Luis

2013-11-01

Assessment of the cardiac Left Ventricle (LV) wall motion is generally based on visual inspection or quantitative analysis of 2D+t sequences acquired in short-axis cardiac cine-Magnetic Resonance Imaging (MRI). Most often, cardiac dynamic is globally analized from two particular phases of the cardiac cycle. In this paper, we propose an automated method to classify regional wall motion in LV function based on spatio-temporal pro les and Support Vector Machines (SVM). This approach allows to obtain a binary classi cation between normal and abnormal motion, without the need of pre-processing and by exploiting all the images of the cardiac cycle. In each short- axis MRI slice level (basal, median, and apical), the spatio-temporal pro les are extracted from the selection of a subset of diametrical lines crossing opposites LV segments. Initialized at end-diastole phase, the pro les are concatenated with their corresponding projections into the succesive temporal phases of the cardiac cycle. These pro les are associated to di erent types of information that derive from the image (gray levels), Fourier, Wavelet or Curvelet domains. The approach has been tested on a set of 14 abnormal and 6 healthy patients by using a leave-one-out cross validation and two kernel functions for SVM classi er. The best classi cation performance is yielded by using four-level db4 wavelet transform and SVM with a linear kernel. At each slice level the results provided a classi cation rate of 87.14% in apical level, 95.48% in median level and 93.65% in basal level.

Fused off-axis object illumination direct-to-digital holography with a plurality of illumination sources

DOEpatents

Price, Jeffery R.; Bingham, Philip R.

2005-11-08

Systems and methods are described for rapid acquisition of fused off-axis illumination direct-to-digital holography. A method of recording a plurality of off-axis object illuminated spatially heterodyne holograms, each of the off-axis object illuminated spatially heterodyne holograms including spatially heterodyne fringes for Fourier analysis, includes digitally recording, with a first illumination source of an interferometer, a first off-axis object illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; and digitally recording, with a second illumination source of the interferometer, a second off-axis object illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis.

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

PubMed

Takeda, Mitsuo

2013-01-01

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Water Vapor in the Middle Atmosphere of Venus from the Data of the Venera-15 IR Fourier Spectrometer

NASA Astrophysics Data System (ADS)

Ignat'ev, N. I.; Moroz, V. I.; Zasova, L. V.; Khatuntsev, I. V.

In 1983, the Fourier spectrometer experiment onboard Venera-15 returned spectra of IR radiation (6-50 micron) of the Venusian atmosphere which contained information about temperature, aerosols, and minor constituents, including water vapor. The currently available techniques of radiation-transfer modeling and the H2O-abundance reconstruction allowed us to reanalyze these data, and the most recent results of this analysis are presented here. Most of the measurements are in the range 5-15 ppm. Temporal and spatial variations of the water-vapor abundance were measured. The estimates of H2O abundance calculated from the spectra refer to a certain altitude approximately determined by the level where the optical depth tau in the aerosol continuum near the H2O bands region is close to unity. This altitude varies from 62.5 +/- 2 km at low latitudes to 56 +/- 2 km at high altitudes, but the mean measured water-vapor abundance is found to be roughly the same for both areas, about 10 ppm. At low and middle latitudes, the H2O mixing ratio is maximum on the dayside of the planet and minimum on the nightside. Although the direct reconstruction of the H2O vertical profile from the spectra failed, its indirect estimates confirming the decrease of the mixing ratio with altitude were obtained.

Chaotic dynamics of a microswimmer in Poiseuille flow.

PubMed

Chacón, Ricardo

2013-11-01

The chaotic dynamics of pointlike, spherical particles in cylindrical Poiseuille flow is theoretically characterized and numerically confirmed when their own intrinsic swimming velocity undergoes temporal fluctuations around an average value. Two dimensionless ratios associated with the three significant temporal scales of the problem are identified that fully determine the chaos scenario. In particular, small but finite periodic fluctuations of swimming speed result in chaotic or regular motion depending on the position and orientation of the microswimmer with respect to the flow center line. Remarkably, the spatial extension of chaotic microswimmers is found to depend crucially on the fluctuations' period and amplitude and to be highly sensitive to the Fourier spectrum of the fluctuations. This has implications for the design of artificial microswimmers.

Blind Compressed Sensing Enables 3-Dimensional Dynamic Free Breathing Magnetic Resonance Imaging of Lung Volumes and Diaphragm Motion.

PubMed

Bhave, Sampada; Lingala, Sajan Goud; Newell, John D; Nagle, Scott K; Jacob, Mathews

2016-06-01

The objective of this study was to increase the spatial and temporal resolution of dynamic 3-dimensional (3D) magnetic resonance imaging (MRI) of lung volumes and diaphragm motion. To achieve this goal, we evaluate the utility of the proposed blind compressed sensing (BCS) algorithm to recover data from highly undersampled measurements. We evaluated the performance of the BCS scheme to recover dynamic data sets from retrospectively and prospectively undersampled measurements. We also compared its performance against that of view-sharing, the nuclear norm minimization scheme, and the l1 Fourier sparsity regularization scheme. Quantitative experiments were performed on a healthy subject using a fully sampled 2D data set with uniform radial sampling, which was retrospectively undersampled with 16 radial spokes per frame to correspond to an undersampling factor of 8. The images obtained from the 4 reconstruction schemes were compared with the fully sampled data using mean square error and normalized high-frequency error metrics. The schemes were also compared using prospective 3D data acquired on a Siemens 3 T TIM TRIO MRI scanner on 8 healthy subjects during free breathing. Two expert cardiothoracic radiologists (R1 and R2) qualitatively evaluated the reconstructed 3D data sets using a 5-point scale (0-4) on the basis of spatial resolution, temporal resolution, and presence of aliasing artifacts. The BCS scheme gives better reconstructions (mean square error = 0.0232 and normalized high frequency = 0.133) than the other schemes in the 2D retrospective undersampling experiments, producing minimally distorted reconstructions up to an acceleration factor of 8 (16 radial spokes per frame). The prospective 3D experiments show that the BCS scheme provides visually improved reconstructions than the other schemes do. The BCS scheme provides improved qualitative scores over nuclear norm and l1 Fourier sparsity regularization schemes in the temporal blurring and spatial blurring categories. The qualitative scores for aliasing artifacts in the images reconstructed by nuclear norm scheme and BCS scheme are comparable.The comparisons of the tidal volume changes also show that the BCS scheme has less temporal blurring as compared with the nuclear norm minimization scheme and the l1 Fourier sparsity regularization scheme. The minute ventilation estimated by BCS for tidal breathing in supine position (4 L/min) and the measured supine inspiratory capacity (1.5 L) is in good correlation with the literature. The improved performance of BCS can be explained by its ability to efficiently adapt to the data, thus providing a richer representation of the signal. The feasibility of the BCS scheme was demonstrated for dynamic 3D free breathing MRI of lung volumes and diaphragm motion. A temporal resolution of ∼500 milliseconds, spatial resolution of 2.7 × 2.7 × 10 mm, with whole lung coverage (16 slices) was achieved using the BCS scheme.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

A wavelet-based technique to predict treatment outcome for Major Depressive Disorder.

PubMed

Mumtaz, Wajid; Xia, Likun; Mohd Yasin, Mohd Azhar; Azhar Ali, Syed Saad; Malik, Aamir Saeed

2017-01-01

Treatment management for Major Depressive Disorder (MDD) has been challenging. However, electroencephalogram (EEG)-based predictions of antidepressant's treatment outcome may help during antidepressant's selection and ultimately improve the quality of life for MDD patients. In this study, a machine learning (ML) method involving pretreatment EEG data was proposed to perform such predictions for Selective Serotonin Reuptake Inhibitor (SSRIs). For this purpose, the acquisition of experimental data involved 34 MDD patients and 30 healthy controls. Consequently, a feature matrix was constructed involving time-frequency decomposition of EEG data based on wavelet transform (WT) analysis, termed as EEG data matrix. However, the resultant EEG data matrix had high dimensionality. Therefore, dimension reduction was performed based on a rank-based feature selection method according to a criterion, i.e., receiver operating characteristic (ROC). As a result, the most significant features were identified and further be utilized during the training and testing of a classification model, i.e., the logistic regression (LR) classifier. Finally, the LR model was validated with 100 iterations of 10-fold cross-validation (10-CV). The classification results were compared with short-time Fourier transform (STFT) analysis, and empirical mode decompositions (EMD). The wavelet features extracted from frontal and temporal EEG data were found statistically significant. In comparison with other time-frequency approaches such as the STFT and EMD, the WT analysis has shown highest classification accuracy, i.e., accuracy = 87.5%, sensitivity = 95%, and specificity = 80%. In conclusion, significant wavelet coefficients extracted from frontal and temporal pre-treatment EEG data involving delta and theta frequency bands may predict antidepressant's treatment outcome for the MDD patients.

Fourier Analysis and the Rhythm of Conversation.

ERIC Educational Resources Information Center

Dabbs, James M., Jr.

Fourier analysis, a common technique in engineering, breaks down a complex wave form into its simple sine wave components. Communication researchers have recently suggested that this technique may provide an index of the rhythm of conversation, since vocalizing and pausing produce a complex wave form pattern of alternation between two speakers. To…

A statistical evaluation of spectral fingerprinting methods using analysis of variance and principal component analysis

USDA-ARS?s Scientific Manuscript database

Six methods were compared with respect to spectral fingerprinting of a well-characterized series of broccoli samples. Spectral fingerprints were acquired for finely-powdered solid samples using Fourier transform-infrared (IR) and Fourier transform-near infrared (NIR) spectrometry and for aqueous met...

Introduction to Flight Test Engineering (Introduction aux techniques des essais en vol)

DTIC Science & Technology

2005-07-01

or aircraft parameters • Calculations in the frequency domain ( Fast Fourier Transform) • Data analysis with dedicated software for: • Signal...density Fast Fourier Transform Transfer function analysis Frequency response analysis Etc. PRESENTATION Color/black & white Display screen...envelope by operating the airplane at increasing ranges - representing increasing risk - of engine operation, airspeeds both fast and slow, altitude

Signal-to-noise ratio comparison of encoding methods for hyperpolarized noble gas MRI

NASA Technical Reports Server (NTRS)

Zhao, L.; Venkatesh, A. K.; Albert, M. S.; Panych, L. P.

2001-01-01

Some non-Fourier encoding methods such as wavelet and direct encoding use spatially localized bases. The spatial localization feature of these methods enables optimized encoding for improved spatial and temporal resolution during dynamically adaptive MR imaging. These spatially localized bases, however, have inherently reduced image signal-to-noise ratio compared with Fourier or Hadamad encoding for proton imaging. Hyperpolarized noble gases, on the other hand, have quite different MR properties compared to proton, primarily the nonrenewability of the signal. It could be expected, therefore, that the characteristics of image SNR with respect to encoding method will also be very different from hyperpolarized noble gas MRI compared to proton MRI. In this article, hyperpolarized noble gas image SNRs of different encoding methods are compared theoretically using a matrix description of the encoding process. It is shown that image SNR for hyperpolarized noble gas imaging is maximized for any orthonormal encoding method. Methods are then proposed for designing RF pulses to achieve normalized encoding profiles using Fourier, Hadamard, wavelet, and direct encoding methods for hyperpolarized noble gases. Theoretical results are confirmed with hyperpolarized noble gas MRI experiments. Copyright 2001 Academic Press.

Encoding of a spectrally-complex communication sound in the bullfrog's auditory nerve.

PubMed

Schwartz, J J; Simmons, A M

1990-02-01

1. A population study of eighth nerve responses in the bullfrog, Rana catesbeiana, was undertaken to analyze how the eighth nerve codes the complex spectral and temporal structure of the species-specific advertisement call over a biologically-realistic range of intensities. Synthetic advertisement calls were generated by Fourier synthesis and presented to individual eighth nerve fibers of anesthetized bullfrogs. Fiber responses were analyzed by calculating rate responses based on post-stimulus-time (PST) histograms and temporal responses based on Fourier transforms of period histograms. 2. At stimulus intensities of 70 and 80 dB SPL, normalized rate responses provide a fairly good representation of the complex spectral structure of the stimulus, particularly in the low- and mid-frequency range. At higher intensities, rate responses saturate, and very little of the spectral structure of the complex stimulus can be seen in the profile of rate responses of the population. 3. Both AP and BP fibers phase-lock strongly to the fundamental (100 Hz) of the complex stimulus. These effects are relatively resistant to changes in stimulus intensity. Only a small number of fibers synchronize to the low-frequency spectral energy in the stimulus. The underlying spectral complexity of the stimulus is not accurately reflected in the timing of fiber firing, presumably because firing is 'captured' by the fundamental frequency. 4. Plots of average localized synchronized rate (ALSR), which combine both spectral and temporal information, show a similar, low-pass shape at all stimulus intensities. ALSR plots do not generally provide an accurate representation of the structure of the advertisement call. 5. The data suggest that anuran peripheral auditory fibers may be particularly sensitive to the amplitude envelope of sounds.

Autoregressive modeling for the spectral analysis of oceanographic data

NASA Technical Reports Server (NTRS)

Gangopadhyay, Avijit; Cornillon, Peter; Jackson, Leland B.

1989-01-01

Over the last decade there has been a dramatic increase in the number and volume of data sets useful for oceanographic studies. Many of these data sets consist of long temporal or spatial series derived from satellites and large-scale oceanographic experiments. These data sets are, however, often 'gappy' in space, irregular in time, and always of finite length. The conventional Fourier transform (FT) approach to the spectral analysis is thus often inapplicable, or where applicable, it provides questionable results. Here, through comparative analysis with the FT for different oceanographic data sets, the possibilities offered by autoregressive (AR) modeling to perform spectral analysis of gappy, finite-length series, are discussed. The applications demonstrate that as the length of the time series becomes shorter, the resolving power of the AR approach as compared with that of the FT improves. For the longest data sets examined here, 98 points, the AR method performed only slightly better than the FT, but for the very short ones, 17 points, the AR method showed a dramatic improvement over the FT. The application of the AR method to a gappy time series, although a secondary concern of this manuscript, further underlines the value of this approach.

Development of Michelson interferometer based spatial phase-shift digital shearography

NASA Astrophysics Data System (ADS)

Xie, Xin

Digital shearography is a non-contact, full field, optical measurement method, which has the capability of directly measuring the gradient of deformation. For high measurement sensitivity, phase evaluation method has to be introduced into digital shearography by phase-shift technique. Catalog by phase-shift method, digital phase-shift shearography can be divided into Temporal Phase-Shift Digital Shearography (TPS-DS) and Spatial Phase-Shift Digital Shearography (SPS-DS). TPS-DS is the most widely used phase-shift shearography system, due to its simple algorithm, easy operation and good phase-map quality. However, the application of TPS-DS is only limited in static/step-by-step loading measurement situation, due to its multi-step shifting process. In order to measure the strain under dynamic/continuous loading situation, a SPS-DS system has to be developed. This dissertation aims to develop a series of Michelson Interferometer based SPS-DS measurement methods to achieve the strain measurement by using only a single pair of speckle pattern images. The Michelson Interferometer based SPS-DS systems utilize special designed optical setup to introduce extra carrier frequency into the laser wavefront. The phase information corresponds to the strain field can be separated on the Fourier domain using a Fourier Transform and can further be evaluated with a Windowed Inverse Fourier Transform. With different optical setups and carrier frequency arrangements, the Michelson Interferometer based SPS-DS method is capable to achieve a variety of measurement tasks using only single pair of speckle pattern images. Catalog by the aimed measurand, these capable measurement tasks can be divided into five categories: 1) measurement of out-of-plane strain field with small shearing amount; 2) measurement of relative out-of-plane deformation field with big shearing amount; 3) simultaneous measurement of relative out-of-plane deformation field and deformation gradient field by using multiple carrier frequencies; 4) simultaneous measurement of two directional strain field using dual measurement channels 5) measurement of pure in-plane strain and pure out-of-plane strain with multiple carrier frequencies. The basic theory, optical path analysis, preliminary studies, results analysis and research plan are shown in detail in this dissertation.

Noise Gating Solar Images

NASA Astrophysics Data System (ADS)

DeForest, Craig; Seaton, Daniel B.; Darnell, John A.

2017-08-01

I present and demonstrate a new, general purpose post-processing technique, "3D noise gating", that can reduce image noise by an order of magnitude or more without effective loss of spatial or temporal resolution in typical solar applications.Nearly all scientific images are, ultimately, limited by noise. Noise can be direct Poisson "shot noise" from photon counting effects, or introduced by other means such as detector read noise. Noise is typically represented as a random variable (perhaps with location- or image-dependent characteristics) that is sampled once per pixel or once per resolution element of an image sequence. Noise limits many aspects of image analysis, including photometry, spatiotemporal resolution, feature identification, morphology extraction, and background modeling and separation.Identifying and separating noise from image signal is difficult. The common practice of blurring in space and/or time works because most image "signal" is concentrated in the low Fourier components of an image, while noise is evenly distributed. Blurring in space and/or time attenuates the high spatial and temporal frequencies, reducing noise at the expense of also attenuating image detail. Noise-gating exploits the same property -- "coherence" -- that we use to identify features in images, to separate image features from noise.Processing image sequences through 3-D noise gating results in spectacular (more than 10x) improvements in signal-to-noise ratio, while not blurring bright, resolved features in either space or time. This improves most types of image analysis, including feature identification, time sequence extraction, absolute and relative photometry (including differential emission measure analysis), feature tracking, computer vision, correlation tracking, background modeling, cross-scale analysis, visual display/presentation, and image compression.I will introduce noise gating, describe the method, and show examples from several instruments (including SDO/AIA , SDO/HMI, STEREO/SECCHI, and GOES-R/SUVI) that explore the benefits and limits of the technique.

Do's and don'ts in Fourier analysis of steady-state potentials.

PubMed

Bach, M; Meigen, T

1999-01-01

Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically: * In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so 'windowing' and calculation of the 'periodogram' are not necessary. * It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator. * The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods. * The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number 'spills' noise into the response frequency. * There is no need to feel tied to a power-of-two number of data points as required by standard FFT, 'resampling' is an easy and efficient alternative. * Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise. These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.

Faster processing of multiple spatially-heterodyned direct to digital holograms

DOEpatents

Hanson, Gregory R.; Bingham, Philip R.

2006-10-03

Systems and methods are described for faster processing of multiple spatially-heterodyned direct to digital holograms. A method includes of obtaining multiple spatially-heterodyned holograms, includes: digitally recording a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; digitally recording a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a first angle between a first reference beam and a first, object beam; applying a first digital filter to cut off signals around the first original origin and performing an inverse Fourier transform on the result; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a second angle between a second reference beam and a second object beam; and applying a second digital filter to cut off signals around the second original origin and performing an inverse Fourier transform on the result, wherein digitally recording the first spatially-heterodyned hologram is completed before digitally recording the second spatially-heterodyned hologram and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Faster processing of multiple spatially-heterodyned direct to digital holograms

DOEpatents

Hanson, Gregory R [Clinton, TN; Bingham, Philip R [Knoxville, TN

2008-09-09

Systems and methods are described for faster processing of multiple spatially-heterodyned direct to digital holograms. A method includes of obtaining multiple spatially-heterodyned holograms, includes: digitally recording a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; digitally recording a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a first angle between a first reference beam and a first object beam; applying a first digital filter to cut off signals around the first original origin and performing an inverse Fourier transform on the result; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a second angle between a second reference beam and a second object beam; and applying a second digital filter to cut off signals around the second original origin and performing an inverse Fourier transform on the result, wherein digitally recording the first spatially-heterodyned hologram is completed before digitally recording the second spatially-heterodyned hologram and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Interferogram conditioning for improved Fourier analysis and application to X-ray phase imaging by grating interferometry.

PubMed

Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme

2015-11-02

An interferogram conditioning procedure, for subsequent phase retrieval by Fourier demodulation, is presented here as a fast iterative approach aiming at fulfilling the classical boundary conditions imposed by Fourier transform techniques. Interference fringe patterns with typical edge discontinuities were simulated in order to reveal the edge artifacts that classically appear in traditional Fourier analysis, and were consecutively used to demonstrate the correction efficiency of the proposed conditioning technique. Optimization of the algorithm parameters is also presented and discussed. Finally, the procedure was applied to grating-based interferometric measurements performed in the hard X-ray regime. The proposed algorithm enables nearly edge-artifact-free retrieval of the phase derivatives. A similar enhancement of the retrieved absorption and fringe visibility images is also achieved.

The Fourier analysis applied to the relationship between (7)Be activity in the Serbian atmosphere and meteorological parameters.

PubMed

Rajačić, M M; Todorović, D J; Krneta Nikolić, J D; Janković, M M; Djurdjević, V S

2016-09-01

Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

Random Positions of Dendritic Spines in Human Cerebral Cortex

PubMed Central

Morales, Juan; Benavides-Piccione, Ruth; Dar, Mor; Fernaud, Isabel; Rodríguez, Angel; Anton-Sanchez, Laura; Bielza, Concha; Larrañaga, Pedro; DeFelipe, Javier

2014-01-01

Dendritic spines establish most excitatory synapses in the brain and are located in Purkinje cell's dendrites along helical paths, perhaps maximizing the probability to contact different axons. To test whether spine helixes also occur in neocortex, we reconstructed >500 dendritic segments from adult human cortex obtained from autopsies. With Fourier analysis and spatial statistics, we analyzed spine position along apical and basal dendrites of layer 3 pyramidal neurons from frontal, temporal, and cingulate cortex. Although we occasionally detected helical positioning, for the great majority of dendrites we could not reject the null hypothesis of spatial randomness in spine locations, either in apical or basal dendrites, in neurons of different cortical areas or among spines of different volumes and lengths. We conclude that in adult human neocortex spine positions are mostly random. We discuss the relevance of these results for spine formation and plasticity and their functional impact for cortical circuits. PMID:25057209

From Mars to Greenland: Charting gravity with space and airborne instruments - Fields, tides, methods, results

NASA Technical Reports Server (NTRS)

Colombo, Oscar L. (Editor)

1992-01-01

This symposium on space and airborne techniques for measuring gravity fields, and related theory, contains papers on gravity modeling of Mars and Venus at NASA/GSFC, an integrated laser Doppler method for measuring planetary gravity fields, observed temporal variations in the earth's gravity field from 16-year Starlette orbit analysis, high-resolution gravity models combining terrestrial and satellite data, the effect of water vapor corrections for satellite altimeter measurements of the geoid, and laboratory demonstrations of superconducting gravity and inertial sensors for space and airborne gravity measurements. Other papers are on airborne gravity measurements over the Kelvin Seamount; the accuracy of GPS-derived acceleration from moving platform tests; airborne gravimetry, altimetry, and GPS navigation errors; controlling common mode stabilization errors in airborne gravity gradiometry, GPS/INS gravity measurements in space and on a balloon, and Walsh-Fourier series expansion of the earth's gravitational potential.

Teaching Fourier optics through ray matrices

NASA Astrophysics Data System (ADS)

Moreno, I.; Sánchez-López, M. M.; Ferreira, C.; Davis, J. A.; Mateos, F.

2005-03-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.

Cosine beamforming

NASA Astrophysics Data System (ADS)

Ruigrok, Elmer; Wapenaar, Kees

2014-05-01

In various application areas, e.g., seismology, astronomy and geodesy, arrays of sensors are used to characterize incoming wavefields due to distant sources. Beamforming is a general term for phased-adjusted summations over the different array elements, for untangling the directionality and elevation angle of the incoming waves. For characterizing noise sources, beamforming is conventionally applied with a temporal Fourier and a 2D spatial Fourier transform, possibly with additional weights. These transforms become aliased for higher frequencies and sparser array-element distributions. As a partial remedy, we derive a kernel for beamforming crosscorrelated data and call it cosine beamforming (CBF). By applying beamforming not directly to the data, but to crosscorrelated data, the sampling is effectively increased. We show that CBF, due to this better sampling, suffers less from aliasing and yields higher resolution than conventional beamforming. As a flip-side of the coin, the CBF output shows more smearing for spherical waves than conventional beamforming.

Improving Thin Bed Identification in Sarawak Basin Field using Short Time Fourier Transform Half Cepstrum (STFTHC) method

NASA Astrophysics Data System (ADS)

Nizarul, O.; Hermana, M.; Bashir, Y.; Ghosh, D. P.

2016-02-01

In delineating complex subsurface geological feature, broad band of frequencies are needed to unveil the often hidden features of hydrocarbon basin such as thin bedding. The ability to resolve thin geological horizon on seismic data is recognized to be a fundamental importance for hydrocarbon exploration, seismic interpretation and reserve prediction. For thin bedding, high frequency content is needed to enable tuning, which can be done by applying the band width extension technique. This paper shows an application of Short Time Fourier Transform Half Cepstrum (STFTHC) method, a frequency bandwidth expansion technique for non-stationary seismic signal in increasing the temporal resolution to uncover thin beds and improve characterization of the basin. A wedge model and synthetic seismic data is used to quantify the algorithm as well as real data from Sarawak basin were used to show the effectiveness of this method in enhancing the resolution.

Miniaturized multiple Fourier-horn ultrasonic droplet generators for biomedical applications.

PubMed

Tsai, Chen S; Mao, Rong W; Lin, Shih K; Wang, Ning; Tsai, Shirley C

2010-10-21

Here we report micro-electro-mechanical system (MEMS)-based miniaturized silicon ultrasonic droplet generators of a new and simple nozzle architecture with multiple Fourier horns in resonance but without a central channel. The centimetre-sized nozzles operate at one to two MHz and a single vibration mode which readily facilitates temporal instability of Faraday waves to produce monodisperse droplets. Droplets with diameter range 2.2-4.6 μm are produced at high throughput of 420 μl min(-1) and very low electrical drive power of 80 mW. We also report the first theoretical prediction of the droplet diameter. The resulting MHz ultrasonic devices possess important advantages and demonstrate superior performance over earlier devices with a central channel and thus have high potential for biomedical applications such as efficient and effective delivery of inhaled medications and encapsulated therapy to the lung.

Definition of a metrology servo-system for a solar imaging fourier transform spectrometer working in the far UV (IFTSUV)

NASA Astrophysics Data System (ADS)

Ruiz de Galarreta Fanju, C.; Philippon, A.; Bouzit, M.; Appourchaux, T.; Vial, J.-C.; Maillard, J.-P.; Lemaire, P.

2017-11-01

The understanding of the solar outer atmosphere requires a simultaneous combination of imaging and spectral observations concerning the far UV lines that arise from the high chromospheres up to the corona. These observations must be performed with enough spectral, spatial and temporal resolution to reveal the small atmospheric structures and to resolve the solar dynamics. An Imaging Fourier Transform Spectrometer working in the far-UV (IFTSUV, Figure 1) is an attractive instrumental solution to fulfill these requirements. However, due to the short wavelength, to preserve IFTSUV spectral precision and Signal to Noise Ratio (SNR) requires a high optical surface quality and a very accurate (linear and angular) metrology to maintain the optical path difference (OPD) during the entire scanning process by: optical path difference sampling trigger; and dynamic alignment for tip/tilt compensation (Figure 2).

Spectral analysis for GNSS coordinate time series using chirp Fourier transform

NASA Astrophysics Data System (ADS)

Feng, Shengtao; Bo, Wanju; Ma, Qingzun; Wang, Zifan

2017-12-01

Spectral analysis for global navigation satellite system (GNSS) coordinate time series provides a principal tool to understand the intrinsic mechanism that affects tectonic movements. Spectral analysis methods such as the fast Fourier transform, Lomb-Scargle spectrum, evolutionary power spectrum, wavelet power spectrum, etc. are used to find periodic characteristics in time series. Among spectral analysis methods, the chirp Fourier transform (CFT) with less stringent requirements is tested with synthetic and actual GNSS coordinate time series, which proves the accuracy and efficiency of the method. With the length of series only limited to even numbers, CFT provides a convenient tool for windowed spectral analysis. The results of ideal synthetic data prove CFT accurate and efficient, while the results of actual data show that CFT is usable to derive periodic information from GNSS coordinate time series.

Risk assessment of environmentally influenced airway diseases based on time-series analysis.

PubMed

Herbarth, O

1995-09-01

Threshold values are of prime importance in providing a sound basis for public health decisions. A key issue is determining threshold or maximum exposure values for pollutants and assessing their potential health risks. Environmental epidemiology could be instrumental in assessing these levels, especially since the assessment of ambient exposures involves relatively low concentrations of pollutants. This paper presents a statistical method that allows the determination of threshold values as well as the assessment of the associated risk using a retrospective, longitudinal study design with a prospective follow-up. Morbidity data were analyzed using the Fourier method, a time-series analysis that is based on the assumption of a high temporal resolution of the data. This method eliminates time-dependent responses like temporal inhomogeneity and pseudocorrelation. The frequency of calls for respiratory distress conditions to the regional Mobile Medical Emergency Service (MMES) in the city of Leipzig were investigated. The entire population of Leipzig served as a pool for data collection. In addition to the collection of morbidity data, air pollution measurements were taken every 30 min for the entire study period using sulfur dioxide as the regional indicator variable. This approach allowed the calculation of a dose-response curve for respiratory diseases and air pollution indices in children and adults. Significantly higher morbidities were observed above a 24-hr mean value of 0.6 mg SO2/m3 air for children and 0.8 mg SO2/m3 for adults.(ABSTRACT TRUNCATED AT 250 WORDS)

Spatial and temporal age-related spectral alterations in benign human breast tissue

NASA Astrophysics Data System (ADS)

Theophilou, Georgios; Fogarty, Simon W.; Trevisan, Júlio; Strong, Rebecca J.; Heys, Kelly A.; Patel, Imran I.; Stringfellow, Helen F.; Martin-Hirsch, Pierre L.; Martin, Francis L.

2016-02-01

Epidemiological evidence suggests that cancers attributable to exogenous carcinogenic agents may appear decades after initiating exposures. Environmental factors including lifestyle and/or diet have been implicated in the aetiology of breast cancer. Breast tissue undergoes continuous molecular and morphological changes from the time of thelarche to menopause and thereafter. These alterations are both cyclical and longitudinal, and can be influenced by several environmental factors including exposure to oestrogens. Research into the latent period leading to breast carcinogenesis has been mostly limited to when hyperplastic lesions are present. Investigations to identify a biomarker of commitment to disease in normal breast tissue are hindered by the molecular and histological diversity of disease-free breast tissue. Benign tissue from reduction mammoplasties provides an opportunity to study biochemical differences between women of similar ages as well as alterations with advancing age. Herein, synchrotron radiation-based Fourier-transform infrared (SR-FTIR) microspectroscopy was used to examine the terminal ductal lobular epithelium (TDLU) and, intra- and inter-lobular epithelium to identify spatial and temporal changes within these areas. Principal component analysis (PCA) followed by linear discriminant analysis of mid-infrared spectra revealed unambiguous inter-individual as well as age-related differences in each histological compartment interrogated. Moreover, exploratory PCA of luminal and myoepithelial cells within the TDLU indicated the presence of specific cells, potentially stem cells. Understanding alterations within benign tissue may assist in the identification of alterations in latent pre-clinical stages of breast cancer.

Synthesis, Analysis, and Processing of Fractal Signals

DTIC Science & Technology

1991-10-01

coordinator in hockey, squash, volleyball, and softball, but also for reminding me periodically that 1/f noise can exist outside a computer. More...similar signals as Fourier-based representations are for stationary and periodic signals. Furthermore, because wave- let transformations can be...and periodic signals. Furthermore, just as the discovery of fast Fourier transform (FFT) algorithms dramatically increased the viability the Fourier

Quantitative lung perfusion evaluation using Fourier decomposition perfusion MRI.

PubMed

Kjørstad, Åsmund; Corteville, Dominique M R; Fischer, Andre; Henzler, Thomas; Schmid-Bindert, Gerald; Zöllner, Frank G; Schad, Lothar R

2014-08-01

To quantitatively evaluate lung perfusion using Fourier decomposition perfusion MRI. The Fourier decomposition (FD) method is a noninvasive method for assessing ventilation- and perfusion-related information in the lungs, where the perfusion maps in particular have shown promise for clinical use. However, the perfusion maps are nonquantitative and dimensionless, making follow-ups and direct comparisons between patients difficult. We present an approach to obtain physically meaningful and quantifiable perfusion maps using the FD method. The standard FD perfusion images are quantified by comparing the partially blood-filled pixels in the lung parenchyma with the fully blood-filled pixels in the aorta. The percentage of blood in a pixel is then combined with the temporal information, yielding quantitative blood flow values. The values of 10 healthy volunteers are compared with SEEPAGE measurements which have shown high consistency with dynamic contrast enhanced-MRI. All pulmonary blood flow (PBF) values are within the expected range. The two methods are in good agreement (mean difference = 0.2 mL/min/100 mL, mean absolute difference = 11 mL/min/100 mL, mean PBF-FD = 150 mL/min/100 mL, mean PBF-SEEPAGE = 151 mL/min/100 mL). The Bland-Altman plot shows a good spread of values, indicating no systematic bias between the methods. Quantitative lung perfusion can be obtained using the Fourier Decomposition method combined with a small amount of postprocessing. Copyright © 2013 Wiley Periodicals, Inc.

Interval analysis of interictal EEG: pathology of the alpha rhythm in focal epilepsy

NASA Astrophysics Data System (ADS)

Pyrzowski, Jan; Siemiński, Mariusz; Sarnowska, Anna; Jedrzejczak, Joanna; Nyka, Walenty M.

2015-11-01

The contemporary use of interictal scalp electroencephalography (EEG) in the context of focal epilepsy workup relies on the visual identification of interictal epileptiform discharges. The high-specificity performance of this marker comes, however, at a cost of only moderate sensitivity. Zero-crossing interval analysis is an alternative to Fourier analysis for the assessment of the rhythmic component of EEG signals. We applied this method to standard EEG recordings of 78 patients divided into 4 subgroups: temporal lobe epilepsy (TLE), frontal lobe epilepsy (FLE), psychogenic nonepileptic seizures (PNES) and nonepileptic patients with headache. Interval-analysis based markers were capable of effectively discriminating patients with epilepsy from those in control subgroups (AUC~0.8) with diagnostic sensitivity potentially exceeding that of visual analysis. The identified putative epilepsy-specific markers were sensitive to the properties of the alpha rhythm and displayed weak or non-significant dependences on the number of antiepileptic drugs (AEDs) taken by the patients. Significant AED-related effects were concentrated in the theta interval range and an associated marker allowed for identification of patients on AED polytherapy (AUC~0.9). Interval analysis may thus, in perspective, increase the diagnostic yield of interictal scalp EEG. Our findings point to the possible existence of alpha rhythm abnormalities in patients with epilepsy.

Broadband turbulent spectra in gamma-ray burst light curves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Putten, Maurice H. P. M.; Guidorzi, Cristiano; Frontera, Filippo, E-mail: mvp@sejong.ac.kr

2014-05-10

Broadband power density spectra offer a window to understanding turbulent behavior in the emission mechanism and, at the highest frequencies, in the putative inner engines powering long gamma-ray bursts (GRBs). We describe a chirp search method alongside Fourier analysis for signal detection in the Poisson noise-dominated, 2 kHz sampled, BeppoSAX light curves. An efficient numerical implementation is described in O(Nnlog n) operations, where N is the number of chirp templates and n is the length of the light-curve time series, suited for embarrassingly parallel processing. For the detection of individual chirps over a 1 s duration, the method is onemore » order of magnitude more sensitive in signal-to-noise ratio than Fourier analysis. The Fourier-chirp spectra of GRB 010408 and GRB 970816 show a continuation of the spectral slope with up to 1 kHz of turbulence identified in low-frequency Fourier analysis. The same continuation is observed in an average spectrum of 42 bright, long GRBs. An outlook on a similar analysis of upcoming gravitational wave data is included.« less

Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.

1999-01-01

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

Understanding the Influence of Turbulence in Imaging Fourier-Transform Spectrometry of Smokestack Plumes

DTIC Science & Technology

2011-03-01

capability of FTS to estimate plume effluent concentrations by comparing intrusive measurements of aircraft engine exhaust with those from an FTS. A... turbojet engine. Temporal averaging was used to reduce SCAs in the spectra, and spatial maps of temperature and concentration were generated. The time...density function ( PDF ) is the de- fined as the derivative of the CDF, and describes the probability of obtaining a given value of X. For a normally

Low-Loss and Broadband Metamaterials for Negative Index and Transformational Optics Applications

DTIC Science & Technology

2012-05-22

the temporal electric field, multiplying by ǫ(ω), and then inverse Fourier transforming the result. The quantities ∂wE/∂t and ∂qE/∂t were formed...force occurs in a material with gain. Imaging and antenna opportunities are described for metal-insulator stack lenses, and analytic models are...and Transformational Optics Applications Award Number: W911NF-10-1-0492 Kevin J. Webb School of Electrical and Computer Engineering Purdue University

An Extension of the Time-Spectral Method to Overset Solvers

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas

2013-01-01

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

Compressed sensing reconstruction of cardiac cine MRI using golden angle spiral trajectories

NASA Astrophysics Data System (ADS)

Tolouee, Azar; Alirezaie, Javad; Babyn, Paul

2015-11-01

In dynamic cardiac cine Magnetic Resonance Imaging (MRI), the spatiotemporal resolution is limited by the low imaging speed. Compressed sensing (CS) theory has been applied to improve the imaging speed and thus the spatiotemporal resolution. The purpose of this paper is to improve CS reconstruction of under sampled data by exploiting spatiotemporal sparsity and efficient spiral trajectories. We extend k-t sparse algorithm to spiral trajectories to achieve high spatio temporal resolutions in cardiac cine imaging. We have exploited spatiotemporal sparsity of cardiac cine MRI by applying a 2D + time wavelet-Fourier transform. For efficient coverage of k-space, we have used a modified version of multi shot (interleaved) spirals trajectories. In order to reduce incoherent aliasing artifact, we use different random undersampling pattern for each temporal frame. Finally, we have used nonuniform fast Fourier transform (NUFFT) algorithm to reconstruct the image from the non-uniformly acquired samples. The proposed approach was tested in simulated and cardiac cine MRI data. Results show that higher acceleration factors with improved image quality can be obtained with the proposed approach in comparison to the existing state-of-the-art method. The flexibility of the introduced method should allow it to be used not only for the challenging case of cardiac imaging, but also for other patient motion where the patient moves or breathes during acquisition.

The application and improvement of Fourier transform spectrometer experiment

NASA Astrophysics Data System (ADS)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

Application of Fourier analysis to multispectral/spatial recognition

NASA Technical Reports Server (NTRS)

Hornung, R. J.; Smith, J. A.

1973-01-01

One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

Fourier analysis of human soft tissue facial shape: sex differences in normal adults.

PubMed Central

Ferrario, V F; Sforza, C; Schmitz, J H; Miani, A; Taroni, G

1995-01-01

Sexual dimorphism in human facial form involves both size and shape variations of the soft tissue structures. These variations are conventionally appreciated using linear and angular measurements, as well as ratios, taken from photographs or radiographs. Unfortunately this metric approach provides adequate quantitative information about size only, eluding the problems of shape definition. Mathematical methods such as the Fourier series allow a correct quantitative analysis of shape and of its changes. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed, and applied to analyse sex differences in shape of the soft tissue facial contour in a group of healthy young adults. When standardised for size, no sex differences were found between both cosine and sine coefficients of the Fourier series expansion. This shape similarity was largely overwhelmed by the very evident size differences and it could be measured only using the proper mathematical methods. PMID:8586558

Time-Frequency Approach for Stochastic Signal Detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Ripul; Akula, Aparna; Kumar, Satish

2011-10-20

The detection of events in a stochastic signal has been a subject of great interest. One of the oldest signal processing technique, Fourier Transform of a signal contains information regarding frequency content, but it cannot resolve the exact onset of changes in the frequency, all temporal information is contained in the phase of the transform. On the other hand, Spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Therefore, time-frequency representations are considered for energetic characterisation of the non-stationary signals. Wigner Villemore » Distribution (WVD) is the most prominent quadratic time-frequency signal representation and used for analysing frequency variations in signals.WVD allows for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. This paper through simulations describes the way time frequency models are applied for the detection of event in a stochastic signal.« less

Time-Frequency Approach for Stochastic Signal Detection

NASA Astrophysics Data System (ADS)

Ghosh, Ripul; Akula, Aparna; Kumar, Satish; Sardana, H. K.

2011-10-01

The detection of events in a stochastic signal has been a subject of great interest. One of the oldest signal processing technique, Fourier Transform of a signal contains information regarding frequency content, but it cannot resolve the exact onset of changes in the frequency, all temporal information is contained in the phase of the transform. On the other hand, Spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Therefore, time-frequency representations are considered for energetic characterisation of the non-stationary signals. Wigner Ville Distribution (WVD) is the most prominent quadratic time-frequency signal representation and used for analysing frequency variations in signals.WVD allows for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. This paper through simulations describes the way time frequency models are applied for the detection of event in a stochastic signal.

Time-Distance Helioseismology

NASA Technical Reports Server (NTRS)

Duvall, Thomas L., Jr.

2010-01-01

Time-distance helioseismology is a method of ambient noise imaging using the solar oscillations. The basic realization that led to time-distance helioseismology was that the temporal cross correlation of the signals at two 'surface' (or photospheric) locations should show a feature at the time lag corresponding to the subsurface travel time between the locations. The temporal cross correlation, as a function of the location separation, is the Fourier transform of the spatio-temporal power spectrum of the solar oscillations, a commonly used function in helioseismology. It is therefore likely the characteristic ridge structure of the correlation function had been seen before without appreciation of its significance. Travel times are measured from the cross correlations. The times are sensitive to a number of important subsurface solar phenomena. These include sound speed variations, flows, and magnetic fields. There has been much interesting progress in the 17 years since the first paper on this subject (Duvall et al., Nature, 1993, 362, 430-432). This progress will be reviewed in this paper.

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

PubMed

Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

2017-07-07

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.

Program for the analysis of time series. [by means of fast Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Brown, T. J.; Brown, C. G.; Hardin, J. C.

1974-01-01

A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.

Polarization Ratio Determination with Two Identical Linearly Polarized Antennas

DTIC Science & Technology

2017-01-17

Fourier transform analysis of 21 measurements with one of the antennas rotating about its axis a circular polarization ratio is derived which can be...deter- mined directly from a discrete Fourier transform (DFT) of (5). However, leakage between closely spaced DFT bins requires improving the... Fourier transform and a mechanical antenna rotation to separate the principal and opposite circular polarization components followed by a basis

Fourier Transform Infrared Spectroscopy as a Tool in Analysis of Proteus mirabilis Endotoxins.

PubMed

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

Fourier transform infrared spectroscopy (FT-IR) was used to scan whole bacterial cells as well as lipopolysaccharides (LPSs, endotoxins) isolated from them. Proteus mirabilis cells, with chemically defined LPSs, served as a model for the ATR FT-IR method. The paper focuses on three steps of infrared spectroscopy: (1) sample preparation, (2) IR scanning, and (3) multivariate analysis of IR data (principal component analysis, PCA).

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein-Gordon potentials

DOE PAGES

Baczewski, Andrew David; Vikram, Melapudi; Shanker, Balasubramaniam; ...

2010-08-27

Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(N s 2N t 2), where N s and N t are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The firstmore » scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(N sN tlog 2N t). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.« less

Fourier Analysis of Musical Intervals

ERIC Educational Resources Information Center

LoPresto, Michael C.

2008-01-01

Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…

Automated vessel segmentation using cross-correlation and pooled covariance matrix analysis.

PubMed

Du, Jiang; Karimi, Afshin; Wu, Yijing; Korosec, Frank R; Grist, Thomas M; Mistretta, Charles A

2011-04-01

Time-resolved contrast-enhanced magnetic resonance angiography (CE-MRA) provides contrast dynamics in the vasculature and allows vessel segmentation based on temporal correlation analysis. Here we present an automated vessel segmentation algorithm including automated generation of regions of interest (ROIs), cross-correlation and pooled sample covariance matrix analysis. The dynamic images are divided into multiple equal-sized regions. In each region, ROIs for artery, vein and background are generated using an iterative thresholding algorithm based on the contrast arrival time map and contrast enhancement map. Region-specific multi-feature cross-correlation analysis and pooled covariance matrix analysis are performed to calculate the Mahalanobis distances (MDs), which are used to automatically separate arteries from veins. This segmentation algorithm is applied to a dual-phase dynamic imaging acquisition scheme where low-resolution time-resolved images are acquired during the dynamic phase followed by high-frequency data acquisition at the steady-state phase. The segmented low-resolution arterial and venous images are then combined with the high-frequency data in k-space and inverse Fourier transformed to form the final segmented arterial and venous images. Results from volunteer and patient studies demonstrate the advantages of this automated vessel segmentation and dual phase data acquisition technique. Copyright © 2011 Elsevier Inc. All rights reserved.

Analysis of the Characteristics of Inertia-Gravity Waves during an Orographic Precipitation Event

NASA Astrophysics Data System (ADS)

Liu, Lu; Ran, Lingkun; Gao, Shouting

2018-05-01

A numerical experiment was performed using the Weather Research and Forecasting (WRF) model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichuan area on 17 August 2014. To examine the spatial and temporal structures of the inertia-gravity waves and identify the wave types, three wavenumber-frequency spectral analysis methods (Fourier analysis, cross-spectral analysis, and wavelet cross-spectrum analysis) were applied. During the storm, inertia-gravity waves appeared at heights of 10-14 km, with periods of 80-100 min and wavelengths of 40-50 km. These waves were generated over a mountain and propagated eastward at an average speed of 15-20 m s-1. Meanwhile, comparison between the reconstructed inertia-gravity waves and accumulated precipitation showed there was a mutual promotion process between them. The Richardson number and Scorer parameter were used to demonstrate that the eastward-moving inertia-gravity waves were trapped in an effective atmospheric ducting zone with favorable reflector and critical level conditions, which were the primary causes of the long lives of the waves. Finally, numerical experiments to test the sensitivity to terrain and diabatic heating were conducted, and the results suggested a cooperative effect of terrain and diabatic heating contributed to the propagation and enhancement of the waves.

INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections

NASA Astrophysics Data System (ADS)

Caliari, Marco; Zuccher, Simone

2017-04-01

Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of arbitrary points are quite rare, especially in MATLAB language. Here we employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis, and D. Potts), a C library designed for this purpose, and provide a Matlab® and GNU Octave interface that makes NFFT easily available to the Numerical Analysis community. We test the effectiveness of our package in the framework of quantum vortex reconnections, where pseudospectral Fourier methods are commonly used and local high resolution is required in the post-processing stage. We show that the efficient evaluation of a truncated Fourier series at arbitrary points provides excellent results at a computational cost much smaller than carrying out a numerical simulation of the problem on a sufficiently fine regular grid that can reproduce comparable details of the reconnecting vortices.

Parametric spectro-temporal analyzer (PASTA) for ultrafast optical performance monitoring

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wong, Kenneth K. Y.

2013-12-01

Ultrafast optical spectrum monitoring is one of the most challenging tasks in observing ultrafast phenomena, such as the spectroscopy, dynamic observation of the laser cavity, and spectral encoded imaging systems. However, conventional method such as optical spectrum analyzer (OSA) spatially disperses the spectrum, but the space-to-time mapping is realized by mechanical rotation of a grating, so are incapable of operating at high speed. Besides the spatial dispersion, temporal dispersion provided by dispersive fiber can also stretches the spectrum in time domain in an ultrafast manner, but is primarily confined in measuring short pulses. In view of these constraints, here we present a real-time spectrum analyzer called parametric spectro-temporal analyzer (PASTA), which is based on the time-lens focusing mechanism. It achieves a 100-MHz frame rate and can measure arbitrary waveforms. For the first time, we observe the dynamic spectrum of an ultrafast swept-source: Fourier domain mode-locked (FDML) laser, and the spectrum evolution of a laser cavity during its stabilizing process. In addition to the basic single-lens structure, the multi-lens configurations (e.g. telescope or wide-angle scope) will provide a versatile operating condition, which can zoom in to achieve 0.05-nm resolution and zoom out to achieve 10-nm observation range, namely 17 times zoom in/out ratio. In view of the goal of achieving spectrum analysis with fine accuracy, PASTA provides a promising path to study the real-time spectrum of some dynamic phenomena and non-repetitive events, with orders of magnitude enhancement in the frame rate over conventional OSAs.

Spectral methods for time dependent problems

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1990-01-01

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Heisler, R.

1978-01-01

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Comparison of time-frequency distribution techniques for analysis of spinal somatosensory evoked potential.

PubMed

Hu, Y; Luk, K D; Lu, W W; Holmes, A; Leong, J C

2001-05-01

Spinal somatosensory evoked potential (SSEP) has been employed to monitor the integrity of the spinal cord during surgery. To detect both temporal and spectral changes in SSEP waveforms, an investigation of the application of time-frequency analysis (TFA) techniques was conducted. SSEP signals from 30 scoliosis patients were analysed using different techniques; short time Fourier transform (STFT), Wigner-Ville distribution (WVD), Choi-Williams distribution (CWD), cone-shaped distribution (CSD) and adaptive spectrogram (ADS). The time-frequency distributions (TFD) computed using these methods were assessed and compared with each other. WVD, ADS, CSD and CWD showed better resolution than STFT. Comparing normalised peak widths, CSD showed the sharpest peak width (0.13+/-0.1) in the frequency dimension, and a mean peak width of 0.70+/-0.12 in the time dimension. Both WVD and CWD produced cross-term interference, distorting the TFA distribution, but this was not seen with CSD and ADS. CSD appeared to give a lower mean peak power bias (10.3%+/-6.2%) than ADS (41.8%+/-19.6%). Application of the CSD algorithm showed both good resolution and accurate spectrograms, and is therefore recommended as the most appropriate TFA technique for the analysis of SSEP signals.

Acoustic Observation of the Time Dependence of the Roughness of Sandy Seafloors

DTIC Science & Technology

2009-11-25

relations between acoustic and roughness temporal correlations are developed and applied. Manuscript received April 23, 2007; revised June 04. 2008 and...Fourier transform of the relief function as follows: (F(K2, t2)F*(Klt h)) = W(KU tu t2)6{Ki - K2) . (6) The presence of the Dirac delta function is only...appropriate if /(R, t) is stationary with infinite extent in the spatial coordi- nates. As a result of the windowing assumed here, the delta func

Angular acceptance analysis of an infrared focal plane array with a built-in stationary Fourier transform spectrometer.

PubMed

Gillard, Frédéric; Ferrec, Yann; Guérineau, Nicolas; Rommeluère, Sylvain; Taboury, Jean; Chavel, Pierre

2012-06-01

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis to explain and describe the fringe formation inside the FTIR-FPA structure when illuminated by an extended source positioned at a finite distance from the detection plane. The results are then exploited to propose a simple front lens design compatible with a handheld package.

Radial and temporal variations in surface heat transfer during cryogen spray cooling.

PubMed

Franco, Walfre; Liu, Jie; Wang, Guo-Xiang; Nelson, J Stuart; Aguilar, Guillermo

2005-01-21

Cryogen spray cooling (CSC) is a heat extraction process that protects the epidermis from thermal damage during dermatologic laser surgery. The objective of the present work is to investigate radial and temporal variations in the heat transferred through the surface of a skin phantom during CSC. A fast-response thermal sensor is used to measure surface temperatures every 1 mm across a 16 mm diameter of the sprayed surface of the phantom. An analytical expression based on Fourier's law and Duhamel's theorem is used to compute surface heat fluxes from temperature measurements. Results show that radial and temporal variations of the boundary conditions have a strong influence on the homogeneity of heat extraction from the skin phantom. However, there is a subregion of uniform cooling whose size is time dependent. It is also observed that the surface heat flux undergoes a marked dynamic variation, with a maximum heat flux occurring at the centre of the sprayed surface early in the spurt followed by a quick decrease. The study shows that radial and temporal variations of boundary conditions must be taken into account and ideally controlled to guarantee uniform protection during CSC of human skin.

A new BP Fourier algorithm and its application in English teaching evaluation

NASA Astrophysics Data System (ADS)

Pei, Xuehui; Pei, Guixin

2017-08-01

BP neural network algorithm has wide adaptability and accuracy when used in complicated system evaluation, but its calculation defects such as slow convergence have limited its practical application. The paper tries to speed up the calculation convergence of BP neural network algorithm with Fourier basis functions and presents a new BP Fourier algorithm for complicated system evaluation. First, shortages and working principle of BP algorithm are analyzed for subsequent targeted improvement; Second, the presented BP Fourier algorithm adopts Fourier basis functions to simplify calculation structure, designs new calculation transfer function between input and output layers, and conducts theoretical analysis to prove the efficiency of the presented algorithm; Finally, the presented algorithm is used in evaluating university English teaching and the application results shows that the presented BP Fourier algorithm has better performance in calculation efficiency and evaluation accuracy and can be used in evaluating complicated system practically.

Method of estimating pulse response using an impedance spectrum

DOEpatents

Morrison, John L; Morrison, William H; Christophersen, Jon P; Motloch, Chester G

2014-10-21

Electrochemical Impedance Spectrum data are used to predict pulse performance of an energy storage device. The impedance spectrum may be obtained in-situ. A simulation waveform includes a pulse wave with a period greater than or equal to the lowest frequency used in the impedance measurement. Fourier series coefficients of the pulse train can be obtained. The number of harmonic constituents in the Fourier series are selected so as to appropriately resolve the response, but the maximum frequency should be less than or equal to the highest frequency used in the impedance measurement. Using a current pulse as an example, the Fourier coefficients of the pulse are multiplied by the impedance spectrum at corresponding frequencies to obtain Fourier coefficients of the voltage response to the desired pulse. The Fourier coefficients of the response are then summed and reassembled to obtain the overall time domain estimate of the voltage using the Fourier series analysis.

15 CFR Supplement No. 6 to Part 774 - Sensitive List

Code of Federal Regulations, 2014 CFR

2014-01-01

... filtering and beamforming using Fast Fourier or other transforms or processes. (vi) 6A001.a.2.d. (vii) 6A001... processing and correlation, including spectral analysis, digital filtering and beamforming using Fast Fourier...

Determination of the Optimal Fourier Number on the Dynamic Thermal Transmission

NASA Astrophysics Data System (ADS)

Bruzgevičius, P.; Burlingis, A.; Norvaišienė, R.

2016-12-01

This article represents the result of experimental research on transient heat transfer in a multilayered (heterogeneous) wall. Our non-steady thermal transmission simulation is based on a finite-difference calculation method. The value of a Fourier number shows the similarity of thermal variation in conditional layers of an enclosure. Most scientists recommend using no more than a value of 0.5 for the Fourier number when performing calculations on dynamic (transient) heat transfer. The value of the Fourier number is determined in order to acquire reliable calculation results with optimal accuracy. To compare the results of simulation with experimental research, a transient heat transfer calculation spreadsheet was created. Our research has shown that a Fourier number of around 0.5 or even 0.32 is not sufficient ({≈ }17 % of oscillation amplitude) for calculations of transient heat transfer in a multilayered wall. The least distorted calculation results were obtained when the multilayered enclosure was divided into conditional layers with almost equal Fourier number values and when the value of the Fourier number was around 1/6, i.e., approximately 0.17. Statistical deviation analysis using the Statistical Analysis System was applied to assess the accuracy of the spreadsheet calculation and was developed on the basis of our established methodology. The mean and median absolute error as well as their confidence intervals has been estimated by the two methods with optimal accuracy ({F}_{oMDF}= 0.177 and F_{oEPS}= 0.1633 values).

Measuring sperm movement within the female reproductive tract using Fourier analysis.

PubMed

Nicovich, Philip R; Macartney, Erin L; Whan, Renee M; Crean, Angela J

2015-02-01

The adaptive significance of variation in sperm phenotype is still largely unknown, in part due to the difficulties of observing and measuring sperm movement in its natural, selective environment (i.e., within the female reproductive tract). Computer-assisted sperm analysis systems allow objective and accurate measurement of sperm velocity, but rely on being able to track individual sperm, and are therefore unable to measure sperm movement in species where sperm move in trains or bundles. Here we describe a newly developed computational method for measuring sperm movement using Fourier analysis to estimate sperm tail beat frequency. High-speed time-lapse videos of sperm movement within the female tract of the neriid fly Telostylinus angusticollis were recorded, and a map of beat frequencies generated by converting the periodic signal of an intensity versus time trace at each pixel to the frequency domain using the Fourier transform. We were able to detect small decreases in sperm tail beat frequency over time, indicating the method is sensitive enough to identify consistent differences in sperm movement. Fourier analysis can be applied to a wide range of species and contexts, and should therefore facilitate novel exploration of the causes and consequences of variation in sperm movement.

A wavelet-based technique to predict treatment outcome for Major Depressive Disorder

PubMed Central

Xia, Likun; Mohd Yasin, Mohd Azhar; Azhar Ali, Syed Saad

2017-01-01

Treatment management for Major Depressive Disorder (MDD) has been challenging. However, electroencephalogram (EEG)-based predictions of antidepressant’s treatment outcome may help during antidepressant’s selection and ultimately improve the quality of life for MDD patients. In this study, a machine learning (ML) method involving pretreatment EEG data was proposed to perform such predictions for Selective Serotonin Reuptake Inhibitor (SSRIs). For this purpose, the acquisition of experimental data involved 34 MDD patients and 30 healthy controls. Consequently, a feature matrix was constructed involving time-frequency decomposition of EEG data based on wavelet transform (WT) analysis, termed as EEG data matrix. However, the resultant EEG data matrix had high dimensionality. Therefore, dimension reduction was performed based on a rank-based feature selection method according to a criterion, i.e., receiver operating characteristic (ROC). As a result, the most significant features were identified and further be utilized during the training and testing of a classification model, i.e., the logistic regression (LR) classifier. Finally, the LR model was validated with 100 iterations of 10-fold cross-validation (10-CV). The classification results were compared with short-time Fourier transform (STFT) analysis, and empirical mode decompositions (EMD). The wavelet features extracted from frontal and temporal EEG data were found statistically significant. In comparison with other time-frequency approaches such as the STFT and EMD, the WT analysis has shown highest classification accuracy, i.e., accuracy = 87.5%, sensitivity = 95%, and specificity = 80%. In conclusion, significant wavelet coefficients extracted from frontal and temporal pre-treatment EEG data involving delta and theta frequency bands may predict antidepressant’s treatment outcome for the MDD patients. PMID:28152063

Ultra-high-resolution paleoenvironmental records via direct laser-based analysis of lipid biomarkers in sediment core samples

PubMed Central

Wörmer, Lars; Elvert, Marcus; Fuchser, Jens; Lipp, Julius Sebastian; Buttigieg, Pier Luigi; Zabel, Matthias; Hinrichs, Kai-Uwe

2014-01-01

Marine microorganisms adapt to their habitat by structural modification of their membrane lipids. This concept is the basis of numerous molecular proxies used for paleoenvironmental reconstruction. Archaeal tetraether lipids from ubiquitous marine planktonic archaea are particularly abundant, well preserved in the sedimentary record and used in several molecular proxies. We here introduce the direct, extraction-free analysis of these compounds in intact sediment core sections using laser desorption ionization (LDI) coupled to Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS). LDI FTICR-MS can detect the target lipids in single submillimeter-sized spots on sediment sections, equivalent to a sample mass in the nanogram range, and could thus pave the way for biomarker-based reconstruction of past environments and ecosystems at subannual to decadal resolution. We demonstrate that ratios of selected archaeal tetraethers acquired by LDI FTICR-MS are highly correlated with values obtained by conventional liquid chromatography/MS protocols. The ratio of the major archaeal lipids, caldarchaeol and crenarchaeol, analyzed in a 6.2-cm intact section of Mediterranean sapropel S1 at 250-µm resolution (∼4-y temporal resolution), provides an unprecedented view of the fine-scale patchiness of sedimentary biomarker distributions and the processes involved in proxy signal formation. Temporal variations of this lipid ratio indicate a strong influence of the ∼200-y de Vries solar cycle on reconstructed sea surface temperatures with possible amplitudes of several degrees, and suggest signal amplification by a complex interplay of ecological and environmental factors. Laser-based biomarker analysis of geological samples has the potential to revolutionize molecular stratigraphic studies of paleoenvironments. PMID:25331871

Three-wave and four-wave interactions in gravity wave turbulence

NASA Astrophysics Data System (ADS)

Aubourg, Quentin; Campagne, Antoine; Peureux, Charles; Ardhuin, Fabrice; Sommeria, Joel; Viboud, Samuel; Mordant, Nicolas

2017-11-01

Weak-turbulence theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We set up an isotropic state of interacting gravity waves in the Coriolis facility (13-m-diam circular wave tank) by exciting waves at 1 Hz by wedge wave makers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved in both space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and the field observations in the Black Sea by Leckler et al. [F. Leckler et al., J. Phys. Oceanogr. 45, 2484 (2015), 10.1175/JPO-D-14-0237.1]. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wave-vector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler et al. for comparison with the laboratory data. Three-wave coupling is characterized by and shown to involve mostly quasiresonances of waves with second- or higher-order harmonics. Four-wave coupling is not observed in the laboratory but is evidenced in the field data. We discuss temporal scale separation to explain our observations.

Discrete Fourier Transform Analysis in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

PubMed

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

Santa Maria, Odilyn L.

1999-01-01

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

Dynamic torsional misalignment of eyes during laser in-situ keratomileusis.

PubMed

Shajari, Mehdi; Bühren, Jens; Kohnen, Thomas

2016-05-01

To determine the amount and characteristics of dynamic torsional misalignment of eyes during excimer ablation in laser in-situ keratomileusis (LASIK). Retrospective trial for evaluation of dynamic intraoperative torsional misalignment of 179 eyes that underwent LASIK for correction of myopia and/or astigmatism. Patients were treated with the Keracor 217z excimer laser implementing 25 Hz dynamic eye tracker ACE 100 (both Technolas Perfect Vision, Munich, Germany). From dynamic torsional misalignments, temporal power spectra were obtained by Fourier analysis up to a frequency of 12.5 Hz and an amplitude of ±15° from initial torsional status (limited by the tracking system). The f90, f95, and f99 criteria were defined as the frequency below which 90 %, 95 %, and 99 % of misalignments occur. A Wilcoxon rank sum test was performed to detect differences of f90, f95, and f99 in groups' gender, age, and eye (if both eyes underwent surgery at same day). Multiple regression analysis (MRA) was performed to evaluate possible preoperative predictors of f90, f95, and f99. Fourier analysis showed a dominance of high-frequency, low-power dynamic torsional misalignment. Mean f95 threshold of rotational movements was 4.89±2.12 Hz (median 4.54, ranging from 0.44 to 9.23 Hz). Wilcoxon rank sum test showed no differences in f90, f95, and f99 between groups' gender, age, and eye. MRA revealed age, gender, and optical zone as preoperative predictors on intraoperative f90, f95, and f99. Dynamic intraoperative torsional misalignments of eyes undergoing LASIK are dominated by low-frequency (slow), high-power (large) movements, with 95 % being slower than 4.89Hz regarding the spectrum analyzed (0-12.5Hz, ±15°). Movements can be predicted preoperatively by eye treated, patients' gender, and age in pre-LASIK diagnostics.

Predicting Treatment Windows for Invasive Buffelgrass in Southern Arizona using MODIS and Climate Data

NASA Astrophysics Data System (ADS)

Wallace, C.; Weltzin, J. F.; Skirvin, S. M.; Patrick-Birdwell, C.; Raichle, H.

2014-12-01

The increasing spread and abundance of an invasive perennial grass, buffelgrass (Pennisetum ciliare), represents an important shift in the vegetation composition of the Sonoran Desert in southern Arizona. Buffelgrass out-competes native species and alters fire regimes, and its control and management is a high-priority issue for resource managers who seek to preserve the unique and iconic Sonoran Desert flora. Herbicidal treatment of buffelgrass is most effective when the vegetation is actively growing; however, the erratic timing and length of active buffelgrass growth periods in southern Arizona confound effective management decision-making. The goal of our research is to enable the strategic application of buffelgrass herbicide by using remote sensing data to detect when and where buffelgrass is photosynthetically active. We integrated ground-based observations of buffelgrass phenology (green-up and senescence) in the Tucson, Arizona area with climate information and Moderate-resolution Imaging Spectroradiometer (MODIS) satellite imagery at 250m spatial and both 8-day and 16-day composite temporal resolution to understand dynamics, relationships and resonance between these disparate datasets during 2011 to 2013. Fourier harmonics analysis was used to derive land surface phenology (LSP) metrics from MODIS Enhanced Vegetation Index (EVI) greenness data and to quantify the temporal patterns of the climate and phenophase abundance datasets. Regression analyses and statistical tests were used to identify correlations between temporal patterns of the data sets. Our results reveal strong correlations between the observed greenness of in-situ buffelgrass and satellite LSP metrics, confirming that MODIS-EVI data can be a useful indicator of active buffelgrass growth at multiple scales. The analysis also reveals strong harmonics between precipitation and greenness, but with a lagged response, suggesting that precipitation can be a predictor of the location and intensity of buffelgrass green-up at landscape scales. This information can be used by resource managers to treat buffelgrass during optimal conditions.

Fully automated corneal endothelial morphometry of images captured by clinical specular microscopy

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2010-02-01

The corneal endothelium serves as the posterior barrier of the cornea. Factors such as clarity and refractive properties of the cornea are in direct relationship to the quality of the endothelium. The endothelial cell density is considered the most important morphological factor of the corneal endothelium. Pathological conditions and physical trauma may threaten the endothelial cell density to such an extent that the optical property of the cornea and thus clear eyesight is threatened. Diagnosis of the corneal endothelium through morphometry is an important part of several clinical applications. Morphometry of the corneal endothelium is presently carried out by semi automated analysis of pictures captured by a Clinical Specular Microscope (CSM). Because of the occasional need of operator involvement, this process can be tedious, having a negative impact on sampling size. This study was dedicated to the development and use of fully automated analysis of a very large range of images of the corneal endothelium, captured by CSM, using Fourier analysis. Software was developed in the mathematical programming language Matlab. Pictures of the corneal endothelium, captured by CSM, were read into the analysis software. The software automatically performed digital enhancement of the images, normalizing lights and contrasts. The digitally enhanced images of the corneal endothelium were Fourier transformed, using the fast Fourier transform (FFT) and stored as new images. Tools were developed and applied for identification and analysis of relevant characteristics of the Fourier transformed images. The data obtained from each Fourier transformed image was used to calculate the mean cell density of its corresponding corneal endothelium. The calculation was based on well known diffraction theory. Results in form of estimated cell density of the corneal endothelium were obtained, using fully automated analysis software on 292 images captured by CSM. The cell density obtained by the fully automated analysis was compared to the cell density obtained from classical, semi-automated analysis and a relatively large correlation was found.

To See the World in a Grain of Sand: Recognizing the Origin of Sand Specimens by Diffuse Reflectance Infrared Fourier Transform Spectroscopy and Multivariate Exploratory Data Analysis

ERIC Educational Resources Information Center

Pezzolo, Alessandra De Lorenzi

2011-01-01

The diffuse reflectance infrared Fourier transform (DRIFT) spectra of sand samples exhibit features reflecting their composition. Basic multivariate analysis (MVA) can be used to effectively sort subsets of homogeneous specimens collected from nearby locations, as well as pointing out similarities in composition among sands of different origins.…

Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.

PubMed

Li, Xin; Zhong, Yongmin; Smith, Julian; Gu, Chengfan

2017-01-02

Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model.

Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation

PubMed Central

Li, Xin; Zhong, Yongmin; Smith, Julian; Gu, Chengfan

2017-01-01

ABSTRACT Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model. PMID:27690290

A versatile pitch tracking algorithm: from human speech to killer whale vocalizations.

PubMed

Shapiro, Ari Daniel; Wang, Chao

2009-07-01

In this article, a pitch tracking algorithm [named discrete logarithmic Fourier transformation-pitch detection algorithm (DLFT-PDA)], originally designed for human telephone speech, was modified for killer whale vocalizations. The multiple frequency components of some of these vocalizations demand a spectral (rather than temporal) approach to pitch tracking. The DLFT-PDA algorithm derives reliable estimations of pitch and the temporal change of pitch from the harmonic structure of the vocal signal. Scores from both estimations are combined in a dynamic programming search to find a smooth pitch track. The algorithm is capable of tracking killer whale calls that contain simultaneous low and high frequency components and compares favorably across most signal to noise ratio ranges to the peak-picking and sidewinder algorithms that have been used for tracking killer whale vocalizations previously.

Time-frequency representation of autoionization dynamics in helium

NASA Astrophysics Data System (ADS)

Busto, D.; Barreau, L.; Isinger, M.; Turconi, M.; Alexandridi, C.; Harth, A.; Zhong, S.; Squibb, R. J.; Kroon, D.; Plogmaker, S.; Miranda, M.; Jiménez-Galán, Á.; Argenti, L.; Arnold, C. L.; Feifel, R.; Martín, F.; Gisselbrecht, M.; L'Huillier, A.; Salières, P.

2018-02-01

Autoionization, which results from the interference between direct photoionization and photoexcitation to a discrete state decaying to the continuum by configuration interaction, is a well known example of the important role of electron correlation in light-matter interaction. Information on this process can be obtained by studying the spectral, or equivalently, temporal complex amplitude of the ionized electron wave packet. Using an energy-resolved interferometric technique, we measure the spectral amplitude and phase of autoionized wave packets emitted via the sp2+ and sp3+ resonances in helium. These measurements allow us to reconstruct the corresponding temporal profiles by Fourier transform. In addition, applying various time-frequency representations, we observe the build-up of the wave packets in the continuum, monitor the instantaneous frequencies emitted at any time and disentangle the dynamics of the direct and resonant ionization channels.

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral decomposition. New method for the best approximation of the square-integrable function by multiple Fourier series summed over the elliptic levels are established. Using the best approximation, the Lebesgue constant corresponding to the elliptic partial sums is estimated. The latter is applied to obtain an estimation for the maximal operator in the classes of Liouville.

A generalized formulation for downscaling data based on Fourier Transform and inversion: Mathematical rationale and application to the Max-Planck-Institute aerosol climatology data

NASA Astrophysics Data System (ADS)

Zhang, Taiping; Stackhouse, Paul W.; Gupta, Shashi K.; Cox, Stephen J.; Mikovitz, J. Colleen

2017-02-01

Occasionally, a need arises to downscale a time series of data from a coarse temporal resolution to a finer one, a typical example being from monthly means to daily means. For this case, daily means derived as such are used as inputs of climatic or atmospheric models so that the model results may exhibit variance on the daily time scale and retain the monthly mean of the original data set without an abrupt change from the end of one month to the beginning of the next. Different methods have been developed which often need assumptions, free parameters and the solution of simultaneous equations. Here we derive a generalized formulation by means of Fourier transform and inversion so that it can be used to directly compute daily means from a series of an arbitrary number of monthly means. The formulation can be used to transform any coarse temporal resolution to a finer one. From the derived results, the original data can be recovered almost identically. As a real application, we use this method to derive the daily counterpart of the MAC-v1 aerosol climatology that provides monthly mean aerosol properties for 18 shortwave bands and 12 longwave bands for the years from 1860 to 2100. The derived daily means are to be used as inputs of the shortwave and longwave algorithms of the NASA GEWEX SRB project.

Rod Electroretinograms Elicited by Silent Substitution Stimuli from the Light-Adapted Human Eye

PubMed Central

Maguire, John; Parry, Neil R. A.; Kremers, Jan; Kommanapalli, Deepika; Murray, Ian J.; McKeefry, Declan J.

2016-01-01

Purpose To demonstrate that silent substitution stimuli can be used to generate electroretinograms (ERGs) that effectively isolate rod photoreceptor function in humans without the need for dark adaptation, and that this approach constitutes a viable alternative to current clinical standard testing protocols. Methods Rod-isolating and non-isolating sinusoidal flicker stimuli were generated on a 4 primary light-emitting diode (LED) Ganzfeld stimulator to elicit ERGs from participants with normal and compromised rod function who had not undergone dark-adaptation. Responses were subjected to Fourier analysis, and the amplitude and phase of the fundamental were used to examine temporal frequency and retinal illuminance response characteristics. Results Electroretinograms elicited by rod-isolating silent substitution stimuli exhibit low-pass temporal frequency response characteristics with an upper response limit of 30 Hz. Responses are optimal between 5 and 8 Hz and between 10 and 100 photopic trolands (Td). There is a significant correlation between the response amplitudes obtained with the silent substitution method and current standard clinical protocols. Analysis of signal-to-noise ratios reveals significant differences between subjects with normal and compromised rod function. Conclusions Silent substitution provides an effective method for the isolation of human rod photoreceptor function in subjects with normal as well as compromised rod function when stimuli are used within appropriate parameter ranges. Translational Relevance This method of generating rod-mediated ERGs can be achieved without time-consuming periods of dark adaptation, provides improved isolation of rod- from cone-based activity, and will lead to the development of faster clinical electrophysiologic testing protocols with improved selectivity. PMID:27617180

Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

PubMed

Singh, Iqbal

2008-01-01

To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Semiconductor-laser Fourier processors of electric signals

NASA Astrophysics Data System (ADS)

Blok, A. S.; Bukhenskii, A. F.; Krupitskii, É. I.; Morozov, S. V.; Pelevin, V. Yu; Sergeenko, T. N.; Yakovlev, V. I.

1995-10-01

An investigation is reported of acousto-optical and fibre-optic Fourier processors of electric signals, based on semiconductor lasers. A description is given of practical acousto-optical processors with an analysis band 120 MHz wide, a resolution of 200 kHz, and 7 cm × 8 cm × 18 cm dimensions. Fibre-optic Fourier processors are considered: they represent a new class of devices which are promising for the processing of gigahertz signals.

Is Fourier analysis performed by the visual system or by the visual investigator.

PubMed

Ochs, A L

1979-01-01

A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.

Robust Global Image Registration Based on a Hybrid Algorithm Combining Fourier and Spatial Domain Techniques

DTIC Science & Technology

2012-09-01

Robust global image registration based on a hybrid algorithm combining Fourier and spatial domain techniques Peter N. Crabtree, Collin Seanor...00-00-2012 to 00-00-2012 4. TITLE AND SUBTITLE Robust global image registration based on a hybrid algorithm combining Fourier and spatial domain...demonstrate performance of a hybrid algorithm . These results are from analysis of a set of images of an ISO 12233 [12] resolution chart captured in the

A Fast Fourier transform stochastic analysis of the contaminant transport problem

USGS Publications Warehouse

Deng, F.W.; Cushman, J.H.; Delleur, J.W.

1993-01-01

A three-dimensional stochastic analysis of the contaminant transport problem is developed in the spirit of Naff (1990). The new derivation is more general and simpler than previous analysis. The fast Fourier transformation is used extensively to obtain numerical estimates of the mean concentration and various spatial moments. Data from both the Borden and Cape Cod experiments are used to test the methodology. Results are comparable to results obtained by other methods, and to the experiments themselves.

Insertion of Guest Molecules into a Mixed Ligand Metal-Organic Framework via Single-Crystal-to-Single Crystal Guest Exchange

DTIC Science & Technology

2014-07-01

powder x-ray diffraction (PXRD), thermogravimentric analysis (TGA), and Fourier transform infrared (FTIR). 15. SUBJECT TERMS Metal organic frame work...the inclusion by using a variety of analytical techniques, such as powder x-ray diffraction (PXRD), thermo-gravimetric analysis (TGA), Fourier...Characterizations Analysis of the MOF and the complexes with the MOF and the guest molecules was performed using an Agilent GC-MS (Model 6890N GC and Model 5973N

Modelling fourier regression for time series data- a case study: modelling inflation in foods sector in Indonesia

NASA Astrophysics Data System (ADS)

Prahutama, Alan; Suparti; Wahyu Utami, Tiani

2018-03-01

Regression analysis is an analysis to model the relationship between response variables and predictor variables. The parametric approach to the regression model is very strict with the assumption, but nonparametric regression model isn’t need assumption of model. Time series data is the data of a variable that is observed based on a certain time, so if the time series data wanted to be modeled by regression, then we should determined the response and predictor variables first. Determination of the response variable in time series is variable in t-th (yt), while the predictor variable is a significant lag. In nonparametric regression modeling, one developing approach is to use the Fourier series approach. One of the advantages of nonparametric regression approach using Fourier series is able to overcome data having trigonometric distribution. In modeling using Fourier series needs parameter of K. To determine the number of K can be used Generalized Cross Validation method. In inflation modeling for the transportation sector, communication and financial services using Fourier series yields an optimal K of 120 parameters with R-square 99%. Whereas if it was modeled by multiple linear regression yield R-square 90%.

The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.

ERIC Educational Resources Information Center

King, Roy W.; Williams, Kathryn R.

1989-01-01

Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)

Fourier Analysis and Structure Determination. Part II: Pulse NMR and NMR Imaging.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Uses simple pulse NMR experiments to discuss Fourier transforms. Studies the generation of spin echoes used in the imaging procedure. Shows that pulse NMR experiments give signals that are additions of sinusoids of differing amplitudes, frequencies, and phases. (MVL)

ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.

EPA Science Inventory

Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...

A numerical spectral approach to solve the dislocation density transport equation

NASA Astrophysics Data System (ADS)

Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

2015-09-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers.

PubMed

Eigenwillig, Christoph M; Wieser, Wolfgang; Todor, Sebastian; Biedermann, Benjamin R; Klein, Thomas; Jirauschek, Christian; Huber, Robert

2013-01-01

Ultrafast lasers have a crucial function in many fields of science; however, up to now, high-energy pulses directly from compact, efficient and low-power semiconductor lasers are not available. Therefore, we introduce a new approach based on temporal compression of the continuous-wave, wavelength-swept output of Fourier domain mode-locked lasers, where a narrowband optical filter is tuned synchronously to the round-trip time of light in a kilometre-long laser cavity. So far, these rapidly swept lasers enabled orders-of-magnitude speed increase in optical coherence tomography. Here we report on the generation of ~60-70 ps pulses at 390 kHz repetition rate. As energy is stored optically in the long-fibre delay line and not as population inversion in the laser-gain medium, high-energy pulses can now be generated directly from a low-power, compact semiconductor-based oscillator. Our theory predicts subpicosecond pulses with this new technique in the future.

Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers

NASA Astrophysics Data System (ADS)

Eigenwillig, Christoph M.; Wieser, Wolfgang; Todor, Sebastian; Biedermann, Benjamin R.; Klein, Thomas; Jirauschek, Christian; Huber, Robert

2013-05-01

Ultrafast lasers have a crucial function in many fields of science; however, up to now, high-energy pulses directly from compact, efficient and low-power semiconductor lasers are not available. Therefore, we introduce a new approach based on temporal compression of the continuous-wave, wavelength-swept output of Fourier domain mode-locked lasers, where a narrowband optical filter is tuned synchronously to the round-trip time of light in a kilometre-long laser cavity. So far, these rapidly swept lasers enabled orders-of-magnitude speed increase in optical coherence tomography. Here we report on the generation of ~60-70 ps pulses at 390 kHz repetition rate. As energy is stored optically in the long-fibre delay line and not as population inversion in the laser-gain medium, high-energy pulses can now be generated directly from a low-power, compact semiconductor-based oscillator. Our theory predicts subpicosecond pulses with this new technique in the future.

Feature Extraction for Bearing Prognostics and Health Management (PHM) - A Survey (Preprint)

DTIC Science & Technology

2008-05-01

Envelope analysis • Cepstrum analysis • Higher order spectrum • Short-time Fourier Transform (STFT) • Wigner - Ville distribution ( WVD ) • Empirical mode...techniques are the short-time Fourier transform (STFT), the Wigner - Ville distribution , and the wavelet transform. In this paper we categorize wavelets...diagnosis have shown in many publications, for example, [22]. b) Wigner – Ville distribution : The afore-mentioned STFT is conceptually simple. However

Short time Fourier analysis of the electromyogram - Fast movements and constant contraction

NASA Technical Reports Server (NTRS)

Hannaford, Blake; Lehman, Steven

1986-01-01

Short-time Fourier analysis was applied to surface electromyograms (EMG) recorded during rapid movements, and during isometric contractions at constant forces. A portion of the data to be transformed by multiplying the signal by a Hamming window was selected, and then the discrete Fourier transform was computed. Shifting the window along the data record, a new spectrum was computed each 10 ms. The transformed data were displayed in spectograms or 'voiceprints'. This short-time technique made it possible to see time-dependencies in the EMG that are normally averaged in the Fourier analysis of these signals. Spectra of EMGs during isometric contractions at constant force vary in the short (10-20 ms) term. Short-time spectra from EMGs recorded during rapid movements were much less variable. The windowing technique picked out the typical 'three-burst pattern' in EMG's from both wrist and head movements. Spectra during the bursts were more consistent than those during isometric contractions. Furthermore, there was a consistent shift in spectral statistics in the course of the three bursts. Both the center frequency and the variance of the spectral energy distribution grew from the first burst to the second burst in the same muscle. The analogy between EMGs and speech signals is extended to argue for future applicability of short-time spectral analysis of EMG.

Fourier transform mass spectrometry.

PubMed

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-07-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

Fourier Transform Mass Spectrometry

PubMed Central

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

MEG time-frequency analyses for pre- and post-surgical evaluation of patients with epileptic rhythmic fast activity.

PubMed

Sueda, Keitaro; Takeuchi, Fumiya; Shiraishi, Hideaki; Nakane, Shingo; Asahina, Naoko; Kohsaka, Shinobu; Nakama, Hideyuki; Otsuki, Taisuke; Sawamura, Yutaka; Saitoh, Shinji

2010-02-01

To evaluate the effectiveness of surgery for epilepsy, we analyzed rhythmic fast activity by magnetoencephalography (MEG) before and after surgery using time-frequency analysis. To assess reliability, the results obtained by pre-surgical MEG and intraoperative electrocorticography were compared. Four children with symptomatic localization-related epilepsy caused by circumscribed cortical lesion were examined in the present study using 204-channel helmet-shaped MEG with a sampling rate of 600Hz. One patient had dysembryoplastic neuroepithelial tumor (DNT) and three patients had focal cortical dysplasia (FCD). Aberrant areas were superimposed, to reconstruct 3D MRI images, and illustrated as moving images. In three patients, short-time Fourier transform (STFT) analyses of MEG showed rhythmic activities just above the lesion with FCD and in the vicinity of DNT. In one patient with FCD in the medial temporal lobe, rhythmic activity appeared in the ipsilateral frontal lobe and temporal lateral aspect. These findings correlate well with the results obtained by intraoperative electrocorticography. After the surgery, three patients were relieved of their seizures, and the area of rhythmic MEG activity disappeared or become smaller. One patient had residual rhythmic MEG activity, and she suffered from seizure relapse. Time-frequency analyses using STFT successfully depicted MEG rhythmic fast activity, and would provide valuable information for pre- and post-surgical evaluations to define surgical strategies for patients with epilepsy.

Differential spectral power alteration following acupuncture at different designated places revealed by magnetoencephalography

NASA Astrophysics Data System (ADS)

You, Youbo; Bai, Lijun; Dai, Ruwei; Xue, Ting; Zhong, Chongguang; Liu, Zhenyu; Wang, Hu; Feng, Yuanyuan; Wei, Wenjuan; Tian, Jie

2012-03-01

As an ancient therapeutic technique in Traditional Chinese Medicine, acupuncture has been used increasingly in modern society to treat a range of clinical conditions as an alternative and complementary therapy. However, acupoint specificity, lying at the core of acupuncture, still faces many controversies. Considering previous neuroimaging studies on acupuncture have mainly employed functional magnetic resonance imaging, which only measures the secondary effect of neural activity on cerebral metabolism and hemodynamics, in the current study, we adopted an electrophysiological measurement technique named magnetoencephalography (MEG) to measure the direct neural activity. 28 healthy college students were recruited in this study. We filtered MEG data into 5 consecutive frequency bands (delta, theta, alpha, beta and gamma band) and grouped 140 sensors into 10 main brain regions (left/right frontal, central, temporal, parietal and occipital regions). Fast Fourier Transformation (FFT) based spectral analysis approach was further performed to explore the differential band-limited power change patterns of acupuncture at Stomach Meridian 36 (ST36) using a nearby nonacupoint (NAP) as control condition. Significantly increased delta power and decreased alpha as well as beta power in bilateral frontal ROIs were observed following stimulation at ST36. Compared with ST36, decreased alpha power in left and right central, right parietal as well as right temporal ROIs were detected in NAP group. Our research results may provide additional evidence for acupoint specificity.

Fully automated corneal endothelial morphometry of images captured by clinical specular microscopy

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2009-02-01

The corneal endothelium serves as the posterior barrier of the cornea. Factors such as clarity and refractive properties of the cornea are in direct relationship to the quality of the endothelium. The endothelial cell density is considered the most important morphological factor. Morphometry of the corneal endothelium is presently done by semi-automated analysis of pictures captured by a Clinical Specular Microscope (CSM). Because of the occasional need of operator involvement, this process can be tedious, having a negative impact on sampling size. This study was dedicated to the development of fully automated analysis of images of the corneal endothelium, captured by CSM, using Fourier analysis. Software was developed in the mathematical programming language Matlab. Pictures of the corneal endothelium, captured by CSM, were read into the analysis software. The software automatically performed digital enhancement of the images. The digitally enhanced images of the corneal endothelium were transformed, using the fast Fourier transform (FFT). Tools were developed and applied for identification and analysis of relevant characteristics of the Fourier transformed images. The data obtained from each Fourier transformed image was used to calculate the mean cell density of its corresponding corneal endothelium. The calculation was based on well known diffraction theory. Results in form of estimated cell density of the corneal endothelium were obtained, using fully automated analysis software on images captured by CSM. The cell density obtained by the fully automated analysis was compared to the cell density obtained from classical, semi-automated analysis and a relatively large correlation was found.

Spatiotemporal topology and temporal sequence identification with an adaptive time-delay neural network

NASA Astrophysics Data System (ADS)

Lin, Daw-Tung; Ligomenides, Panos A.; Dayhoff, Judith E.

1993-08-01

Inspired from the time delays that occur in neurobiological signal transmission, we describe an adaptive time delay neural network (ATNN) which is a powerful dynamic learning technique for spatiotemporal pattern transformation and temporal sequence identification. The dynamic properties of this network are formulated through the adaptation of time-delays and synapse weights, which are adjusted on-line based on gradient descent rules according to the evolution of observed inputs and outputs. We have applied the ATNN to examples that possess spatiotemporal complexity, with temporal sequences that are completed by the network. The ATNN is able to be applied to pattern completion. Simulation results show that the ATNN learns the topology of a circular and figure eight trajectories within 500 on-line training iterations, and reproduces the trajectory dynamically with very high accuracy. The ATNN was also trained to model the Fourier series expansion of the sum of different odd harmonics. The resulting network provides more flexibility and efficiency than the TDNN and allows the network to seek optimal values for time-delays as well as optimal synapse weights.

Statistical analysis of polarization-inhomogeneous Fourier spectra of laser radiation scattered by human skin in the tasks of differentiation of benign and malignant formations

NASA Astrophysics Data System (ADS)

Ushenko, Alexander G.; Dubolazov, Alexander V.; Ushenko, Vladimir A.; Novakovskaya, Olga Y.

2016-07-01

The optical model of formation of polarization structure of laser radiation scattered by polycrystalline networks of human skin in Fourier plane was elaborated. The results of investigation of the values of statistical (statistical moments of the 1st to 4th order) parameters of polarization-inhomogeneous images of skin surface in Fourier plane were presented. The diagnostic criteria of pathological process in human skin and its severity degree differentiation were determined.

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

Robust generation of Fourier-synthesized laser fields and their estimation of the optical phase by using quantum control of molecular tunneling ionization

NASA Astrophysics Data System (ADS)

Yoshida, Tsuyoshi; Saito, Naoaki; Ohmura, Hideki

2018-03-01

Intense (5.0 × 1012 W cm-2) nanosecond Fourier-synthesized laser fields consisting of fundamental, second-, third-, and fourth-harmonic light generated by an interferometer-free Fourier-synthesized laser field generator induce orientation-selective ionization based on directionally asymmetric molecular tunneling ionization (TI). The laser field generator ensures adjustment-free operation, high stability, and high reproducibility. Phase-sensitive, orientation-selective molecular TI provides a simple way to estimate the relative phase differences between the fundamental light and each harmonic by data-fitting analysis. This application of Fourier-synthesized laser fields will facilitate not only lightwave engineering but also the control of matter.

Interactive remote data processing using Pixelize Wavelet Filtration (PWF-method) and PeriodMap analysis

NASA Astrophysics Data System (ADS)

Sych, Robert; Nakariakov, Valery; Anfinogentov, Sergey

Wavelet analysis is suitable for investigating waves and oscillating in solar atmosphere, which are limited in both time and frequency. We have developed an algorithms to detect this waves by use the Pixelize Wavelet Filtration (PWF-method). This method allows to obtain information about the presence of propagating and non-propagating waves in the data observation (cube images), and localize them precisely in time as well in space. We tested the algorithm and found that the results of coronal waves detection are consistent with those obtained by visual inspection. For fast exploration of the data cube, in addition, we applied early-developed Period- Map analysis. This method based on the Fast Fourier Transform and allows on initial stage quickly to look for "hot" regions with the peak harmonic oscillations and determine spatial distribution at the significant harmonics. We propose the detection procedure of coronal waves separate on two parts: at the first part, we apply the PeriodMap analysis (fast preparation) and than, at the second part, use information about spatial distribution of oscillation sources to apply the PWF-method (slow preparation). There are two possible algorithms working with the data: in automatic and hands-on operation mode. Firstly we use multiply PWF analysis as a preparation narrowband maps at frequency subbands multiply two and/or harmonic PWF analysis for separate harmonics in a spectrum. Secondly we manually select necessary spectral subband and temporal interval and than construct narrowband maps. For practical implementation of the proposed methods, we have developed the remote data processing system at Institute of Solar-Terrestrial Physics, Irkutsk. The system based on the data processing server - http://pwf.iszf.irk.ru. The main aim of this resource is calculation in remote access through the local and/or global network (Internet) narrowband maps of wave's sources both in whole spectral band and at significant harmonics. In addition, we can obtain temporal dynamics (mpeg- files) of the main oscillation characteristics: amplitude, power and phase as a spatial-temporal coordinates. For periodogram mapping of data cubes as a method for the pre-analysis, we developed preparation of the color maps where the pixel's colour corresponds to the frequency of the power spectrum maximum. The computer system based on applications ION-scripts, algorithmic languages IDL and PHP, and Apache WEB server. The IDL ION-scripts use for preparation and configuration of network requests at the central data server with subsequent connection to IDL run-unit software and graphic output on FTP-server and screen. Web page is constructed using PHP language.

Water vapor variance measurements using a Raman lidar

NASA Technical Reports Server (NTRS)

Evans, K.; Melfi, S. H.; Ferrare, R.; Whiteman, D.

1992-01-01

Because of the importance of atmospheric water vapor variance, we have analyzed data from the NASA/Goddard Raman lidar to obtain temporal scales of water vapor mixing ratio as a function of altitude over observation periods extending to 12 hours. The ground-based lidar measures water vapor mixing ration from near the earth's surface to an altitude of 9-10 km. Moisture profiles are acquired once every minute with 75 m vertical resolution. Data at each 75 meter altitude level can be displayed as a function of time from the beginning to the end of an observation period. These time sequences have been spectrally analyzed using a fast Fourier transform technique. An example of such a temporal spectrum obtained between 00:22 and 10:29 UT on December 6, 1991 is shown in the figure. The curve shown on the figure represents the spectral average of data from 11 height levels centered on an altitude of 1 km (1 plus or minus .375 km). The spectra shows a decrease in energy density with frequency which generally follows a -5/3 power law over the spectral interval 3x10 (exp -5) to 4x10 (exp -3) Hz. The flattening of the spectrum for frequencies greater than 6x10 (exp -3) Hz is most likely a measure of instrumental noise. Spectra like that shown in the figure are calculated for other altitudes and show changes in spectral features with height. Spectral analysis versus height have been performed for several observation periods which demonstrate changes in water vapor mixing ratio spectral character from one observation period to the next. The combination of these temporal spectra with independent measurements of winds aloft provide an opportunity to infer spatial scales of moisture variance.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trang Nghiêm, T. T.; Chapuis, Pierre-Olivier

The wave property of phonons is employed to explore the thermal transport across a finite periodic array of nano-scatterers such as circular and triangular holes. As thermal phonons are generated in all directions, we study their transmission through a single array for both normal and oblique incidences, using a linear dispersionless time-dependent acoustic frame in a two-dimensional system. Roughness effects can be directly considered within the computations without relying on approximate analytical formulae. Analysis by spatio-temporal Fourier transform allows us to observe the diffraction effects and the conversion of polarization. Frequency-dependent energy transmission coefficients are computed for symmetric and asymmetricmore » objects that are both subject to reciprocity. We demonstrate that the phononic array acts as an efficient thermal barrier by applying the theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering holes in silicon for an exemplifying periodicity of 10 nm in the 5–100 K temperature range. It is observed that the associated thermal conductance has the same temperature dependence as that without phononic filtering.« less

Random positions of dendritic spines in human cerebral cortex.

PubMed

Morales, Juan; Benavides-Piccione, Ruth; Dar, Mor; Fernaud, Isabel; Rodríguez, Angel; Anton-Sanchez, Laura; Bielza, Concha; Larrañaga, Pedro; DeFelipe, Javier; Yuste, Rafael

2014-07-23

Dendritic spines establish most excitatory synapses in the brain and are located in Purkinje cell's dendrites along helical paths, perhaps maximizing the probability to contact different axons. To test whether spine helixes also occur in neocortex, we reconstructed >500 dendritic segments from adult human cortex obtained from autopsies. With Fourier analysis and spatial statistics, we analyzed spine position along apical and basal dendrites of layer 3 pyramidal neurons from frontal, temporal, and cingulate cortex. Although we occasionally detected helical positioning, for the great majority of dendrites we could not reject the null hypothesis of spatial randomness in spine locations, either in apical or basal dendrites, in neurons of different cortical areas or among spines of different volumes and lengths. We conclude that in adult human neocortex spine positions are mostly random. We discuss the relevance of these results for spine formation and plasticity and their functional impact for cortical circuits. Copyright © 2014 the authors 0270-6474/14/3410078-07$15.00/0.

Global Environmental Data for Mapping Infectious Disease Distribution

PubMed Central

Hay, S.I.; Tatem, A.J.; Graham, A.J.; Goetz, S.J.; Rogers, D.J.

2011-01-01

This contribution documents the satellite data archives, data processing methods and temporal Fourier analysis (TFA) techniques used to create the remotely sensed datasets on the DVD distributed with this volume. The aim is to provide a detailed reference guide to the genesis of the data, rather than a standard review. These remotely sensed data cover the entire globe at either 1 × 1 or 8 × 8 km spatial resolution. We briefly evaluate the relationships between the 1 × 1 and 8 × 8 km global TFA products to explore their inter-compatibility. The 8 × 8 km TFA surfaces are used in the mapping procedures detailed in the subsequent disease mapping reviews, since the 1 × 1 km products have been validated less widely. Details are also provided on additional, current and planned sensors that should be able to provide continuity with these environmental variable surfaces, as well as other sources of global data that may be used for mapping infectious disease. PMID:16647967

Fourier transform infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

PubMed

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.

Spatially: resolved heterogeneous dynamics in a strong colloidal gel

NASA Astrophysics Data System (ADS)

Buzzaccaro, Stefano; Alaimo, Matteo David; Secchi, Eleonora; Piazza, Roberto

2015-05-01

We re-examine the classical problem of irreversible colloid aggregation, showing that the application of Digital Fourier Imaging (DFI), a class of optical correlation methods that combine the power of light scattering and imaging, allows one to pick out novel useful evidence concerning the restructuring processes taking place in a strong colloidal gel. In particular, the spatially-resolved displacement fields provided by DFI strongly suggest that the temporally-intermittent local rearrangements taking place in the course of gel ageing are characterized by very long-ranged spatial correlations.

Hilbert-Huang Transform: A Spectral Analysis Tool Applied to Sunspot Number and Total Solar Irradiance Variations, as well as Near-Surface Atmospheric Variables

NASA Astrophysics Data System (ADS)

Barnhart, B. L.; Eichinger, W. E.; Prueger, J. H.

2010-12-01

Hilbert-Huang transform (HHT) is a relatively new data analysis tool which is used to analyze nonstationary and nonlinear time series data. It consists of an algorithm, called empirical mode decomposition (EMD), which extracts the cyclic components embedded within time series data, as well as Hilbert spectral analysis (HSA) which displays the time and frequency dependent energy contributions from each component in the form of a spectrogram. The method can be considered a generalized form of Fourier analysis which can describe the intrinsic cycles of data with basis functions whose amplitudes and phases may vary with time. The HHT will be introduced and compared to current spectral analysis tools such as Fourier analysis, short-time Fourier analysis, wavelet analysis and Wigner-Ville distributions. A number of applications are also presented which demonstrate the strengths and limitations of the tool, including analyzing sunspot number variability and total solar irradiance proxies as well as global averaged temperature and carbon dioxide concentration. Also, near-surface atmospheric quantities such as temperature and wind velocity are analyzed to demonstrate the nonstationarity of the atmosphere.

Identification and characterization of salmonella serotypes using DNA spectral characteristics by fourier transform infrared (FT-IR) spectroscopy

USDA-ARS?s Scientific Manuscript database

Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...

Turbulent Fluid Motion 5: Fourier Analysis, the Spectral Form of the Continuum Equations, and Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Background material on Fourier analysis and on the spectral form of the continuum equations, both averaged and unaveraged, are given. The equations are applied to a number of cases of homogeneous turbulence with and without mean gradients. Spectral transfer of turbulent activity between scales of motion is studied in some detail. The effects of mean shear, heat transfer, normal strain, and buoyancy are included in the analyses.

Fourier analysis of the SOR iteration

NASA Technical Reports Server (NTRS)

Leveque, R. J.; Trefethen, L. N.

1986-01-01

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. It is shown that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

Recording multiple spatially-heterodyned direct to digital holograms in one digital image

DOEpatents

Hanson, Gregory R [Clinton, TN; Bingham, Philip R [Knoxville, TN

2008-03-25

Systems and methods are described for recording multiple spatially-heterodyned direct to digital holograms in one digital image. A method includes digitally recording, at a first reference beam-object beam angle, a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram to sit on top of a first spatial-heterodyne carrier frequency defined by the first reference beam-object beam angle; digitally recording, at a second reference beam-object beam angle, a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram to sit on top of a second spatial-heterodyne carrier frequency defined by the second reference beam-object beam angle; applying a first digital filter to cut off signals around the first original origin and define a first result; performing a first inverse Fourier transform on the first result; applying a second digital filter to cut off signals around the second original origin and define a second result; and performing a second inverse Fourier transform on the second result, wherein the first reference beam-object beam angle is not equal to the second reference beam-object beam angle and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Fast live cell imaging at nanometer scale using annihilating filter-based low-rank Hankel matrix approach

NASA Astrophysics Data System (ADS)

Min, Junhong; Carlini, Lina; Unser, Michael; Manley, Suliana; Ye, Jong Chul

2015-09-01

Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered as major limitation of localization microscopy. However, this higher density imaging needs to incorporate advanced localization algorithms to deal with overlapping point spread functions (PSFs). In order to address this technical challenges, previously we developed a localization algorithm called FALCON1, 2 using a quasi-continuous localization model with sparsity prior on image space. It was demonstrated in both 2D/3D live cell imaging. However, it has several disadvantages to be further improved. Here, we proposed a new localization algorithm using annihilating filter-based low rank Hankel structured matrix approach (ALOHA). According to ALOHA principle, sparsity in image domain implies the existence of rank-deficient Hankel structured matrix in Fourier space. Thanks to this fundamental duality, our new algorithm can perform data-adaptive PSF estimation and deconvolution of Fourier spectrum, followed by truly grid-free localization using spectral estimation technique. Furthermore, all these optimizations are conducted on Fourier space only. We validated the performance of the new method with numerical experiments and live cell imaging experiment. The results confirmed that it has the higher localization performances in both experiments in terms of accuracy and detection rate.

Reducing acquisition times in multidimensional NMR with a time-optimized Fourier encoding algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zhiyong; Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, Fujian 361005; Smith, Pieter E. S.

Speeding up the acquisition of multidimensional nuclear magnetic resonance (NMR) spectra is an important topic in contemporary NMR, with central roles in high-throughput investigations and analyses of marginally stable samples. A variety of fast NMR techniques have been developed, including methods based on non-uniform sampling and Hadamard encoding, that overcome the long sampling times inherent to schemes based on fast-Fourier-transform (FFT) methods. Here, we explore the potential of an alternative fast acquisition method that leverages a priori knowledge, to tailor polychromatic pulses and customized time delays for an efficient Fourier encoding of the indirect domain of an NMR experiment. Bymore » porting the encoding of the indirect-domain to the excitation process, this strategy avoids potential artifacts associated with non-uniform sampling schemes and uses a minimum number of scans equal to the number of resonances present in the indirect dimension. An added convenience is afforded by the fact that a usual 2D FFT can be used to process the generated data. Acquisitions of 2D heteronuclear correlation NMR spectra on quinine and on the anti-inflammatory drug isobutyl propionic phenolic acid illustrate the new method's performance. This method can be readily automated to deal with complex samples such as those occurring in metabolomics, in in-cell as well as in in vivo NMR applications, where speed and temporal stability are often primary concerns.« less

Iterative pixelwise approach applied to computer-generated holograms and diffractive optical elements.

PubMed

Hsu, Wei-Feng; Lin, Shih-Chih

2018-01-01

This paper presents a novel approach to optimizing the design of phase-only computer-generated holograms (CGH) for the creation of binary images in an optical Fourier transform system. Optimization begins by selecting an image pixel with a temporal change in amplitude. The modulated image function undergoes an inverse Fourier transform followed by the imposition of a CGH constraint and the Fourier transform to yield an image function associated with the change in amplitude of the selected pixel. In iterations where the quality of the image is improved, that image function is adopted as the input for the next iteration. In cases where the image quality is not improved, the image function before the pixel changed is used as the input. Thus, the proposed approach is referred to as the pixelwise hybrid input-output (PHIO) algorithm. The PHIO algorithm was shown to achieve image quality far exceeding that of the Gerchberg-Saxton (GS) algorithm. The benefits were particularly evident when the PHIO algorithm was equipped with a dynamic range of image intensities equivalent to the amplitude freedom of the image signal. The signal variation of images reconstructed from the GS algorithm was 1.0223, but only 0.2537 when using PHIO, i.e., a 75% improvement. Nonetheless, the proposed scheme resulted in a 10% degradation in diffraction efficiency and signal-to-noise ratio.

Enhanced dual-frequency pattern scheme based on spatial-temporal fringes method

NASA Astrophysics Data System (ADS)

Wang, Minmin; Zhou, Canlin; Si, Shuchun; Lei, Zhenkun; Li, Xiaolei; Li, Hui; Li, YanJie

2018-07-01

One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et al proposed a dual-frequency method based on the Fourier transform profilometry, yet the low-frequency lobes are close to each other for accurate band-pass filtering. In the light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequencies are required. The low-frequency phase is obtained from two low-frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high-frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method.

New Substrate-Guided Method of Predicting Slow Conducting Isthmuses of Ventricular Tachycardia: Preliminary Analysis to the Combined Use of Voltage Limit Adjustment and Fast-Fourier Transform Analysis.

PubMed

Kuroki, Kenji; Nogami, Akihiko; Igarashi, Miyako; Masuda, Keita; Kowase, Shinya; Kurosaki, Kenji; Komatsu, Yuki; Naruse, Yoshihisa; Machino, Takeshi; Yamasaki, Hiro; Xu, Dongzhu; Murakoshi, Nobuyuki; Sekiguchi, Yukio; Aonuma, Kazutaka

2018-04-01

Several conducting channels of ventricular tachycardia (VT) can be identified using voltage limit adjustment (VLA) of substrate mapping. However, the sensitivity or specificity to predict a VT isthmus is not high by using VLA alone. This study aimed to evaluate the efficacy of the combined use of VLA and fast-Fourier transform analysis to predict VT isthmuses. VLA and fast-Fourier transform analyses of local ventricular bipolar electrograms during sinus rhythm were performed in 9 postinfarction patients who underwent catheter ablation for a total of 13 monomorphic VTs. Relatively higher voltage areas on an electroanatomical map were defined as high voltage channels (HVCs), and relatively higher fast-Fourier transform areas were defined as high-frequency channels (HFCs). HVCs were classified into full or partial HVCs (the entire or >30% of HVC can be detectable, respectively). Twelve full HVCs were identified in 7 of 9 patients. HFCs were located on 7 of 12 full HVCs. Five VT isthmuses (71%) were included in the 7 full HVC+/HFC+ sites, whereas no VT isthmus was found in the 5 full HVC+/HFC- sites. HFCs were identical to 9 of 16 partial HVCs. Eight VT isthmuses (89%) were included in the 9 partial HVC+/HFC+ sites, whereas no VT isthmus was found in the 7 partial HVC+/HFC- sites. All HVC+/HFC+ sites predicted VT isthmus with a sensitivity of 100% and a specificity of 80%. Combined use of VLA and fast-Fourier transform analysis may be a useful method to detect VT isthmuses. © 2018 American Heart Association, Inc.

Limitations and potential of spectral subtractions in fourier-transform infrared (FTIR) spectroscopy of soil samples

USDA-ARS?s Scientific Manuscript database

Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...

Chemometric Analysis of Multicomponent Biodegradable Plastics by Fourier Transform Infrared Spectrometry: The R-Matrix Method

USDA-ARS?s Scientific Manuscript database

A new chemometric method based on absorbance ratios from Fourier transform infrared spectra was devised to analyze multicomponent biodegradable plastics. The method uses the BeerLambert law to directly compute individual component concentrations and weight losses before and after biodegradation of c...

Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy

NASA Astrophysics Data System (ADS)

Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks

2016-06-01

Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.

Characteristics of peripapillary retinal nerve fiber layer in preterm children.

PubMed

Wang, Jingyun; Spencer, Rand; Leffler, Joel N; Birch, Eileen E

2012-05-01

To examine quantitatively characteristics of the peripapillary retinal nerve fiber layer (RNFL) in preterm children using Fourier-domain optical coherence tomography (FD-OCT). Prospective cross-sectional study. A 3-mm high-resolution FD-OCT peripapillary RNFL circular scan centered on the optic disc was obtained from right eyes of 25 preterm children (10.6 ± 3.7 years old, 8 preterm and 17 with regressed retinopathy of prematurity with normal-appearing posterior poles) and 54 full-term controls (9.8 ± 3.2 years old). Images were analyzed using Spectralis FD-OCT software to obtain average thickness measurements for 6 sectors (temporal superior, temporal, temporal inferior, nasal inferior, nasal, nasal superior), and the global average. The RNFL global average for preterm children was 8% thinner than for full-term controls. In the preterm group, peripapillary RNFL thickness on the temporal side of the disc was 6% thicker than in full-term controls, while all other peripapillary RNFL sectors were 9% to 13% thinner. In the preterm group, temporal sector peripapillary RNFL thickness was correlated with gestational age (r = -0.47, P < .001), with foveal center total thickness (r = 0.48, P = .008, 1-tailed), and with visual acuity (r = 0.42; P = .026, 1-tailed). The significantly thinner RNFL global average for preterm children suggests that prematurity is associated with subclinical optic nerve hypoplasia. Significant correlations between temporal sector RNFL thickness and both the foveal thickness and visual acuity suggest that the peripapillary RNFL is related to abnormalities in macular development as a result of preterm birth. Copyright © 2012 Elsevier Inc. All rights reserved.

Frequency Management for Electromagnetic Continuous Wave Conductivity Meters

PubMed Central

Mazurek, Przemyslaw; Putynkowski, Grzegorz

2016-01-01

Ground conductivity meters use electromagnetic fields for the mapping of geological variations, like the determination of water amount, depending on ground layers, which is important for the state analysis of embankments. The VLF band is contaminated by numerous natural and artificial electromagnetic interference signals. Prior to the determination of ground conductivity, the meter’s working frequency is not possible, due to the variable frequency of the interferences. Frequency management based on the analysis of the selected band using track-before-detect (TBD) algorithms, which allows dynamical frequency changes of the conductivity of the meter transmitting part, is proposed in the paper. Naive maximum value search, spatio-temporal TBD (ST-TBD), Viterbi TBD and a new algorithm that uses combined ST-TBD and Viterbi TBD are compared. Monte Carlo tests are provided for the numerical analysis of the properties for a single interference signal in the considered band, and a new approach based on combined ST-TBD and Viterbi algorithms shows the best performance. The considered algorithms process spectrogram data for the selected band, so DFT (Discrete Fourier Transform) could be applied for the computation of the spectrogram. Real–time properties, related to the latency, are discussed also, and it is shown that TBD algorithms are feasible for real applications. PMID:27070608

Three-Way Analysis of Spectrospatial Electromyography Data: Classification and Interpretation

PubMed Central

Kauppi, Jukka-Pekka; Hahne, Janne; Müller, Klaus-Robert; Hyvärinen, Aapo

2015-01-01

Classifying multivariate electromyography (EMG) data is an important problem in prosthesis control as well as in neurophysiological studies and diagnosis. With modern high-density EMG sensor technology, it is possible to capture the rich spectrospatial structure of the myoelectric activity. We hypothesize that multi-way machine learning methods can efficiently utilize this structure in classification as well as reveal interesting patterns in it. To this end, we investigate the suitability of existing three-way classification methods to EMG-based hand movement classification in spectrospatial domain, as well as extend these methods by sparsification and regularization. We propose to use Fourier-domain independent component analysis as preprocessing to improve classification and interpretability of the results. In high-density EMG experiments on hand movements across 10 subjects, three-way classification yielded higher average performance compared with state-of-the art classification based on temporal features, suggesting that the three-way analysis approach can efficiently utilize detailed spectrospatial information of high-density EMG. Phase and amplitude patterns of features selected by the classifier in finger-movement data were found to be consistent with known physiology. Thus, our approach can accurately resolve hand and finger movements on the basis of detailed spectrospatial information, and at the same time allows for physiological interpretation of the results. PMID:26039100

Frequency Management for Electromagnetic Continuous Wave Conductivity Meters.

PubMed

Mazurek, Przemyslaw; Putynkowski, Grzegorz

2016-04-07

Ground conductivity meters use electromagnetic fields for the mapping of geological variations, like the determination of water amount, depending on ground layers, which is important for the state analysis of embankments. The VLF band is contaminated by numerous natural and artificial electromagnetic interference signals. Prior to the determination of ground conductivity, the meter's working frequency is not possible, due to the variable frequency of the interferences. Frequency management based on the analysis of the selected band using track-before-detect (TBD) algorithms, which allows dynamical frequency changes of the conductivity of the meter transmitting part, is proposed in the paper. Naive maximum value search, spatio-temporal TBD (ST-TBD), Viterbi TBD and a new algorithm that uses combined ST-TBD and Viterbi TBD are compared. Monte Carlo tests are provided for the numerical analysis of the properties for a single interference signal in the considered band, and a new approach based on combined ST-TBD and Viterbi algorithms shows the best performance. The considered algorithms process spectrogram data for the selected band, so DFT (Discrete Fourier Transform) could be applied for the computation of the spectrogram. Real-time properties, related to the latency, are discussed also, and it is shown that TBD algorithms are feasible for real applications.

Validation of Fourier analysis of videokeratographic data.

PubMed

Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios

2017-06-15

The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.

High resolution frequency analysis techniques with application to the redshift experiment

NASA Technical Reports Server (NTRS)

Decher, R.; Teuber, D.

1975-01-01

High resolution frequency analysis methods, with application to the gravitational probe redshift experiment, are discussed. For this experiment a resolution of .00001 Hz is required to measure a slowly varying, low frequency signal of approximately 1 Hz. Major building blocks include fast Fourier transform, discrete Fourier transform, Lagrange interpolation, golden section search, and adaptive matched filter technique. Accuracy, resolution, and computer effort of these methods are investigated, including test runs on an IBM 360/65 computer.

A Study of the Applicability of Atomic Emission Spectroscopy (AES), Fourier Transform Infrared (FT-IR) Spectroscopy, Direct Reading and Analytical Ferrography on High Performance Aircraft Engine Lubricating Oils

DTIC Science & Technology

1998-01-01

Ferrography on High Performance Aircraft Engine Lubricating Oils Allison M. Toms, Sharon 0. Hem, Tim Yarborough Joint Oil Analysis Program Technical...turbine engines by spectroscopy (AES and FT-IR) and direct reading and analytical ferrography . A statistical analysis of the data collected is...presented. Key Words: Analytical ferrography ; atomic emission spectroscopy; condition monitoring; direct reading ferrography ; Fourier transform infrared

Bladed wheels damage detection through Non-Harmonic Fourier Analysis improved algorithm

NASA Astrophysics Data System (ADS)

Neri, P.

2017-05-01

Recent papers introduced the Non-Harmonic Fourier Analysis for bladed wheels damage detection. This technique showed its potential in estimating the frequency of sinusoidal signals even when the acquisition time is short with respect to the vibration period, provided that some hypothesis are fulfilled. Anyway, previously proposed algorithms showed severe limitations in cracks detection at their early stage. The present paper proposes an improved algorithm which allows to detect a blade vibration frequency shift due to a crack whose size is really small compared to the blade width. Such a technique could be implemented for condition-based maintenance, allowing to use non-contact methods for vibration measurements. A stator-fixed laser sensor could monitor all the blades as they pass in front of the spot, giving precious information about the wheel health. This configuration determines an acquisition time for each blade which become shorter as the machine rotational speed increases. In this situation, traditional Discrete Fourier Transform analysis results in poor frequency resolution, being not suitable for small frequency shift detection. Non-Harmonic Fourier Analysis instead showed high reliability in vibration frequency estimation even with data samples collected in a short time range. A description of the improved algorithm is provided in the paper, along with a comparison with the previous one. Finally, a validation of the method is presented, based on finite element simulations results.

Fourier analysis of a vibrating string through a low-cost experimental setup and a smartphone

NASA Astrophysics Data System (ADS)

Pereyra, C. J.; Osorio, M.; Laguarda, A.; Gau, D. L.

2018-07-01

In this work we present a simple and low-cost setup to illustrate the dependence of the behaviour of a standing wave in a guitar string with the initial conditions. To do so, we impose two kinds of initial conditions; in the first instance, the initial shape of the string is varied. Secondly, different nodes are imposed on the string. This dependence was studied using the Fourier analysis of the sound produced by the vibration of the string with a smartphone. The simplicity of the proposed activity makes it suitable to be implemented in any classroom to illustrate the concept of normal modes and as an example of Fourier series in a real system that is also familiar for the students.

Content-based fused off-axis object illumination direct-to-digital holography

DOEpatents

Price, Jeffery R.

2006-05-02

Systems and methods are described for content-based fused off-axis illumination direct-to-digital holography. A method includes calculating an illumination angle with respect to an optical axis defined by a focusing lens as a function of data representing a Fourier analyzed spatially heterodyne hologram; reflecting a reference beam from a reference mirror at a non-normal angle; reflecting an object beam from an object the object beam incident upon the object at the illumination angle; focusing the reference beam and the object beam at a focal plane of a digital recorder to from the content-based off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; and digitally recording the content based off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis.

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

NASA Astrophysics Data System (ADS)

Chekroun, Mickaël D.; Kondrashov, Dmitri

2017-09-01

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey, furthermore, a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled—provided the decay of temporal correlations is sufficiently well-resolved—within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.

A new transform for the analysis of complex fractionated atrial electrograms

PubMed Central

2011-01-01

Background Representation of independent biophysical sources using Fourier analysis can be inefficient because the basis is sinusoidal and general. When complex fractionated atrial electrograms (CFAE) are acquired during atrial fibrillation (AF), the electrogram morphology depends on the mix of distinct nonsinusoidal generators. Identification of these generators using efficient methods of representation and comparison would be useful for targeting catheter ablation sites to prevent arrhythmia reinduction. Method A data-driven basis and transform is described which utilizes the ensemble average of signal segments to identify and distinguish CFAE morphologic components and frequencies. Calculation of the dominant frequency (DF) of actual CFAE, and identification of simulated independent generator frequencies and morphologies embedded in CFAE, is done using a total of 216 recordings from 10 paroxysmal and 10 persistent AF patients. The transform is tested versus Fourier analysis to detect spectral components in the presence of phase noise and interference. Correspondence is shown between ensemble basis vectors of highest power and corresponding synthetic drivers embedded in CFAE. Results The ensemble basis is orthogonal, and efficient for representation of CFAE components as compared with Fourier analysis (p ≤ 0.002). When three synthetic drivers with additive phase noise and interference were decomposed, the top three peaks in the ensemble power spectrum corresponded to the driver frequencies more closely as compared with top Fourier power spectrum peaks (p ≤ 0.005). The synthesized drivers with phase noise and interference were extractable from their corresponding ensemble basis with a mean error of less than 10%. Conclusions The new transform is able to efficiently identify CFAE features using DF calculation and by discerning morphologic differences. Unlike the Fourier transform method, it does not distort CFAE signals prior to analysis, and is relatively robust to jitter in periodic events. Thus the ensemble method can provide a useful alternative for quantitative characterization of CFAE during clinical study. PMID:21569421

CHARACTERIZATION OF AMBIENT PM2.5 AEROSOL AT A SOUTHEASTERN US SITE: FOURIER TRANSFORM INFRARED ANALYSIS OR PARTICLE PHASE

EPA Science Inventory

During a field study in the summer of 2000 in the Research Triangle Park (RTP), aerosol samples were collected using a five stage cascade impactor and subsequently analyzed using Fourier Transform Infrared Spectroscopy (FTIR). The impaction surfaces were stainless steel disks....

Novel hybrid optical correlator: theory and optical simulation.

PubMed

Casasent, D; Herold, R L

1975-02-01

The inverse transform of the product of two Fourier transform holograms is analyzed and shown to contain the correlation of the two images from which the holograms were formed. The theory, analysis, and initial experimental demonstration of the feasibility of a novel correlation scheme using this multiplied Fourier transform hologram system are presented.

Abel inversion using fast Fourier transforms.

PubMed

Kalal, M; Nugent, K A

1988-05-15

A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given.

Fourier analysis of blazar variability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Finke, Justin D.; Becker, Peter A., E-mail: justin.finke@nrl.navy.mil

Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and timemore » lag behaviors associated with variability in the synchrotron, synchrotron self-Compton, and external Compton emission components, from submillimeter to γ-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We also find that FSRQs should have steeper γ-ray PSD power-law indices than BL Lac objects at Fourier frequencies ≲ 10{sup –4} Hz, in qualitative agreement with previously reported observations by the Fermi Large Area Telescope.« less

On the Limitations of Taylor’s Hypothesis in Parker Solar Probe’s Measurements near the Alfvén Critical Point

NASA Astrophysics Data System (ADS)

Bourouaine, Sofiane; Perez, Jean C.

2018-05-01

In this Letter, we present an analysis of two-point, two-time correlation functions from high-resolution numerical simulations of Reflection-driven Alfvén Turbulence near the Alfvén critical point r c. The simulations model the turbulence in a prescribed background solar wind model chosen to match observational constraints. This analysis allows us to investigate the temporal decorrelation of solar wind turbulence and the validity of Taylor’s approximation near the heliocentric distance r c, which Parker Solar Probe (PSP) is expected to explore in the coming years. The simulations show that the temporal decay of the Fourier-transformed turbulence decorrelation function is better described by a Gaussian model rather than a pure exponential time decay, and that the decorrelation frequency is almost linear with perpendicular wave number k ⊥ (perpendicular with respect to the background magnetic field {{\\boldsymbol{B}}}0). Based on the simulations, we conclude that Taylor’s approximation cannot be used in this instance to provide a connection between the frequency ω of the time signal (measured in the probe frame) and the wavevector k ⊥ of the fluctuations because the frequency k ⊥ V sc (V sc is the spacecraft speed) near r c is comparable to the estimated decorrelation frequency. However, the use of Taylor’s approximation still leads to the correct spectral indices of the power spectra measured at the spacecraft frame. In this Letter, based on a Gaussian model, we suggest a modified relationship between ω and k ⊥, which might be useful in the interpretation of future PSP measurements.

Analysis of precipitable water vapor from GPS measurements in Chengdu region: Distribution and evolution characteristics in autumn

NASA Astrophysics Data System (ADS)

Wang, Hao; Wei, Ming; Li, Guoping; Zhou, Shenghui; Zeng, Qingfeng

2013-08-01

The rainfall process of Chengdu region in autumn has obvious regional features. Especially, the night-time rain rate of this region in this season is very high in China. Studying the spatial distribution and temporal variation of regional atmospheric precipitable water vapor (PWV) is important for our understanding of water vapor related processes, such as rainfall, evaporation, convective activity, among others in this area. Since GPS detection technology has the unique characteristics, such as all-weather, high accuracy, high spatial and temporal resolution as well as low cost, tracking and monitoring techniques on water vapor has achieved rapid developments in recent years. With GPS-PWV data at 30-min interval gathered from six GPS observational stations in Chengdu region in two autumns (September 2007-December 2007 and September 2008-December 2008), it is revealed that negative correlations exist between seasonally averaged value of GPS-PWV as well as its variation amplitude and local terrain altitude. The variation of PWV in the upper atmosphere of this region results from the water vapor variation from surface to 850 hPa. With the help of Fast Fourier Transform (FFT), it is found that the autumn PWV in Chengdu region has a multi-scale feature, which includes a seasonal cycle, 22.5 days period (quasi-tri-weekly oscillation). The variation of the GPS-PWV is related to periodical change in the transmitting of the water vapor caused by zonal and meridional wind strengths’ change and to the East Asian monsoon system. According to seasonal variation characteristics, we concluded that the middle October is the critical turning point in PWV content. On a shorter time scale, the relationship between autumn PWV and ground meteorological elements was obtained using the composite analysis approach.

Separation analysis, a tool for analyzing multigrid algorithms

NASA Technical Reports Server (NTRS)

Costiner, Sorin; Taasan, Shlomo

1995-01-01

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Schridubger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to choose performance relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.

AGARD Flight Test Techniques Series. Volume 14. Introduction to Flight Test Engineering (Introduction a la Technique d’essais en vol)

DTIC Science & Technology

1995-09-01

path and aircraft attitude and other flight or aircraft parameters • Calculations in the frequency domain ( Fast Fourier Transform) • Data analysis...Signal filtering Image processing of video and radar data Parameter identification Statistical analysis Power spectral density Fast Fourier Transform...airspeeds both fast and slow, altitude, load factor both above and below 1g, centers of gravity (fore and aft), and with system/subsystem failures. Whether

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Weighted network analysis of high-frequency cross-correlation measures

NASA Astrophysics Data System (ADS)

Iori, Giulia; Precup, Ovidiu V.

2007-03-01

In this paper we implement a Fourier method to estimate high-frequency correlation matrices from small data sets. The Fourier estimates are shown to be considerably less noisy than the standard Pearson correlation measures and thus capable of detecting subtle changes in correlation matrices with just a month of data. The evolution of correlation at different time scales is analyzed from the full correlation matrix and its minimum spanning tree representation. The analysis is performed by implementing measures from the theory of random weighted networks.

A fluctuation-induced plasma transport diagnostic based upon fast-Fourier transform spectral analysis

NASA Technical Reports Server (NTRS)

Powers, E. J.; Kim, Y. C.; Hong, J. Y.; Roth, J. R.; Krawczonek, W. M.

1978-01-01

A diagnostic, based on fast Fourier-transform spectral analysis techniques, that provides experimental insight into the relationship between the experimentally observable spectral characteristics of the fluctuations and the fluctuation-induced plasma transport is described. The model upon which the diagnostic technique is based and its experimental implementation is discussed. Some characteristic results obtained during the course of an experimental study of fluctuation-induced transport in the electric field dominated NASA Lewis bumpy torus plasma are presented.

An Interactive System For Fourier Analysis Of Artichoke Flower Shape.

NASA Astrophysics Data System (ADS)

Impedovo, Sebastiano; Fanelli, Anna M.; Ligouras, Panagiotis

1984-06-01

In this paper we present an interactive system which allows the Fourier analysis of the artichoke flower-head profile. The system consistsof a DEC pdp 11/34 computer with both a a track-following device and a Tektronix 4010/1 graphic and alpha numeric display on-line. Some experiments have been carried out taking into account some different parental types of artichoke flower-head samples. It is shown here that a narrow band of only eight harmonics is sufficient to classify different artichoke flower shapes.

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

NASA Technical Reports Server (NTRS)

Shakib, Farzin; Hughes, Thomas J. R.

1991-01-01

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

Synthesis of samarium doped gadolinium oxide nanorods, its spectroscopic and physical properties

NASA Astrophysics Data System (ADS)

Boopathi, G.; Gokul Raj, S.; Ramesh Kumar, G.; Mohan, R.; Mohan, S.

2018-06-01

One-dimensional samarium doped gadolinium oxide [Sm:Gd2O3] nanorods have been synthesized successfully through co-precipitation technique in aqueous solution. The as-synthesized and calcined products were characterized by using powder X-ray diffraction pattern, Fourier transform Raman spectroscopy, thermogravimetric/differential thermal analysis, scanning electron microscopy with energy-dispersive X-ray analysis, transmission electron microscopy, Fourier transform infrared spectroscopy, Ultraviolet-Visible spectrometry, photoluminescence spectrophotometer and X-ray photoelectron spectroscopy techniques. The obtained results are discussed in detailed manner.

New insight in quantitative analysis of vascular permeability during immune reaction (Conference Presentation)

NASA Astrophysics Data System (ADS)

Kalchenko, Vyacheslav; Molodij, Guillaume; Kuznetsov, Yuri; Smolyakov, Yuri; Israeli, David; Meglinski, Igor; Harmelin, Alon

2016-03-01

The use of fluorescence imaging of vascular permeability becomes a golden standard for assessing the inflammation process during experimental immune response in vivo. The use of the optical fluorescence imaging provides a very useful and simple tool to reach this purpose. The motivation comes from the necessity of a robust and simple quantification and data presentation of inflammation based on a vascular permeability. Changes of the fluorescent intensity, as a function of time is a widely accepted method to assess the vascular permeability during inflammation related to the immune response. In the present study we propose to bring a new dimension by applying a more sophisticated approach to the analysis of vascular reaction by using a quantitative analysis based on methods derived from astronomical observations, in particular by using a space-time Fourier filtering analysis followed by a polynomial orthogonal modes decomposition. We demonstrate that temporal evolution of the fluorescent intensity observed at certain pixels correlates quantitatively to the blood flow circulation at normal conditions. The approach allows to determine the regions of permeability and monitor both the fast kinetics related to the contrast material distribution in the circulatory system and slow kinetics associated with extravasation of the contrast material. Thus, we introduce a simple and convenient method for fast quantitative visualization of the leakage related to the inflammatory (immune) reaction in vivo.

Time-frequency analysis of neuronal populations with instantaneous resolution based on noise-assisted multivariate empirical mode decomposition.

PubMed

Alegre-Cortés, J; Soto-Sánchez, C; Pizá, Á G; Albarracín, A L; Farfán, F D; Felice, C J; Fernández, E

2016-07-15

Linear analysis has classically provided powerful tools for understanding the behavior of neural populations, but the neuron responses to real-world stimulation are nonlinear under some conditions, and many neuronal components demonstrate strong nonlinear behavior. In spite of this, temporal and frequency dynamics of neural populations to sensory stimulation have been usually analyzed with linear approaches. In this paper, we propose the use of Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD), a data-driven template-free algorithm, plus the Hilbert transform as a suitable tool for analyzing population oscillatory dynamics in a multi-dimensional space with instantaneous frequency (IF) resolution. The proposed approach was able to extract oscillatory information of neurophysiological data of deep vibrissal nerve and visual cortex multiunit recordings that were not evidenced using linear approaches with fixed bases such as the Fourier analysis. Texture discrimination analysis performance was increased when Noise-Assisted Multivariate Empirical Mode plus Hilbert transform was implemented, compared to linear techniques. Cortical oscillatory population activity was analyzed with precise time-frequency resolution. Similarly, NA-MEMD provided increased time-frequency resolution of cortical oscillatory population activity. Noise-Assisted Multivariate Empirical Mode Decomposition plus Hilbert transform is an improved method to analyze neuronal population oscillatory dynamics overcoming linear and stationary assumptions of classical methods. Copyright © 2016 Elsevier B.V. All rights reserved.

Buoyancy Effects on Flow Structure and Instability of Low-Density Gas Jets

NASA Technical Reports Server (NTRS)

Pasumarthi, Kasyap Sriramachandra

2004-01-01

A low-density gas jet injected into a high-density ambient gas is known to exhibit self-excited global oscillations accompanied by large vortical structures interacting with the flow field. The primary objective of the proposed research is to study buoyancy effects on the origin and nature of the flow instability and structure in the near-field of low-density gas jets. Quantitative rainbow schlieren deflectometry, Computational fluid dynamics (CFD) and Linear stability analysis were the techniques employed to scale the buoyancy effects. The formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and RMS concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed. The laminar, axisymmetric, unsteady jet flow of helium injected into air was simulated using CFD. Global oscillations were observed in the flow field. The computed oscillation frequency agreed qualitatively with the experimentally measured frequency. Contours of helium concentration, vorticity and velocity provided information about the evolution and propagation of vortices in the oscillating flow field. Buoyancy effects on the instability mode were evaluated by rainbow schlieren flow visualization and concentration measurements in the near-field of self-excited helium jets undergoing gravitational change in the microgravity environment of 2.2s drop tower at NASA John H. Glenn Research Center. The jet Reynolds number was varied from 200 to 1500 and jet Richardson number was varied from 0.72 to 0.002. Power spectra plots generated from Fast Fourier Transform (FFT) analysis of angular deflection data acquired at a temporal resolution of 1000Hz reveal substantial damping of the oscillation amplitude in microgravity at low Richardson numbers (0.002). Quantitative concentration data in the form of spatial and temporal evolutions of the instability data in Earth gravity and microgravity reveal significant variations in the jet flow structure upon removal of buoyancy forces. Radial variation of the frequency spectra and time traces of helium concentration revealed the importance of gravitational effects in the jet shear layer region. Linear temporal and spatio-temporal stability analyses of a low-density round gas jet injected into a high-density ambient gas were performed by assuming hyper-tan mean velocity and density profiles. The flow was assumed to be non parallel. Viscous and diffusive effects were ignored. The mean flow parameters were represented as the sum of the mean value and a small normal-mode fluctuation. A second order differential equation governing the pressure disturbance amplitude was derived from the basic conservation equations. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the temporal and spatio-temporal results were delineated. A decrease in the density ratio (ratio of the density of the jet to the density of the ambient gas) resulted in an increase in the temporal amplification rate of the disturbances. The temporal growth rate of the disturbances increased as the Froude number was reduced. The spatio-temporal analysis performed to determine the absolute instability characteristics of the jet yield positive absolute temporal growth rates at all Fr and different axial locations. As buoyancy was removed (Fr . 8), the previously existing absolute instability disappeared at all locations establhing buoyancy as the primary instability mechanism in self-excited low-density jets.

A 2D Fourier tool for the analysis of photo-elastic effect in large granular assemblies

NASA Astrophysics Data System (ADS)

Leśniewska, Danuta

2017-06-01

Fourier transforms are the basic tool in constructing different types of image filters, mainly those reducing optical noise. Some DIC or PIV software also uses frequency space to obtain displacement fields from a series of digital images of a deforming body. The paper presents series of 2D Fourier transforms of photo-elastic transmission images, representing large pseudo 2D granular assembly, deforming under varying boundary conditions. The images related to different scales were acquired using the same image resolution, but taken at different distance from the sample. Fourier transforms of images, representing different stages of deformation, reveal characteristic features at the three (`macro-`, `meso-` and `micro-`) scales, which can serve as a data to study internal order-disorder transition within granular materials.

Clustering change patterns using Fourier transformation with time-course gene expression data.

PubMed

Kim, Jaehee

2011-01-01

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a period of time because biologically related gene groups can share the same change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. This work is aimed at discovering gene groups with similar change patterns which share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. We applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns.

[Study on Differential Optical Absorption Spectroscopy Data Processing Based on Chirp-Z Transformation].

PubMed

Zheng, Hai-ming; Li, Guang-jie; Wu, Hao

2015-06-01

Differential optical absorption spectroscopy (DOAS) is a commonly used atmospheric pollution monitoring method. Denoising of monitoring spectral data will improve the inversion accuracy. Fourier transform filtering method is effectively capable of filtering out the noise in the spectral data. But the algorithm itself can introduce errors. In this paper, a chirp-z transform method is put forward. By means of the local thinning of Fourier transform spectrum, it can retain the denoising effect of Fourier transform and compensate the error of the algorithm, which will further improve the inversion accuracy. The paper study on the concentration retrieving of SO2 and NO2. The results show that simple division causes bigger error and is not very stable. Chirp-z transform is proved to be more accurate than Fourier transform. Results of the frequency spectrum analysis show that Fourier transform cannot solve the distortion and weakening problems of characteristic absorption spectrum. Chirp-z transform shows ability in fine refactoring of specific frequency spectrum.

Chemical fingerprinting of Arabidopsis using Fourier transform infrared (FT-IR) spectroscopic approaches.

PubMed

Gorzsás, András; Sundberg, Björn

2014-01-01

Fourier transform infrared (FT-IR) spectroscopy is a fast, sensitive, inexpensive, and nondestructive technique for chemical profiling of plant materials. In this chapter we discuss the instrumental setup, the basic principles of analysis, and the possibilities for and limitations of obtaining qualitative and semiquantitative information by FT-IR spectroscopy. We provide detailed protocols for four fully customizable techniques: (1) Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS): a sensitive and high-throughput technique for powders; (2) attenuated total reflectance (ATR) spectroscopy: a technique that requires no sample preparation and can be used for solid samples as well as for cell cultures; (3) microspectroscopy using a single element (SE) detector: a technique used for analyzing sections at low spatial resolution; and (4) microspectroscopy using a focal plane array (FPA) detector: a technique for rapid chemical profiling of plant sections at cellular resolution. Sample preparation, measurement, and data analysis steps are listed for each of the techniques to help the user collect the best quality spectra and prepare them for subsequent multivariate analysis.

Correcting sample drift using Fourier harmonics.

PubMed

Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L

2018-07-01

During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.

Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle

NASA Astrophysics Data System (ADS)

Oppenheim, Jacob N.; Magnasco, Marcelo O.

2013-01-01

The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than 1/(4π). We study human ability to simultaneously judge the frequency and the timing of a sound. Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold, mostly through remarkable timing acuity. Our results establish a lower bound for the nonlinearity and complexity of the algorithms employed by our brains in parsing transient sounds, rule out simple “linear filter” models of early auditory processing, and highlight timing acuity as a central feature in auditory object processing.

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

NASA Astrophysics Data System (ADS)

Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

2018-06-01

Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

Experimental determination of pore shapes using phase retrieval from q -space NMR diffraction

NASA Astrophysics Data System (ADS)

Demberg, Kerstin; Laun, Frederik Bernd; Bertleff, Marco; Bachert, Peter; Kuder, Tristan Anselm

2018-05-01

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q -space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Regridding reconstruction algorithm for real-time tomographic imaging

PubMed Central

Marone, F.; Stampanoni, M.

2012-01-01

Sub-second temporal-resolution tomographic microscopy is becoming a reality at third-generation synchrotron sources. Efficient data handling and post-processing is, however, difficult when the data rates are close to 10 GB s−1. This bottleneck still hinders exploitation of the full potential inherent in the ultrafast acquisition speed. In this paper the fast reconstruction algorithm gridrec, highly optimized for conventional CPU technology, is presented. It is shown that gridrec is a valuable alternative to standard filtered back-projection routines, despite being based on the Fourier transform method. In fact, the regridding procedure used for resampling the Fourier space from polar to Cartesian coordinates couples excellent performance with negligible accuracy degradation. The stronger dependence of the observed signal-to-noise ratio for gridrec reconstructions on the number of angular views makes the presented algorithm even superior to filtered back-projection when the tomographic problem is well sampled. Gridrec not only guarantees high-quality results but it provides up to 20-fold performance increase, making real-time monitoring of the sub-second acquisition process a reality. PMID:23093766

Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction.

PubMed

Demberg, Kerstin; Laun, Frederik Bernd; Bertleff, Marco; Bachert, Peter; Kuder, Tristan Anselm

2018-05-01

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q-space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Evaluation of parameters of a plankton community's biological rhythms under the natural environment of the Black Sea using the Fourier transform method.

PubMed

Mel'nikova, Ye B

2017-05-01

Night-time changes in bioluminescence intensity in the coastal area of the Black Sea were recorded. It was noted that the biomass of luminous organisms is closely correlated with the biomass of plankton and other pelagic organisms, including commercial pelagic fish. The parameters of plankton communities' basic biological rhythms were determined using the discrete Fourier transform method. These rhythms were manifest as spatial and temporal changes in the bioluminescence intensity. It was shown that changes in the bioluminescence intensity over a 14.0-h period were due to the duration of the light/dark cycles. By contrast, changes in bioluminescence intensity with periods of 4.7 and 2.8 h were due to the endogenous rhythms of the plankton community (feeding and cell division). An original method for evaluating of errors in the calculated periods of the biological rhythms was proposed. A strong correlation (r = 0.906) was observed between the measured and calculated values for the bioluminescence intensity, which provided support for the assumptions made. Copyright © 2016 John Wiley & Sons, Ltd.

Introduction to Fourier Optics

ERIC Educational Resources Information Center

Huggins, Elisha

2007-01-01

Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…

Fourier Descriptor Analysis and Unification of Voice Range Profile Contours: Method and Applications

ERIC Educational Resources Information Center

Pabon, Peter; Ternstrom, Sten; Lamarche, Anick

2011-01-01

Purpose: To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. Method: A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the…

Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method

ERIC Educational Resources Information Center

Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.

2013-01-01

Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…

Rapid identification and classification of Listeria spp. and serotype assignment of Listeria monocytogenes using fourier transform-infrared spectroscopy and artificial neural network analysis

USDA-ARS?s Scientific Manuscript database

The use of Fourier Transform-Infrared Spectroscopy (FT-IR) in conjunction with Artificial Neural Network software, NeuroDeveloper™ was examined for the rapid identification and classification of Listeria species and serotyping of Listeria monocytogenes. A spectral library was created for 245 strains...

Assessing the Atrial Electromechanical Coupling during Atrial Focal Tachycardia, Flutter, and Fibrillation using Electromechanical Wave Imaging in Humans

PubMed Central

Provost, Jean; Costet, Alexandre; Wan, Elaine; Gambhir, Alok; Whang, William; Garan, Hasan; Konofagou, Elisa E.

2015-01-01

Minimally-invasive treatments of cardiac arrhythmias such as radio-frequency ablation are gradually gaining in importance in clinical practice but still lack a noninvasive imaging modality which provides insight into the source or focus of an arrhythmia. Cardiac deformations imaged at high temporal and spatial resolution can be used to elucidate the electrical activation sequence in normal and paced human subjects non-invasively and could potentially aid to better plan and monitor ablation-based arrhythmia treatments. In this study, a novel ultrasound-based method is presented that can be used to quantitatively characterize focal and reentrant arrhythmias. Spatio-temporal maps of the full-view of the atrial and ventricular mechanics were obtained in a single heartbeat, revealing with otherwise unobtainable detail the electromechanical patterns of atrial flutter, fibrillation, and tachycardia in humans. During focal arrhythmias such as premature ventricular complex and focal atrial tachycardia, the previously developed electromechanical wave imaging methodology is hereby shown capable of identifying the location of the focal zone and the subsequent propagation of cardiac activation. During reentrant arrhythmias such as atrial flutter and fibrillation, Fourier analysis of the strains revealed highly correlated mechanical and electrical cycle lengths and propagation patterns. High frame rate ultrasound imaging of the heart can be used non-invasively and in real time, to characterize the lesser-known mechanical aspects of atrial and ventricular arrhythmias, also potentially assisting treatment planning for intraoperative and longitudinal monitoring of arrhythmias. PMID:26361338

Temporal Variability of Total Ozone in the Asian Region Inferred from Ground-Based and Satellite Measurement Data

NASA Astrophysics Data System (ADS)

Visheratin, K. N.; Nerushev, A. F.; Orozaliev, M. D.; Zheng, Xiangdong; Sun, Shumen; Liu, Li

2017-12-01

This paper reports investigation data on the temporal variability of total ozone content (TOC) in the Central Asian and Tibet Plateau mountain regions obtained by conventional methods, as well as by spectral, cross-wavelet, and composite analyses. The data of ground-based observation stations located at Huang He, Kunming, and Lake Issyk-Kul, along with the satellite data obtained at SBUV/SBUV2 (SBUV merged total and profile ozone data, Version 8.6) for 1980-2013 and OMI (Ozone Monitoring Instrument) and TOU (Total Ozone Unit) for 2009-2013 have been used. The average relative deviation from the SBUV/SBUV2 data is less than 1% in Kunming and Issyk-Kul for the period of 1980-2013, while the Huang He Station is characterized by an excess of the satellite data over the ground-based information at an average deviation of 2%. According to the Fourier analysis results, the distribution of amplitudes and the periods of TOC oscillations within a range of over 14 months is similar for all series analyzed. Meanwhile, according to the cross-wavelet and composite analyses results, the phase relationships between the series may considerably differ, especially in the periods of 5-7 years. The phase of quasi-decennial oscillations in the Kunming Station is close to the 11-year oscillations of the solar cycle, while in the Huang He and Issyk-Kul stations the TOC variations go ahead of the solar cycle.

A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

Thermal Stress Analysis of a Continuous and Pulsed End-Pumped Nd:YAG Rod Crystal Using Non-Classic Conduction Heat Transfer Theory

NASA Astrophysics Data System (ADS)

Mojahedi, Mahdi; Shekoohinejad, Hamidreza

2018-02-01

In this paper, temperature distribution in the continuous and pulsed end-pumped Nd:YAG rod crystal is determined using nonclassical and classical heat conduction theories. In order to find the temperature distribution in crystal, heat transfer differential equations of crystal with consideration of boundary conditions are derived based on non-Fourier's model and temperature distribution of the crystal is achieved by an analytical method. Then, by transferring non-Fourier differential equations to matrix equations, using finite element method, temperature and stress of every point of crystal are calculated in the time domain. According to the results, a comparison between classical and nonclassical theories is represented to investigate rupture power values. In continuous end pumping with equal input powers, non-Fourier theory predicts greater temperature and stress compared to Fourier theory. It also shows that with an increase in relaxation time, crystal rupture power decreases. Despite of these results, in single rectangular pulsed end-pumping condition, with an equal input power, Fourier theory indicates higher temperature and stress rather than non-Fourier theory. It is also observed that, when the relaxation time increases, maximum amounts of temperature and stress decrease.

Two-dimensional auto-correlation analysis and Fourier-transform analysis of second-harmonic-generation image for quantitative analysis of collagen fiber in human facial skin

NASA Astrophysics Data System (ADS)

Ogura, Yuki; Tanaka, Yuji; Hase, Eiji; Yamashita, Toyonobu; Yasui, Takeshi

2018-02-01

We compare two-dimensional auto-correlation (2D-AC) analysis and two-dimensional Fourier transform (2D-FT) for evaluation of age-dependent structural change of facial dermal collagen fibers caused by intrinsic aging and extrinsic photo-aging. The age-dependent structural change of collagen fibers for female subjects' cheek skin in their 20s, 40s, and 60s were more noticeably reflected in 2D-AC analysis than in 2D-FT analysis. Furthermore, 2D-AC analysis indicated significantly higher correlation with the skin elasticity measured by Cutometer® than 2D-AC analysis. 2D-AC analysis of SHG image has a high potential for quantitative evaluation of not only age-dependent structural change of collagen fibers but also skin elasticity.

Image quality analysis of a color LCD as well as a monochrome LCD using a Foveon color CMOS camera

NASA Astrophysics Data System (ADS)

Dallas, William J.; Roehrig, Hans; Krupinski, Elizabeth A.

2007-09-01

We have combined a CMOS color camera with special software to compose a multi-functional image-quality analysis instrument. It functions as a colorimeter as well as measuring modulation transfer functions (MTF) and noise power spectra (NPS). It is presently being expanded to examine fixed-pattern noise and temporal noise. The CMOS camera has 9 μm square pixels and a pixel matrix of 2268 x 1512 x 3. The camera uses a sensor that has co-located pixels for all three primary colors. We have imaged sections of both a color and a monochrome LCD monitor onto the camera sensor with LCD-pixel-size to camera-pixel-size ratios of both 12:1 and 17.6:1. When used as an imaging colorimeter, each camera pixel is calibrated to provide CIE color coordinates and tristimulus values. This capability permits the camera to simultaneously determine chromaticity in different locations on the LCD display. After the color calibration with a CS-200 colorimeter the color coordinates of the display's primaries determined from the camera's luminance response are very close to those found from the CS-200. Only the color coordinates of the display's white point were in error. For calculating the MTF a vertical or horizontal line is displayed on the monitor. The captured image is color-matrix preprocessed, Fourier transformed then post-processed. For NPS, a uniform image is displayed on the monitor. Again, the image is pre-processed, transformed and processed. Our measurements show that the horizontal MTF's of both displays have a larger negative slope than that of the vertical MTF's. This behavior indicates that the horizontal MTF's are poorer than the vertical MTF's. However the modulations at the Nyquist frequency seem lower for the color LCD than for the monochrome LCD. The spatial noise of the color display in both directions is larger than that of the monochrome display. Attempts were also made to analyze the total noise in terms of spatial and temporal noise by applying subtractions of images taken at exactly the same exposure. Temporal noise seems to be significantly lower than spatial noise.

Transitions between central and peripheral vision create spatial/temporal distortions: a hypothesis concerning the perceived break of the curveball.

PubMed

Shapiro, Arthur; Lu, Zhong-Lin; Huang, Chang-Bing; Knight, Emily; Ennis, Robert

2010-10-13

The human visual system does not treat all parts of an image equally: the central segments of an image, which fall on the fovea, are processed with a higher resolution than the segments that fall in the visual periphery. Even though the differences between foveal and peripheral resolution are large, these differences do not usually disrupt our perception of seamless visual space. Here we examine a motion stimulus in which the shift from foveal to peripheral viewing creates a dramatic spatial/temporal discontinuity. The stimulus consists of a descending disk (global motion) with an internal moving grating (local motion). When observers view the disk centrally, they perceive both global and local motion (i.e., observers see the disk's vertical descent and the internal spinning). When observers view the disk peripherally, the internal portion appears stationary, and the disk appears to descend at an angle. The angle of perceived descent increases as the observer views the stimulus from further in the periphery. We examine the first- and second-order information content in the display with the use of a three-dimensional Fourier analysis and show how our results can be used to describe perceived spatial/temporal discontinuities in real-world situations. The perceived shift of the disk's direction in the periphery is consistent with a model in which foveal processing separates first- and second-order motion information while peripheral processing integrates first- and second-order motion information. We argue that the perceived distortion may influence real-world visual observations. To this end, we present a hypothesis and analysis of the perception of the curveball and rising fastball in the sport of baseball. The curveball is a physically measurable phenomenon: the imbalance of forces created by the ball's spin causes the ball to deviate from a straight line and to follow a smooth parabolic path. However, the curveball is also a perceptual puzzle because batters often report that the flight of the ball undergoes a dramatic and nearly discontinuous shift in position as the ball nears home plate. We suggest that the perception of a discontinuous shift in position results from differences between foveal and peripheral processing.

Multifocal Visual Evoked Potential in Eyes With Temporal Hemianopia From Chiasmal Compression: Correlation With Standard Automated Perimetry and OCT Findings.

PubMed

Sousa, Rafael M; Oyamada, Maria K; Cunha, Leonardo P; Monteiro, Mário L R

2017-09-01

To verify whether multifocal visual evoked potential (mfVEP) can differentiate eyes with temporal hemianopia due to chiasmal compression from healthy controls. To assess the relationship between mfVEP, standard automated perimetry (SAP), and Fourier domain-optical coherence tomography (FD-OCT) macular and peripapillary retinal nerve fiber layer (RNFL) thickness measurements. Twenty-seven eyes with permanent temporal visual field (VF) defects from chiasmal compression on SAP and 43 eyes of healthy controls were submitted to mfVEP and FD-OCT scanning. Multifocal visual evoked potential was elicited using a stimulus pattern of 60 sectors and the responses were averaged for the four quadrants and two hemifields. Optical coherence tomography macular measurements were averaged in quadrants and halves, while peripapillary RNFL thickness was averaged in four sectors around the disc. Visual field loss was estimated in four quadrants and each half of the 24-2 strategy test points. Multifocal visual evoked potential measurements in the two groups were compared using generalized estimated equations, and the correlations between mfVEP, VF, and OCT findings were quantified. Multifocal visual evoked potential-measured temporal P1 and N2 amplitudes were significantly smaller in patients than in controls. No significant difference in amplitude was observed for nasal parameters. A significant correlation was found between mfVEP amplitudes and temporal VF loss, and between mfVEP amplitudes and the corresponding OCT-measured macular and RNFL thickness parameters. Multifocal visual evoked potential amplitude parameters were able to differentiate eyes with temporal hemianopia from controls and were significantly correlated with VF and OCT findings, suggesting mfVEP is a useful tool for the detection of visual abnormalities in patients with chiasmal compression.

Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse

NASA Astrophysics Data System (ADS)

Kalasinsky, Kathryn S.; Levine, Barry K.; Smith, Michael L.; Magluilo, Joseph J.; Schaefer, Teresa

1994-01-01

Cryogenic deposition techniques for Gas Chromatography/Fourier Transform Infrared (GC/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography/Mass Spectrometry (GC/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of abuse can be confused with over-the-counter medications or naturally occurring amines. Hair analysis has been important in drug testing when adulteration of urine samples has been a question. Functional group mapping can further assist the analysis and track drug use versus time.

A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis

NASA Technical Reports Server (NTRS)

Ioup, G. E.

1980-01-01

Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.

Fourier analysis of conductive heat transfer for glazed roofing materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja

For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heatmore » transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.« less

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia.

PubMed

Samsir, Sri A'jilah; Bunawan, Hamidun; Yen, Choong Chee; Noor, Normah Mohd

2016-09-01

In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600-3100 cm(-) (1) in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA) of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (South) were clustered together in one group while samples from Perak, Kedah, Penang, Selangor, Kelantan, and Terengganu (North and East Coast) were in another clustered group.

Detection of increase in corneal irregularity due to pterygium using Fourier series harmonic analyses with multiple diameters.

PubMed

Minami, Keiichiro; Miyata, Kazunori; Otani, Atsushi; Tokunaga, Tadatoshi; Tokuda, Shouta; Amano, Shiro

2018-05-01

To determine steep increase of corneal irregularity induced by advancement of pterygium. A total of 456 eyes from 456 consecutive patients with primary pterygia were examined for corneal topography and advancement of pterygium with respect to the corneal diameter. Corneal irregularity induced by the pterygium advancement was evaluated by Fourier harmonic analyses of the topographic data that were modified for a series of analysis diameters from 1 mm to 6 mm. Incidences of steep increases in the asymmetry or higher-order irregularity components (inflection points) were determined by using segmented regression analysis for each analysis diameter. The pterygium advancement ranged from 2% to 57%, with a mean of 22.0%. Both components showed steep increases from the inflection points. The inflection points in the higher-order irregularity component altered with the analysis diameter (14.0%-30.6%), while there was no alternation in the asymmetry components (35.5%-36.8%). For the former component, the values at the inflection points were obtained in a range of 0.16 to 0.25 D. The Fourier harmonic analyses for a series of analysis diameters revealed that the higher-order irregularity component increased with the pterygium advancement. The analysis results confirmed the precedence of corneal irregularity due to pterygium advancement.

Analysis of the Fourier Spectrum of the ν2 Inversion Band of the 15NHD2 Molecule

NASA Astrophysics Data System (ADS)

Fomchenko, A. L.; Belova, A. S.; Bekhtereva, E. S.; Kwabia Tchana, F.

2018-06-01

To determine high-resolution rovibrational levels of the inversion vibrational (v2 = 1) state of the 15NHD2 molecule, the Fourier spectrum in the range from 650 to 1150 cm-1 is studied. The data obtained are used to determine the parameters of the effective Hamiltonian of the examined molecule.

Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods

NASA Astrophysics Data System (ADS)

Garbanzo-Salas, Marcial; Hocking, Wayne. K.

2015-09-01

In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.

Molecular Isotopic Distribution Analysis (MIDAs) with Adjustable Mass Accuracy

NASA Astrophysics Data System (ADS)

Alves, Gelio; Ogurtsov, Aleksey Y.; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

Molecular Isotopic Distribution Analysis (MIDAs) with adjustable mass accuracy.

PubMed

Alves, Gelio; Ogurtsov, Aleksey Y; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

Holographic maps of quasiparticle interference

NASA Astrophysics Data System (ADS)

Dalla Torre, Emanuele G.; He, Yang; Demler, Eugene

2016-11-01

The analysis of Fourier-transformed scanning tunnelling microscopy images with subatomic resolution is a common tool for studying the properties of quasiparticle excitations in strongly correlated materials. Although Fourier amplitudes are generally complex valued, earlier analysis primarily focused on their absolute values. Their complex phases were often deemed random, and thus irrelevant, due to the unknown positions of the impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously unknown information about the electronic structures. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that d-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in scanning tunnelling microscopy.

Fourier analysis: from cloaking to imaging

NASA Astrophysics Data System (ADS)

Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping

2016-04-01

Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.

Application of open-path Fourier transform infrared spectroscopy for atmospheric monitoring of a CO2 back-production experiment at the Ketzin pilot site (Germany).

PubMed

Sauer, Uta; Borsdorf, H; Dietrich, P; Liebscher, A; Möller, I; Martens, S; Möller, F; Schlömer, S; Schütze, C

2018-02-03

During a controlled "back-production experiment" in October 2014 at the Ketzin pilot site, formerly injected CO 2 was retrieved from the storage formation and directly released to the atmosphere via a vent-off stack. Open-path Fourier transform infrared (OP FTIR) spectrometers, on-site meteorological parameter acquisition systems, and distributed CO 2 point sensors monitored gas dispersion processes in the near-surface part of the atmospheric boundary layer. The test site provides a complex and challenging mosaic-like surface setting for atmospheric monitoring which can also be found at other storage sites. The main aims of the atmospheric monitoring of this experiment were (1) to quantify temporal and spatial variations in atmospheric CO 2 concentrations around the emitting vent-off stack and (2) to test if and how atmospheric monitoring can cope with typical environmental and operational challenges. A low environmental risk was encountered during the whole CO 2 back-production experiment. The study confirms that turbulent wind conditions favor atmospheric mixing processes and are responsible for rapid dilution of the released CO 2 leading to decreased detectability at all sensors. In contrast, calm and extremely stable wind conditions (especially occurring during the night) caused an accumulation of gases in the near-ground atmospheric layer with the highest amplitudes in measured gas concentration. As an important benefit of OP FTIR spectroscopic measurements and their ability to detect multiple gas species simultaneously, emission sources could be identified to a much higher certainty. Moreover, even simulation models using simplified assumptions help to find suitable monitoring network designs and support data analysis for certain wind conditions in such a complex environment.

A low-cost experiment to visualise the Fourier series: video analysis of a real plucked coiled spring

NASA Astrophysics Data System (ADS)

de Jesus, V. L. B.; Haubrichs, C.; de Oliveira, A. L.; Sasaki, D. G. G.

2018-03-01

In the present work, we develop a low-cost and simple experiment to visualise Fourier’s synthesis using a short, soft, and light plastic coiled spring oscillating in a horizontal plane, and a basic camera (120 fps). It is shown that the spring obeys a linear wave differential equation, as gravitational influence is neglected. A nonlinear criterion is evaluated to determine if magnitudes of the parameters in the initial conditions satisfy the linear wave equation. Our setup promotes some desirable characteristics that make Fourier’s synthesis experiments feasible, visual, and enlightening: (i) it requires few, common, and cheap resources, and the experiment can be carried out even in a high-school laboratory; (ii) since the spring’s tension is small (∼1 N, on average), the frequencies of normal modes are low (close to 2 Hz), and therefore, it is possible to record the oscillations just with the camera and extract a considerable number of position and time data in just one cycle; (iii) when the video is loaded in the Tracker free software, it can be reproduced in slow motion. Since the frequencies involved are low, an interesting and instructive temporal sequence of images of the spring displaying the typical trapezoidal shape appears clearly; (iv) the tools associated with the Tracker software tools can yield the relevant oscillation parameters, such as the damping constant, amplitudes, frequencies, and phases; and (v) it is possible to carry out superposition of a snapshot of the spring in Tracker at any time, and to draw the related Fourier synthesis graphs. The visual match between the shape of the spring and the theoretical graph is remarkable, and can be enhanced by adding the damping term.

From moonlight to movement and synchronized randomness: Fourier and wavelet analyses of animal location time series data

PubMed Central

Polansky, Leo; Wittemyer, George; Cross, Paul C.; Tambling, Craig J.; Getz, Wayne M.

2011-01-01

High-resolution animal location data are increasingly available, requiring analytical approaches and statistical tools that can accommodate the temporal structure and transient dynamics (non-stationarity) inherent in natural systems. Traditional analyses often assume uncorrelated or weakly correlated temporal structure in the velocity (net displacement) time series constructed using sequential location data. We propose that frequency and time–frequency domain methods, embodied by Fourier and wavelet transforms, can serve as useful probes in early investigations of animal movement data, stimulating new ecological insight and questions. We introduce a novel movement model with time-varying parameters to study these methods in an animal movement context. Simulation studies show that the spectral signature given by these methods provides a useful approach for statistically detecting and characterizing temporal dependency in animal movement data. In addition, our simulations provide a connection between the spectral signatures observed in empirical data with null hypotheses about expected animal activity. Our analyses also show that there is not a specific one-to-one relationship between the spectral signatures and behavior type and that departures from the anticipated signatures are also informative. Box plots of net displacement arranged by time of day and conditioned on common spectral properties can help interpret the spectral signatures of empirical data. The first case study is based on the movement trajectory of a lion (Panthera leo) that shows several characteristic daily activity sequences, including an active–rest cycle that is correlated with moonlight brightness. A second example based on six pairs of African buffalo (Syncerus caffer) illustrates the use of wavelet coherency to show that their movements synchronize when they are within ∼1 km of each other, even when individual movement was best described as an uncorrelated random walk, providing an important spatial baseline of movement synchrony and suggesting that local behavioral cues play a strong role in driving movement patterns. We conclude with a discussion about the role these methods may have in guiding appropriately flexible probabilistic models connecting movement with biotic and abiotic covariates. PMID:20503882

Feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory.

PubMed

Wang, Haoyu; Miao, Yanwei; Zhou, Kun; Yu, Yanming; Bao, Shanglian; He, Qiang; Dai, Yongming; Xuan, Stephanie Y; Tarabishy, Bisher; Ye, Yongquan; Hu, Jiani

2010-09-01

To investigate the feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory. Two experiments were designed to investigate the feasibility of using reference image based compressed sensing (RICS) technique in DCE-MRI of the breast. The first experiment examined the capability of RICS to faithfully reconstruct uptake curves using undersampled data sets extracted from fully sampled clinical breast DCE-MRI data. An average approach and an approach using motion estimation and motion compensation (ME/MC) were implemented to obtain reference images and to evaluate their efficacy in reducing motion related effects. The second experiment, an in vitro phantom study, tested the feasibility of RICS for improving temporal resolution without degrading the spatial resolution. For the uptake-curve reconstruction experiment, there was a high correlation between uptake curves reconstructed from fully sampled data by Fourier transform and from undersampled data by RICS, indicating high similarity between them. The mean Pearson correlation coefficients for RICS with the ME/MC approach and RICS with the average approach were 0.977 +/- 0.023 and 0.953 +/- 0.031, respectively. The comparisons of final reconstruction results between RICS with the average approach and RICS with the ME/MC approach suggested that the latter was superior to the former in reducing motion related effects. For the in vitro experiment, compared to the fully sampled method, RICS improved the temporal resolution by an acceleration factor of 10 without degrading the spatial resolution. The preliminary study demonstrates the feasibility of RICS for faithfully reconstructing uptake curves and improving temporal resolution of breast DCE-MRI without degrading the spatial resolution.

Eddy current simulation in thick cylinders of finite length induced by coils of arbitrary geometry.

PubMed

Sanchez Lopez, Hector; Poole, Michael; Crozier, Stuart

2010-12-01

Eddy currents are inevitably induced when time-varying magnetic field gradients interact with the metallic structures of a magnetic resonance imaging (MRI) scanner. The secondary magnetic field produced by this induced current degrades the spatial and temporal performance of the primary field generated by the gradient coils. Although this undesired effect can be minimized by using actively and/or passively shielded gradient coils and current pre-emphasis techniques, a residual eddy current still remains in the MRI scanner structure. Accurate simulation of these eddy currents is important in the successful design of gradient coils and magnet cryostat vessels. Efficient methods for simulating eddy currents are currently restricted to cylindrical-symmetry. The approach presented in this paper divides thick conducting cylinders into thin layers (thinner than the skin depth) and expresses the current density on each as a Fourier series. The coupling between each mode of the Fourier series with every other is modeled with an inductive network method. In this way, the eddy currents induced in realistic cryostat surfaces by coils of arbitrary geometry can be simulated. The new method was validated by simulating a canonical problem and comparing the results against a commercially available software package. An accurate skin depth of 2.76 mm was calculated in 6 min with the new method. The currents induced by an actively shielded x-gradient coil were simulated assuming a finite length cylindrical cryostat consisting of three different conducting materials. Details of the temporal-spatial induced current diffusion process were simulated through all cryostat layers, which could not be efficiently simulated with any other method. With this data, all quantities that depend on the current density, such as the secondary magnetic field, are simply evaluated. Copyright © 2010 Elsevier Inc. All rights reserved.

A VLSI architecture for simplified arithmetic Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.

1992-01-01

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

An Environmental Data Set for Vector-Borne Disease Modeling and Epidemiology

PubMed Central

Chabot-Couture, Guillaume; Nigmatulina, Karima; Eckhoff, Philip

2014-01-01

Understanding the environmental conditions of disease transmission is important in the study of vector-borne diseases. Low- and middle-income countries bear a significant portion of the disease burden; but data about weather conditions in those countries can be sparse and difficult to reconstruct. Here, we describe methods to assemble high-resolution gridded time series data sets of air temperature, relative humidity, land temperature, and rainfall for such areas; and we test these methods on the island of Madagascar. Air temperature and relative humidity were constructed using statistical interpolation of weather station measurements; the resulting median 95th percentile absolute errors were 2.75°C and 16.6%. Missing pixels from the MODIS11 remote sensing land temperature product were estimated using Fourier decomposition and time-series analysis; thus providing an alternative to the 8-day and 30-day aggregated products. The RFE 2.0 remote sensing rainfall estimator was characterized by comparing it with multiple interpolated rainfall products, and we observed significant differences in temporal and spatial heterogeneity relevant to vector-borne disease modeling. PMID:24755954

Molecular-level dynamics of refractory dissolved organic matter

NASA Astrophysics Data System (ADS)

Niggemann, J.; Gerdts, G.; Dittmar, T.

2012-04-01

Refractory dissolved organic matter (DOM) accounts for most of the global oceanic organic carbon inventory. Processes leading to its formation and factors determining its stability are still largely unknown. We hypothesize that refractory DOM carries a universal molecular signature. Characterizing spatial and temporal variability in this universal signature is a key to understanding dynamics of refractory DOM. We present results from a long-term study of the DOM geo-metabolome in the open North Sea. Geo-metabolomics considers the entity of DOM as a population of compounds, each characterized by a specific function and reactivity in the cycling of energy and elements. Ten-thousands of molecular formulae were identified in DOM by ultrahigh resolution mass spectrometry analysis (FT-ICR-MS, Fourier-Transform Ion Cyclotron Resonance Mass Spectrometry). The DOM pool in the North Sea was influenced by a complex interplay of processes that produced, transformed and degraded dissolved molecules. We identified a stable fraction in North Sea DOM with a molecular composition similar to deep ocean DOM. Molecular-level changes in this stable fraction provide novel information on dynamics and interactions of refractory DOM.

Mapping landscape phenology preference of yellow-billed cuckoo with AVHRR data

USGS Publications Warehouse

Wallace, Cynthia S.A.; Villarreal, Miguel; van Riper, Charles

2013-01-01

We mapped habitat for threatened Yellow-billed Cuckoo (Coccycus americanus occidentalis) in the State of Arizona using the temporal greenness dynamics of the landscape, or the landscape phenology. Landscape phenometrics were derived from Advanced Very High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (NDVI) data for 1998 and 1999 by using Fourier harmonic analysis to analyze the waveform of the annual NDVI profile at each pixel. We modeled the spatial distribution of Yellow-billed Cuckoo habitat by coupling the field data of Cuckoo presence or absence and point-based samples of riparian and cottonwood-willow vegetation types with satellite phenometrics for 1998. Models were validated using field and satellite data collected in 1999. The results indicate that Yellow-billed Cuckoo occupy locations within their preferred habitat that exhibit peak greenness after the start of the summer monsoon and are greener and more dynamic than “average” habitat. Identification of preferred phenotypes within recognized habitat areas can be used to refine habitat models, inform predictions of habitat response to climate change, and suggest adaptation strategies.

Analysis on the vegetation phenology of tropical seasonal rain forest in South America

NASA Astrophysics Data System (ADS)

Liang, B.; Chen, X.

2016-12-01

Using Global Land Surface Satellite (GLASS) LAI data during 1982 to 2003, we analyzed spatial and temporal variations of vegetation phenology in the tropical seasonal rain forest of South America. Several methods were used to fit seasonal LAI curves and extract start (SOS) and end (EOS) of the growing season. The results show that Fourier function can most effectively fit LAI curves, and yearly RMSEs for differences between observed and fitted LAI values are less than 0.01. The SOS ranged from 250 to 350 days of year, and occurred earlier in west than in east. Contrarily, the EOS were between 120 and 180 days of year, and appeared earlier in east than in west. Thus, the growing season was longer in west than in east. With regard to linear trends, SOS shows a significant advancement at 7% of pixels and a significant delay at 13% of pixels, whereas EOS advanced significantly at 16% of pixels and was delayed significantly at 18% of pixels. Preseason precipitation is the main influence factor of SOS and EOS in the tropical seasonal rain forest of South America.

Harmonics rejection in pixelated interferograms using spatio-temporal demodulation.

PubMed

Padilla, J M; Servin, M; Estrada, J C

2011-09-26

Pixelated phase-mask interferograms have become an industry standard in spatial phase-shifting interferometry. These pixelated interferograms allow full wavefront encoding using a single interferogram. This allows the study of fast dynamic events in hostile mechanical environments. Recently an error-free demodulation method for ideal pixelated interferograms was proposed. However, non-ideal conditions in interferometry may arise due to non-linear response of the CCD camera, multiple light paths in the interferometer, etc. These conditions generate non-sinusoidal fringes containing harmonics which degrade the phase estimation. Here we show that two-dimensional Fourier demodulation of pixelated interferograms rejects most harmonics except the complex ones at {-3(rd), +5(th), -7(th), +9(th), -11(th),…}. We propose temporal phase-shifting to remove these remaining harmonics. In particular, a 2-step phase-shifting algorithm is used to eliminate the -3(rd) and +5(th) complex harmonics, while a 3-step one is used to remove the -3(rd), +5<(th), -7(th) and +9(th) complex harmonics. © 2011 Optical Society of America

Localised burst reconstruction from space-time PODs in a turbulent channel

NASA Astrophysics Data System (ADS)

Garcia-Gutierrez, Adrian; Jimenez, Javier

2017-11-01

The traditional proper orthogonal decomposition of the turbulent velocity fluctuations in a channel is extended to time under the assumption that the attractor is statistically stationary and can be treated as periodic for long-enough times. The objective is to extract space- and time-localised eddies that optimally represent the kinetic energy (and two-event correlation) of the flow. Using time-resolved data of a small-box simulation at Reτ = 1880 , minimal for y / h 0.25 , PODs are computed from the two-point spectral-density tensor Φ(kx ,kz , y ,y' , ω) . They are Fourier components in x, z and time, and depend on y and on the temporal frequency ω, or, equivalently, on the convection velocity c = ω /kx . Although the latter depends on y, a spatially and temporally localised `burst' can be synthesised by adding a range of PODs with specific phases. The results are localised bursts that are amplified and tilted, in a time-periodic version of Orr-like behaviour. Funded by the ERC COTURB project.

Investigation of thermomechanical effects of lighting conditions on canvas paintings by laser shearography

NASA Astrophysics Data System (ADS)

Meybodi, M. K.; Dobrev, I.; Klausmeyer, P.; Harrington, E. J.; Furlong, C.

Quantitative techniques to characterize thermomechanical effects of light on canvas paintings are necessary in order to better understand the deleterious effects that light has on precious art collections in museum exhibitions. In this paper, we present advances in the development of a customized laser shearography system for temporal characterization of inplane displacements of canvas paintings when subjected to specific lighting conditions. The shearography system is synchronized with a thermal IR camera and concomitant measurements of derivatives of displacements along two orthogonal shearing directions as well as thermal fields are performed. Due to the nature of the measurements, we have developed real-time temporal phase unwrapping algorithms and high-resolution Fast Fourier Transform (FFT) methods to calibrate applied shearing levels. In addition, we are developing methods to isolate thermally-induced components from randomly-induced mechanical vibrations that occur in museum environments by application of IR imaging data. Representative examples are shown, which illustrate capabilities to measure, detect, and map crack propagation as a function of lighting conditions and time.

Speeding up dynamic spiral chemical shift imaging with incoherent sampling and low-rank matrix completion.

PubMed

DeVience, Stephen J; Mayer, Dirk

2017-03-01

To improve the temporal and spatial resolution of dynamic 13 C spiral chemical shift imaging via incoherent sampling and low-rank matrix completion (LRMC). Spiral CSI data were both simulated and acquired in rats, and undersampling was implemented retrospectively and prospectively by pseudorandomly omitting a fraction of the spiral interleaves. Undersampled data were reconstructed with both LRMC and a conventional inverse nonuniform fast Fourier transform (iNUFFT) and compared with fully sampled data. Two-fold undersampling with LRMC reconstruction enabled a two-fold improvement in temporal or spatial resolution without significant artifacts or spatiotemporal distortion. Conversely, undersampling with iNUFFT reconstruction created strong artifacts that obscured the image. LRMC performed better at time points with strong metabolite signal. Incoherent undersampling and LRMC provides a way to increase the spatiotemporal resolution of spiral CSI without degrading data integrity. Magn Reson Med 77:951-960, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Evaluation of natural mandibular shape asymmetry: an approach by using elliptical Fourier analysis.

PubMed

Niño-Sandoval, Tania C; Morantes Ariza, Carlos F; Infante-Contreras, Clementina; Vasconcelos, Belmiro Ce

2018-04-05

The purpose of this study was to demonstrate that asymmetry is a natural occurring phenomenon in the mandibular shape by using elliptical Fourier analysis. 164 digital orthopantomographs from Colombian patients of both sexes aged 18 to 25 years were collected. Curves from left and right hemimandible were digitized. An elliptical Fourier analysis was performed with 20 harmonics. In the general sexual dimorphism a principal component analysis (PCA) and a hotelling T 2 from the multivariate warp space were employed. Exploratory analysis of general asymmetry and sexual dimorphism by side was made with a Procrustes Fit. A non-parametric multivariate analysis of variance (MANOVA) was applied to assess differentiation of skeletal classes of each hemimandible, and a Procrustes analysis of variance (ANOVA) was applied to search any relation between skeletal class and side in both sexes. Significant values were found in general asymmetry, general sexual dimorphism, in dimorphism by side (p < 0.0001), asymmetry by sex, and differences between Class I, II, and III (p < 0.005). However, a relation of skeletal classes and side was not found. The mandibular asymmetry by shape is present in all patients and should not be articulated exclusively to pathological processes, therefore, along with sexual dimorphism and differences between skeletal classes must be taken into account for improving mandibular prediction systems.

Iterative wave-front reconstruction in the Fourier domain.

PubMed

Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry

2017-05-15

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

Reduction and coding of synthetic aperture radar data with Fourier transforms

NASA Technical Reports Server (NTRS)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Nucleic Acid analysis by fourier transform ion cyclotron resonance mass spectrometry at the beginning of the twenty-first century.

PubMed

Frahm, J L; Muddiman, D C

2005-01-01

Mass spectrometers measure an intrinsic property (i.e., mass) of a molecule, which makes it an ideal platform for nucleic acid analysis. Importantly, the unparalleled capabilities of Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry further extend its usefulness for nucleic acid analysis. The beginning of the twenty-first century has been marked with notable advances in the field of FT-ICR mass spectrometry analysis of nucleic acids. Some of these accomplishments include fundamental studies of nucleic acid properties, improvements in sample clean up and preparation, better methods to obtain higher mass measurement accuracy, analysis of noncovalent complexes, tandem mass spectrometry, and characterization of peptide nucleic acids. This diverse range of studies will be presented herein.

Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data

PubMed Central

2015-01-01

The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk. PMID:26421617

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

An alternative approach to characterize nonlinear site effects

USGS Publications Warehouse

Zhang, R.R.; Hartzell, S.; Liang, J.; Hu, Y.

2005-01-01

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

Simplification of multiple Fourier series - An example of algorithmic approach

NASA Technical Reports Server (NTRS)

Ng, E. W.

1981-01-01

This paper describes one example of multiple Fourier series which originate from a problem of spectral analysis of time series data. The example is exercised here with an algorithmic approach which can be generalized for other series manipulation on a computer. The generalized approach is presently pursued towards applications to a variety of multiple series and towards a general purpose algorithm for computer algebra implementation.

[Identification of different Citrus sinensis (L.) Osbeck trees varieties using Fourier transform infrared spectroscopy and hierarchical cluster analysis].

PubMed

Yi, Shi-Lai; Deng, Lie; He, Shao-Lan; Shi, You-Ming; Zheng, Yong-Qiang; Lu, Qiang; Xie, Rang-Jin; Wei, Xian-Guoi; Li, Song-Wei; Jian, Shui-Xian

2012-11-01

Researched on diversity of the spring leaf samples of seven different Citrus sinensis (L.) Osbeck varieties by Fourier transform infrared (FTIR) spectroscopy technology, the results showed that the Fourier transform infrared spectra of seven varieties leaves was composited by the absorption band of cellulose and polysaccharide mainly, the wave number of characteristics absorption peaks were similar at their FTIR spectra. However, there were some differences in shape of peaks and relatively absorption intensity. The conspicuous difference was presented at the region between 1 500 and 700 cm(-1) by second derivative spectra. Through the hierarchical cluster analysis (HCA) of second derivative spectra between 1 500 and 700 cm(-1), the results showed that the clustering of the different varieties of Citrus sinensis (L.) Osbeck varieties was classification according to genetic relationship. The results showed that FTIR spectroscopy combined with hierarchical cluster analysis could be used to identify and classify of citrus varieties rapidly, it was an extension method to study on early leaves of varieties orange seedlings.

Classification and identification of Rhodobryum roseum Limpr. and its adulterants based on fourier-transform infrared spectroscopy (FTIR) and chemometrics.

PubMed

Cao, Zhen; Wang, Zhenjie; Shang, Zhonglin; Zhao, Jiancheng

2017-01-01

Fourier-transform infrared spectroscopy (FTIR) with the attenuated total reflectance technique was used to identify Rhodobryum roseum from its four adulterants. The FTIR spectra of six samples in the range from 4000 cm-1 to 600 cm-1 were obtained. The second-derivative transformation test was used to identify the small and nearby absorption peaks. A cluster analysis was performed to classify the spectra in a dendrogram based on the spectral similarity. Principal component analysis (PCA) was used to classify the species of six moss samples. A cluster analysis with PCA was used to identify different genera. However, some species of the same genus exhibited highly similar chemical components and FTIR spectra. Fourier self-deconvolution and discrete wavelet transform (DWT) were used to enhance the differences among the species with similar chemical components and FTIR spectra. Three scales were selected as the feature-extracting space in the DWT domain. The results show that FTIR spectroscopy with chemometrics is suitable for identifying Rhodobryum roseum and its adulterants.

Rapid update of discrete Fourier transform for real-time signal processing

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.; Kakad, Yogendra P.

2001-10-01

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log2 N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log2 N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.

Estimation of surface heat and moisture fluxes over a prairie grassland. II - Two-dimensional time filtering and site variability

NASA Technical Reports Server (NTRS)

Crosson, William L.; Smith, Eric A.

1992-01-01

The behavior of in situ measurements of surface fluxes obtained during FIFE 1987 is examined by using correlative and spectral techniques in order to assess the significance of fluctuations on various time scales, from subdiurnal up to synoptic, intraseasonal, and annual scales. The objectives of this analysis are: (1) to determine which temporal scales have a significant impact on areal averaged fluxes and (2) to design a procedure for filtering an extended flux time series that preserves the basic diurnal features and longer time scales while removing high frequency noise that cannot be attributed to site-induced variation. These objectives are accomplished through the use of a two-dimensional cross-time Fourier transform, which serves to separate processes inherently related to diurnal and subdiurnal variability from those which impact flux variations on the longer time scales. A filtering procedure is desirable before the measurements are utilized as input with an experimental biosphere model, to insure that model based intercomparisons at multiple sites are uncontaminated by input variance not related to true site behavior. Analysis of the spectral decomposition indicates that subdiurnal time scales having periods shorter than 6 hours have little site-to-site consistency and therefore little impact on areal integrated fluxes.

Interferometric Near-Infrared Spectroscopy (iNIRS) for determination of optical and dynamical properties of turbid media

PubMed Central

Borycki, Dawid; Kholiqov, Oybek; Chong, Shau Poh; Srinivasan, Vivek J.

2016-01-01

We introduce and implement interferometric near-infrared spectroscopy (iNIRS), which simultaneously extracts optical and dynamical properties of turbid media through analysis of a spectral interference fringe pattern. The spectral interference fringe pattern is measured using a Mach-Zehnder interferometer with a frequency-swept narrow linewidth laser. Fourier analysis of the detected signal is used to determine time-of-flight (TOF)-resolved intensity, which is then analyzed over time to yield TOF-resolved intensity autocorrelations. This approach enables quantification of optical properties, which is not possible in conventional, continuous-wave near-infrared spectroscopy (NIRS). Furthermore, iNIRS quantifies scatterer motion based on TOF-resolved autocorrelations, which is a feature inaccessible by well-established diffuse correlation spectroscopy (DCS) techniques. We prove this by determining TOF-resolved intensity and temporal autocorrelations for light transmitted through diffusive fluid phantoms with optical thicknesses of up to 55 reduced mean free paths (approximately 120 scattering events). The TOF-resolved intensity is used to determine optical properties with time-resolved diffusion theory, while the TOF-resolved intensity autocorrelations are used to determine dynamics with diffusing wave spectroscopy. iNIRS advances the capabilities of diffuse optical methods and is suitable for in vivo tissue characterization. Moreover, iNIRS combines NIRS and DCS capabilities into a single modality. PMID:26832264

Optical Design And Analysis Of Carbon Dioxide Laser Fusion Systems Using Interferometry And Fast Fourier Transform Techniques

NASA Astrophysics Data System (ADS)

Viswanathan, V. K.

1980-11-01

The optical design and analysis of the LASL carbon dioxide laser fusion systems required the use of techniques that are quite different from the currently used method in conventional optical design problems. The necessity for this is explored and the method that has been successfully used at Los Alamos to understand these systems is discussed with examples. This method involves characterization of the various optical components in their mounts by a Zernike polynomial set and using fast Fourier transform techniques to propagate the beam, taking diffraction and other nonlinear effects that occur in these types of systems into account. The various programs used for analysis are briefly discussed.

Control of extreme events in the bubbling onset of wave turbulence.

PubMed

Galuzio, P P; Viana, R L; Lopes, S R

2014-04-01

We show the existence of an intermittent transition from temporal chaos to turbulence in a spatially extended dynamical system, namely, the forced and damped one-dimensional nonlinear Schrödinger equation. For some values of the forcing parameter, the system dynamics intermittently switches between ordered states and turbulent states, which may be seen as extreme events in some contexts. In a Fourier phase space, the intermittency takes place due to the loss of transversal stability of unstable periodic orbits embedded in a low-dimensional subspace. We mapped these transversely unstable regions and perturbed the system in order to significantly reduce the occurrence of extreme events of turbulence.

Ultrafast Dephasing and Incoherent Light Photon Echoes in Organic Amorphous Systems

NASA Astrophysics Data System (ADS)

Yano, Ryuzi; Matsumoto, Yoshinori; Tani, Toshiro; Nakatsuka, Hiroki

1989-10-01

Incoherent light photon echoes were observed in organic amorphous systems (cresyl violet in polyvinyl alcohol and 1,4-dihydroxyanthraquinone in polymethacrylic acid) by using temporally-incoherent nanosecond laser pulses. It was found that an echo decay curve of an organic amorphous system is composed of a sharp peak which decays very rapidly and a slowly decaying wing at the tail. We show that the persistent hole burning (PHB) spectra were reproduced by the Fourier-cosine transforms of the echo decay curves. We claim that in general, we must take into account the multi-level feature of the system in order to explain ultrafast dephasing at very low temperatures.

Delta function excitation of waves in the earth's ionosphere

NASA Technical Reports Server (NTRS)

Vidmar, R. J.; Crawford, F. W.; Harker, K. J.

1983-01-01

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.

The conjecture concerning time variations in the solar neutrino flux

NASA Technical Reports Server (NTRS)

Haubold, H. J.; Gerth, E.

1985-01-01

The results of the Fourier transformation of the unequally-spaced time series of the recorded Ar-37 production rate of the solar neutrino experiment (runs 18 to 80, 1970 to 1983) are reviewed. Significance criteria for every period discovered by the harmonic analysis are determined. A Fourier synthesis of certain discovered harmonics are performed. It seems that the solar neutrino flux increases shock-like with a period of approximately 8.3 years and after that breaks down. Possible connections between the periods found by the harmonic analysis and several observed phenomena on the solar surface are indicated.

Quantification of fibre polymerization through Fourier space image analysis

PubMed Central

Nekouzadeh, Ali; Genin, Guy M.

2011-01-01

Quantification of changes in the total length of randomly oriented and possibly curved lines appearing in an image is a necessity in a wide variety of biological applications. Here, we present an automated approach based upon Fourier space analysis. Scaled, band-pass filtered power spectral densities of greyscale images are integrated to provide a quantitative measurement of the total length of lines of a particular range of thicknesses appearing in an image. A procedure is presented to correct for changes in image intensity. The method is most accurate for two-dimensional processes with fibres that do not occlude one another. PMID:24959096

ChromAlign: A two-step algorithmic procedure for time alignment of three-dimensional LC-MS chromatographic surfaces.

PubMed

Sadygov, Rovshan G; Maroto, Fernando Martin; Hühmer, Andreas F R

2006-12-15

We present an algorithmic approach to align three-dimensional chromatographic surfaces of LC-MS data of complex mixture samples. The approach consists of two steps. In the first step, we prealign chromatographic profiles: two-dimensional projections of chromatographic surfaces. This is accomplished by correlation analysis using fast Fourier transforms. In this step, a temporal offset that maximizes the overlap and dot product between two chromatographic profiles is determined. In the second step, the algorithm generates correlation matrix elements between full mass scans of the reference and sample chromatographic surfaces. The temporal offset from the first step indicates a range of the mass scans that are possibly correlated, then the correlation matrix is calculated only for these mass scans. The correlation matrix carries information on highly correlated scans, but it does not itself determine the scan or time alignment. Alignment is determined as a path in the correlation matrix that maximizes the sum of the correlation matrix elements. The computational complexity of the optimal path generation problem is reduced by the use of dynamic programming. The program produces time-aligned surfaces. The use of the temporal offset from the first step in the second step reduces the computation time for generating the correlation matrix and speeds up the process. The algorithm has been implemented in a program, ChromAlign, developed in C++ language for the .NET2 environment in WINDOWS XP. In this work, we demonstrate the applications of ChromAlign to alignment of LC-MS surfaces of several datasets: a mixture of known proteins, samples from digests of surface proteins of T-cells, and samples prepared from digests of cerebrospinal fluid. ChromAlign accurately aligns the LC-MS surfaces we studied. In these examples, we discuss various aspects of the alignment by ChromAlign, such as constant time axis shifts and warping of chromatographic surfaces.

Temporal Characteristics of the Sleep EEG Power Spectrum in Critically Ill Children

PubMed Central

Kudchadkar, Sapna R.; Yaster, Myron; Punjabi, Arjun N.; Quan, Stuart F.; Goodwin, James L.; Easley, R. Blaine; Punjabi, Naresh M.

2015-01-01

Study Objectives: Although empirical evidence is limited, critical illness in children is associated with disruption of the normal sleep-wake rhythm. The objective of the current study was to examine the temporal characteristics of the sleep electroencephalogram (EEG) in a sample of children with critical illness. Methods: Limited montage EEG recordings were collected for at least 24 hours from 8 critically ill children on mechanical ventilation for respiratory failure in a pediatric intensive care unit (PICU) of a tertiary-care hospital. Each PICU patient was age- and gender-matched to a healthy subject from the community. Power spectral analysis with the fast Fourier transform (FFT) was used to characterize EEG spectral power and categorized into 4 frequency bands: δ (0.8 to 4.0 Hz), θ (4.1 to 8.0 Hz), α (8.1 to 13.0 Hz), and β1/β2 (13.1 to 20.0 Hz). Results: PICU patients did not manifest the ultradian variability in EEG power spectra including the typical increase in δ-power during the first third of the night that was observed in healthy children. Differences noted included significantly lower mean nighttime δ and θ power in the PICU patients compared to healthy children (p < 0.001). Moreover, in the PICU patients, mean δ and θ power were higher during daytime hours than nighttime hours (p < 0.001). Conclusions: The results presented herein challenge the assumption that children experience restorative sleep during critical illness, highlighting the need for interventional studies to determine whether sleep promotion improves outcomes in critically ill children undergoing active neurocognitive development. Citation: Kudchadkar SR, Yaster M, Punjabi AN, Quan SF, Goodwin JL, Easley RB, Punjabi NM. Temporal characteristics of the sleep EEG power spectrum in critically ill children. J Clin Sleep Med 2015;11(12):1449–1454. PMID:26194730

Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.

PubMed

Caple, Jodi; Byrd, John; Stephan, Carl N

2017-11-01

The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.

Effects of data gaps on Fourier Analysis

NASA Astrophysics Data System (ADS)

Negrea, Catalin; Munteanu, Costel; Echim, Marius

2014-05-01

Fourier Analysis is a vital and widely used tool in all branches of science that require advanced data processing. The method is often used via the Fast Fourier Transform (FFT) implementation readily available in most programming languages. This is a valid approach for data sets with equally spaced data points and no gaps. Such conditions are not always met in real situations where corrections and adjustments to the method are needed. We investigate the intrinsic limitations of four such methods when data gaps are present: 1) linear interpolations and FFT, 2) a direct implementation of the Discrete Fourier Transform, 3) a Z-Transform and 4) the Lomb-Scargle algorithm. Theoretical analysis tools can provide an insight as to the likely problems of such methods and we discuss the likely modifications to the computed spectra. Also, a time series with no data gaps and a constant sampling frequency is altered by introducing several gap configurations and the resulting spectra with the four methods are compared to highlight changes with respect to the original spectrum. Effects on the amplitude and phase of the resulting power spectral densities are analyzed for non-uniformly sampled solar wind data provided by the Venus Express spacecraft. Phase effects are also studied in the context of a sliding window approach. Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM, and a grant of the Romanian Ministry of National Education, CNCS - UEFISCDI, project number PN-II-ID-PCE-2012-4-0418.

Elliptical Fourier descriptors of outline and morphological analysis in caudal view of foramen magnum of the tropical raccoon (Procyon cancrivorus) (Linnaeus, 1758).

PubMed

Samuel, O M; Casanova, P M; Olopade, J O

2018-03-01

To evaluate sexual-size dimorphism and attempt at categorization of inter-individual shapes of foramen magnum outlines using Fourier descriptors which allow for shape outline evaluations with a resultant specimen character definition. Individual characterization and quantification of foramen magnum shapes in direct caudal view based on elliptical Fourier technique was applied to 46 tropical raccoon skulls (26 females, 20 males). Incremental number of harmonics demonstrates morphological contributions of such descriptors with their relations to specific anatomical constructions established. The initial harmonics (1st to 3rd) described the general foramen shapes while the second (4th to 12th) demonstrated fine morphological details. Sexual-size dimorphism was observed in females (87.1%) and 91.7% in males, normalization of size produces 75% in females and 83% in males. With respect to foramen magnum dimorphism analysis, the result obtained through elliptic Fourier analysis was comparatively better in detail information of outline contours than earlier classical methods. The first four effective principal components defined 70.63% of its shape properties while the rest (22.51%) constituted fine details of morphology. Both size and shape seems important in sexual dimorphisms in this species, this investigation suggest clinical implications, taxonomic and anthropologic perspectives in foramen characterization magnum characterization and further postulates an increased possibility of volume reduction cerebellar protrusion, ontogenic magnum shape irregularities in the sample population with neurologic consequences especially among females. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

Pre-Treatment Objective Diagnosis and Post-Treatment Outcome Evaluation in Patients with Vascular Pulsatile Tinnitus Using Transcanal Recording and Spectro-Temporal Analysis

PubMed Central

Choi, Inyong; Koo, Ja-Won; Lee, Kyogu

2016-01-01

Objective Although vascular pulsatile tinnitus (VPT) has been classified as “objective”, VPT is not easily recognizable or documentable in most cases. In response to this, we have developed transcanal sound recording (TSR) and spectro-temporal analysis (STA) for the objective diagnosis of VPT. By refining our initial method, we were able to apply TSR/STA to post-treatment outcome evaluation, as well as pre-treatment objective diagnosis. Methods TSR was performed on seven VPT patients and five normal controls before and after surgical or interventional treatment. VPT was recorded using an inserted microphone with the subjects placed in both upright and supine positions with 1) a neutral head position, 2) head rotated to the tinnitus side, 3) head rotated to the non-tinnitus side, and 4) a neutral position with ipsi-lesional manual cervical compression. The recorded signals were analyzed in both time and time-frequency domains by performing a short-time Fourier transformation. Results The pre-treatment ear canal signals of all VPT patients demonstrated pulse-synchronous periodic structures and acoustic characteristics that were representative of their presumptive vascular pathologies, whereas those the controls exhibited smaller peaks and weak periodicities. Compared with the pre-treatment signals, the post-treatment signals exhibited significantly reduced peak- and root mean square amplitudes upon time domain analysis. Additionally, further sub-band analysis confirmed that the pulse-synchronous signal of all subjects was not identifiable after treatment and, in particular, that the signal decrement was statistically significant at low frequencies. Moreover, the post-treatment signals of the VPT subjects revealed no significant differences when compared to those of the control group. Conclusion We reconfirmed that the TSR/STA method is an effective modality to objectify VPT. In addition, the potential role of the TSR/STA method in the objective evaluation of treatment outcomes in patients with VPT was proven. Further studies incorporating a larger sample size and more refined recording techniques are warranted. PMID:27351198

Assessment of cardiac time intervals using high temporal resolution real-time spiral phase contrast with UNFOLDed-SENSE.

PubMed

Kowalik, Grzegorz T; Knight, Daniel S; Steeden, Jennifer A; Tann, Oliver; Odille, Freddy; Atkinson, David; Taylor, Andrew; Muthurangu, Vivek

2015-02-01

To develop a real-time phase contrast MR sequence with high enough temporal resolution to assess cardiac time intervals. The sequence utilized spiral trajectories with an acquisition strategy that allowed a combination of temporal encoding (Unaliasing by fourier-encoding the overlaps using the temporal dimension; UNFOLD) and parallel imaging (Sensitivity encoding; SENSE) to be used (UNFOLDed-SENSE). An in silico experiment was performed to determine the optimum UNFOLD filter. In vitro experiments were carried out to validate the accuracy of time intervals calculation and peak mean velocity quantification. In addition, 15 healthy volunteers were imaged with the new sequence, and cardiac time intervals were compared to reference standard Doppler echocardiography measures. For comparison, in silico, in vitro, and in vivo experiments were also carried out using sliding window reconstructions. The in vitro experiments demonstrated good agreement between real-time spiral UNFOLDed-SENSE phase contrast MR and the reference standard measurements of velocity and time intervals. The protocol was successfully performed in all volunteers. Subsequent measurement of time intervals produced values in keeping with literature values and good agreement with the gold standard echocardiography. Importantly, the proposed UNFOLDed-SENSE sequence outperformed the sliding window reconstructions. Cardiac time intervals can be successfully assessed with UNFOLDed-SENSE real-time spiral phase contrast. Real-time MR assessment of cardiac time intervals may be beneficial in assessment of patients with cardiac conditions such as diastolic dysfunction. © 2014 Wiley Periodicals, Inc.

Compact Microwave Fourier Spectrum Analyzer

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry

2009-01-01

A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.

Research on fast Fourier transforms algorithm of huge remote sensing image technology with GPU and partitioning technology.

PubMed

Yang, Xue; Li, Xue-You; Li, Jia-Guo; Ma, Jun; Zhang, Li; Yang, Jan; Du, Quan-Ye

2014-02-01

Fast Fourier transforms (FFT) is a basic approach to remote sensing image processing. With the improvement of capacity of remote sensing image capture with the features of hyperspectrum, high spatial resolution and high temporal resolution, how to use FFT technology to efficiently process huge remote sensing image becomes the critical step and research hot spot of current image processing technology. FFT algorithm, one of the basic algorithms of image processing, can be used for stripe noise removal, image compression, image registration, etc. in processing remote sensing image. CUFFT function library is the FFT algorithm library based on CPU and FFTW. FFTW is a FFT algorithm developed based on CPU in PC platform, and is currently the fastest CPU based FFT algorithm function library. However there is a common problem that once the available memory or memory is less than the capacity of image, there will be out of memory or memory overflow when using the above two methods to realize image FFT arithmetic. To address this problem, a CPU and partitioning technology based Huge Remote Fast Fourier Transform (HRFFT) algorithm is proposed in this paper. By improving the FFT algorithm in CUFFT function library, the problem of out of memory and memory overflow is solved. Moreover, this method is proved rational by experiment combined with the CCD image of HJ-1A satellite. When applied to practical image processing, it improves effect of the image processing, speeds up the processing, which saves the time of computation and achieves sound result.

Creation of Synthetic Surface Temperature and Precipitation Ensembles Through A Computationally Efficient, Mixed Method Approach

NASA Astrophysics Data System (ADS)

Hartin, C.; Lynch, C.; Kravitz, B.; Link, R. P.; Bond-Lamberty, B. P.

2017-12-01

Typically, uncertainty quantification of internal variability relies on large ensembles of climate model runs under multiple forcing scenarios or perturbations in a parameter space. Computationally efficient, standard pattern scaling techniques only generate one realization and do not capture the complicated dynamics of the climate system (i.e., stochastic variations with a frequency-domain structure). In this study, we generate large ensembles of climate data with spatially and temporally coherent variability across a subselection of Coupled Model Intercomparison Project Phase 5 (CMIP5) models. First, for each CMIP5 model we apply a pattern emulation approach to derive the model response to external forcing. We take all the spatial and temporal variability that isn't explained by the emulator and decompose it into non-physically based structures through use of empirical orthogonal functions (EOFs). Then, we perform a Fourier decomposition of the EOF projection coefficients to capture the input fields' temporal autocorrelation so that our new emulated patterns reproduce the proper timescales of climate response and "memory" in the climate system. Through this 3-step process, we derive computationally efficient climate projections consistent with CMIP5 model trends and modes of variability, which address a number of deficiencies inherent in the ability of pattern scaling to reproduce complex climate model behavior.

Optimized spatio-temporal descriptors for real-time fall detection: comparison of support vector machine and Adaboost-based classification

NASA Astrophysics Data System (ADS)

Charfi, Imen; Miteran, Johel; Dubois, Julien; Atri, Mohamed; Tourki, Rached

2013-10-01

We propose a supervised approach to detect falls in a home environment using an optimized descriptor adapted to real-time tasks. We introduce a realistic dataset of 222 videos, a new metric allowing evaluation of fall detection performance in a video stream, and an automatically optimized set of spatio-temporal descriptors which fed a supervised classifier. We build the initial spatio-temporal descriptor named STHF using several combinations of transformations of geometrical features (height and width of human body bounding box, the user's trajectory with her/his orientation, projection histograms, and moments of orders 0, 1, and 2). We study the combinations of usual transformations of the features (Fourier transform, wavelet transform, first and second derivatives), and we show experimentally that it is possible to achieve high performance using support vector machine and Adaboost classifiers. Automatic feature selection allows to show that the best tradeoff between classification performance and processing time is obtained by combining the original low-level features with their first derivative. Hence, we evaluate the robustness of the fall detection regarding location changes. We propose a realistic and pragmatic protocol that enables performance to be improved by updating the training in the current location with normal activities records.

Characterization of non-polar aromatic hydrocarbons in crude oil using atmospheric pressure laser ionization and Fourier transform ion cyclotron resonance mass spectrometry (APLI FT-ICR MS).

PubMed

Schrader, Wolfgang; Panda, Saroj K; Brockmann, Klaus J; Benter, Thorsten

2008-07-01

We report on the successful application of the recently introduced atmospheric pressure laser ionization (APLI) method as a novel tool for the analysis of crude oil and its components. Using Fourier transform ion cyclotron resonance mass spectrometry, unambiguous determination of key compounds in this complex matrix with unprecedented sensitivity is presented.

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

NASA Astrophysics Data System (ADS)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

Four Forms of the Fourier Transform - for Freshmen, using Matlab

NASA Astrophysics Data System (ADS)

Simons, F. J.; Maloof, A. C.

2016-12-01

In 2015, a Fall "Freshman Seminar" at Princeton University (http://geoweb.princeton.edu/people/simons/FRS-SESC.html) taught students to combine field observations of the natural world with quantitative modeling and interpretation, to answer questions like: "How have Earth and human histories been recorded in the geology of Princeton, the Catskills, France and Spain?" (where we took the students on a data-gathering field trip during Fall Break), and "What experiments and analysis can a first-year (possibly non-future-major) do to query such archives of the past?" In the classroom, through problem sets, and around campus, students gained practical experience collecting geological and geophysical data in a geographic context, and analyzing these data using statistical techniques such as regression, time-series and image analysis, with the programming language Matlab. In this presentation I will detail how we instilled basic Matlab skills for quantitative geoscience data analysis through a 6-week progression of topics and exercises. In the 6 weeks after the Fall Break trip, we strengthened these competencies to make our students fully proficient for further learning, as evidenced by their end-of-term independent research work.The particular case study is focused on introducing power-spectral analysis to Freshmen, in a way that even the least quantitative among them could functionally understand. Not counting (0) "inspection", the four ways by which we have successfully instilled the concept of power-spectral analysis in a hands-on fashion are (1) "correlation", (2) "inversion", (3) "stacking", and formal (4) "Fourier transformation". These four provide the main "mappings". Along the way, of course, we also make sure that the students understand that "power-spectral density estimation" is not the same as "Fourier transformation", nor that every Fourier transform has to be "Fast". Hence, concepts from analysis-of-variance techniques, regression, and hypothesis testing, arise in this context, and will be discussed.

Pulse analysis of acoustic emission signals. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Houghton, J. R.

1976-01-01

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio are examined in the frequency domain analysis, and pulse shape deconvolution is developed for use in the time domain analysis. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameters values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emissions associated with: (1) crack propagation, (2) ball dropping on a plate, (3) spark discharge and (4) defective and good ball bearings.

A better understanding of long-range temporal dependence of traffic flow time series

NASA Astrophysics Data System (ADS)

Feng, Shuo; Wang, Xingmin; Sun, Haowei; Zhang, Yi; Li, Li

2018-02-01

Long-range temporal dependence is an important research perspective for modelling of traffic flow time series. Various methods have been proposed to depict the long-range temporal dependence, including autocorrelation function analysis, spectral analysis and fractal analysis. However, few researches have studied the daily temporal dependence (i.e. the similarity between different daily traffic flow time series), which can help us better understand the long-range temporal dependence, such as the origin of crossover phenomenon. Moreover, considering both types of dependence contributes to establishing more accurate model and depicting the properties of traffic flow time series. In this paper, we study the properties of daily temporal dependence by simple average method and Principal Component Analysis (PCA) based method. Meanwhile, we also study the long-range temporal dependence by Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA). The results show that both the daily and long-range temporal dependence exert considerable influence on the traffic flow series. The DFA results reveal that the daily temporal dependence creates crossover phenomenon when estimating the Hurst exponent which depicts the long-range temporal dependence. Furthermore, through the comparison of the DFA test, PCA-based method turns out to be a better method to extract the daily temporal dependence especially when the difference between days is significant.

Resting State Dense Array Gamma Oscillatory Activity as a Response Marker for Cerebellar-Repetitive Transcranial Magnetic Stimulation (rTMS) in Schizophrenia.

PubMed

Tikka, Sai Krishna; Garg, Shobit; Sinha, Vinod Kumar; Nizamie, S Haque; Goyal, Nishant

2015-12-01

As cerebellum and its abnormalities have been implicated in the pathophysiology of schizophrenia, repetitive transcranial magnetic stimulation (rTMS) of this alternate site has been suggested as a novel target for treating patients with this disorder. As resting state gamma activity measures functional brain connectivity, it could be used as a specific treatment marker. To investigate the effect of cerebellar-rTMS on resting state gamma activity, while studying its efficacy in recent onset schizophrenia patients. This rater-blinded prospective study was completed by 11 schizophrenia patients. They received 10 sessions of high-frequency (theta patterned) rTMS to midline cerebellum over 2 weeks. Resting state EEG was recorded using high (192-channel) resolution EEG at baseline and post rTMS. Gamma spectral power was calculated using fast Fourier transformation, Hanning window averaged over 8 scalp segments corresponding 8 lobes. Clinical improvement rated on the Positive and Negative Syndrome Scale and depressive symptoms assessed using the Calgary Depression Scale for Schizophrenia were other outcome variables. Nonparametric statistics were used. Over the treatment course, significant reduction was seen on negative syndrome and depression scores. Gamma spectral power in left frontal and temporal segments reduced significantly. Spearman correlation analysis showed that percentage reduction in psychopathology scores had significant positive correlation with percentage reduction in gamma spectral power. Cerebellar-rTMS might be an effective adjunct to treat intricate and lingering negative and affective symptoms. Resting state gamma spectral power in frontal and temporal regions might be used as a biomarker for treatment response.

Rolling contact of a rigid sphere/sliding of a spherical indenter upon a viscoelastic half-space containing an ellipsoidal inhomogeneity

NASA Astrophysics Data System (ADS)

Koumi, Koffi Espoir; Chaise, Thibaut; Nelias, Daniel

2015-07-01

In this paper, the frictionless rolling contact problem between a rigid sphere and a viscoelastic half-space containing one elastic inhomogeneity is solved. The problem is equivalent to the frictionless sliding of a spherical tip over a viscoelastic body. The inhomogeneity may be of spherical or ellipsoidal shape, the later being of any orientation relatively to the contact surface. The model presented here is three dimensional and based on semi-analytical methods. In order to take into account the viscoelastic aspect of the problem, contact equations are discretized in the spatial and temporal dimensions. The frictionless rolling of the sphere, assumed rigid here for the sake of simplicity, is taken into account by translating the subsurface viscoelastic fields related to the contact problem. Eshelby's formalism is applied at each step of the temporal discretization to account for the effect of the inhomogeneity on the contact pressure distribution, subsurface stresses, rolling friction and the resulting torque. A Conjugate Gradient Method and the Fast Fourier Transforms are used to reduce the computation cost. The model is validated by a finite element model of a rigid sphere rolling upon a homogeneous vciscoelastic half-space, as well as through comparison with reference solutions from the literature. A parametric analysis of the effect of elastic properties and geometrical features of the inhomogeneity is performed. Transient and steady-state solutions are obtained. Numerical results about the contact pressure distribution, the deformed surface geometry, the apparent friction coefficient as well as subsurface stresses are presented, with or without heterogeneous inclusion.

Temporal Dynamics of Sodic Playa Salt Crust Patterns: Implications for Aeolian Dust Emission Potential

NASA Astrophysics Data System (ADS)

Nield, J. M.; King, J.; Bryant, R. G.; Wiggs, G.; Eckardt, F. D.; Thomas, D. S.; Washington, R.

2013-12-01

Salt pans (or playas) are common in arid environments and can be major sources of windblown mineral dust, but there are uncertainties associated with their dust emission potential. These landforms typically form crusts which modify both their erosivity and erodibility by limiting sediment availability, modifying surface and aerodynamic roughness and limiting evaporation rates and sediment production. Here we show the relationship between seasonal surface moisture change and crust pattern development based on both remote-sensing and field surface and atmospheric measurements. We use high resolution (sub-cm) terrestrial laser scanning (TLS; ground-based lidar) surveys over weekly, monthly and annual timescales to accurately characterise crustal ridge thrusting and collapse. This can be as much as 2 mm/day on fresh pan areas that have recently been reset by flooding. Over a two month period, this ridge growth can change aerodynamic roughness length values by 6.5 mm. At the same time, crack densities across the surface increase and this raises the availability of erodible fluffy, low density dust source sediment stored below the crust layer. Ridge spaces are defined in the early stages of crust development, as identified by Fourier Transform analysis, but wider wavelengths become more pronounced over time. We present a conceptual model accounting for the driving forces (subsurface, surface and atmospheric moisture) and feedbacks between these and surface shape that lead to crust pattern trajectories between highly emissive degraded surfaces and less emissive ridged or continuous crusts. These findings improve our understanding of temporal changes in dust availability and supply from playa source regions.

Temporal Characteristics of the Sleep EEG Power Spectrum in Critically Ill Children.

PubMed

Kudchadkar, Sapna R; Yaster, Myron; Punjabi, Arjun N; Quan, Stuart F; Goodwin, James L; Easley, R Blaine; Punjabi, Naresh M

2015-12-15

Although empirical evidence is limited, critical illness in children is associated with disruption of the normal sleep-wake rhythm. The objective of the current study was to examine the temporal characteristics of the sleep electroencephalogram (EEG) in a sample of children with critical illness. Limited montage EEG recordings were collected for at least 24 hours from 8 critically ill children on mechanical ventilation for respiratory failure in a pediatric intensive care unit (PICU) of a tertiary-care hospital. Each PICU patient was age- and gender-matched to a healthy subject from the community. Power spectral analysis with the fast Fourier transform (FFT) was used to characterize EEG spectral power and categorized into 4 frequency bands: δ (0.8 to 4.0 Hz), θ (4.1 to 8.0 Hz), α (8.1 to 13.0 Hz), and β1/β2 (13.1 to 20.0 Hz). PICU patients did not manifest the ultradian variability in EEG power spectra including the typical increase in δ-power during the first third of the night that was observed in healthy children. Differences noted included significantly lower mean nighttime δ and θ power in the PICU patients compared to healthy children (p < 0.001). Moreover, in the PICU patients, mean δ and θ power were higher during daytime hours than nighttime hours (p < 0.001). The results presented herein challenge the assumption that children experience restorative sleep during critical illness, highlighting the need for interventional studies to determine whether sleep promotion improves outcomes in critically ill children undergoing active neurocognitive development. © 2015 American Academy of Sleep Medicine.

Temporal variation in the dispersion patterns of metazoan parasites of a coastal fish species from the Gulf of Mexico.

PubMed

Vidal-Martínez, V M; Pal, P; Aguirre-Macedo, M L; May-Tec, A L; Lewis, J W

2014-03-01

Global climate change (GCC) is expected to affect key environmental variables such as temperature and rainfall, which in turn influence the infection dynamics of metazoan parasites in tropical aquatic hosts. Thus, our aim was to determine how temporal patterns of temperature and rainfall influence the mean abundance and aggregation of three parasite species of the fish Cichlasoma urophthalmus from Yucatán, México. We calculated mean abundance and the aggregation parameter of the negative binomial distribution k for the larval digeneans Oligogonotylus manteri and Ascocotyle (Phagicola) nana and the ectoparasite Argulus yucatanus monthly from April 2005 to December 2010. Fourier analysis of time series and cross-correlations were used to determine potential associations between mean abundance and k for the three parasite species with water temperature and rainfall. Both O. manteri and A. (Ph.) nana exhibited their highest frequency peaks in mean abundance at 6 and 12 months, respectively, while their peak in k occurred every 24 months. For A. yucatanus the frequency peaks in mean abundance and k occurred every 12 months. We suggest that the level of aggregation at 24 months of O. manteri increases the likelihood of fish mortality. Such a scenario is less likely for A. (Ph.) nana and A. yucatanus, due to their low infection levels. Our findings suggest that under the conditions of GCC it would be reasonable to expect higher levels of parasite aggregation in tropical aquatic hosts, in turn leading to a potential increase in parasite-induced host mortality.

Analysis of Franck-Condon factors for CO+ molecule using the Fourier Grid Hamiltonian method

NASA Astrophysics Data System (ADS)

Syiemiong, Arnestar; Swer, Shailes; Jha, Ashok Kumar; Saxena, Atul

2018-04-01

Franck-Condon factors (FCFs) are important parameters and it plays a very important role in determining the intensities of the vibrational bands in electronic transitions. In this paper, we illustrate the Fourier Grid Hamiltonian (FGH) method, a relatively simple method to calculate the FCFs. The FGH is a method used for calculating the vibrational eigenvalues and eigenfunctions of bound electronic states of diatomic molecules. The obtained vibrational wave functions for the ground and the excited states are used to calculate the vibrational overlap integral and then the FCFs. In this computation, we used the Morse potential and Bi-Exponential potential model for constructing and diagonalizing the molecular Hamiltonians. The effects of the change in equilibrium internuclear distance (xe), dissociation energy (De), and the nature of the excited state electronic energy curve on the FCFs have been determined. Here we present our work for the qualitative analysis of Franck-Condon Factorsusing this Fourier Grid Hamiltonian Method.

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

A comb-sampling method for enhanced mass analysis in linear electrostatic ion traps.

PubMed

Greenwood, J B; Kelly, O; Calvert, C R; Duffy, M J; King, R B; Belshaw, L; Graham, L; Alexander, J D; Williams, I D; Bryan, W A; Turcu, I C E; Cacho, C M; Springate, E

2011-04-01

In this paper an algorithm for extracting spectral information from signals containing a series of narrow periodic impulses is presented. Such signals can typically be acquired by pickup detectors from the image-charge of ion bunches oscillating in a linear electrostatic ion trap, where frequency analysis provides a scheme for high-resolution mass spectrometry. To provide an improved technique for such frequency analysis, we introduce the CHIMERA algorithm (Comb-sampling for High-resolution IMpulse-train frequency ExtRAaction). This algorithm utilizes a comb function to generate frequency coefficients, rather than using sinusoids via a Fourier transform, since the comb provides a superior match to the data. This new technique is developed theoretically, applied to synthetic data, and then used to perform high resolution mass spectrometry on real data from an ion trap. If the ions are generated at a localized point in time and space, and the data is simultaneously acquired with multiple pickup rings, the method is shown to be a significant improvement on Fourier analysis. The mass spectra generated typically have an order of magnitude higher resolution compared with that obtained from fundamental Fourier frequencies, and are absent of large contributions from harmonic frequency components. © 2011 American Institute of Physics

Fourier mode analysis of slab-geometry transport iterations in spatially periodic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larsen, E; Zika, M

1999-04-01

We describe a Fourier analysis of the diffusion-synthetic acceleration (DSA) and transport-synthetic acceleration (TSA) iteration schemes for a spatially periodic, but otherwise arbitrarily heterogeneous, medium. Both DSA and TSA converge more slowly in a heterogeneous medium than in a homogeneous medium composed of the volume-averaged scattering ratio. In the limit of a homogeneous medium, our heterogeneous analysis contains eigenvalues of multiplicity two at ''resonant'' wave numbers. In the presence of material heterogeneities, error modes corresponding to these resonant wave numbers are ''excited'' more than other error modes. For DSA and TSA, the iteration spectral radius may occur at these resonantmore » wave numbers, in which case the material heterogeneities most strongly affect iterative performance.« less

Estimation of phase derivatives using discrete chirp-Fourier-transform-based method.

PubMed

Gorthi, Sai Siva; Rastogi, Pramod

2009-08-15

Estimation of phase derivatives is an important task in many interferometric measurements in optical metrology. This Letter introduces a method based on discrete chirp-Fourier transform for accurate and direct estimation of phase derivatives, even in the presence of noise. The method is introduced in the context of the analysis of reconstructed interference fields in digital holographic interferometry. We present simulation and experimental results demonstrating the utility of the proposed method.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2017-05-01

The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

PubMed

Scargle, Jeffrey D; Way, M J; Gazis, P R

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA

PubMed Central

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys. PMID:29628519

Fourier-Mellin moment-based intertwining map for image encryption

NASA Astrophysics Data System (ADS)

Kaur, Manjit; Kumar, Vijay

2018-03-01

In this paper, a robust image encryption technique that utilizes Fourier-Mellin moments and intertwining logistic map is proposed. Fourier-Mellin moment-based intertwining logistic map has been designed to overcome the issue of low sensitivity of an input image. Multi-objective Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on Reinforcement Learning (MNSGA-RL) has been used to optimize the required parameters of intertwining logistic map. Fourier-Mellin moments are used to make the secret keys more secure. Thereafter, permutation and diffusion operations are carried out on input image using secret keys. The performance of proposed image encryption technique has been evaluated on five well-known benchmark images and also compared with seven well-known existing encryption techniques. The experimental results reveal that the proposed technique outperforms others in terms of entropy, correlation analysis, a unified average changing intensity and the number of changing pixel rate. The simulation results reveal that the proposed technique provides high level of security and robustness against various types of attacks.

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

A Fourier method for the analysis of exponential decay curves.

PubMed

Provencher, S W

1976-01-01

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.

Runoff potentiality of a watershed through SCS and functional data analysis technique.

PubMed

Adham, M I; Shirazi, S M; Othman, F; Rahman, S; Yusop, Z; Ismail, Z

2014-01-01

Runoff potentiality of a watershed was assessed based on identifying curve number (CN), soil conservation service (SCS), and functional data analysis (FDA) techniques. Daily discrete rainfall data were collected from weather stations in the study area and analyzed through lowess method for smoothing curve. As runoff data represents a periodic pattern in each watershed, Fourier series was introduced to fit the smooth curve of eight watersheds. Seven terms of Fourier series were introduced for the watersheds 5 and 8, while 8 terms of Fourier series were used for the rest of the watersheds for the best fit of data. Bootstrapping smooth curve analysis reveals that watersheds 1, 2, 3, 6, 7, and 8 are with monthly mean runoffs of 29, 24, 22, 23, 26, and 27 mm, respectively, and these watersheds would likely contribute to surface runoff in the study area. The purpose of this study was to transform runoff data into a smooth curve for representing the surface runoff pattern and mean runoff of each watershed through statistical method. This study provides information of runoff potentiality of each watershed and also provides input data for hydrological modeling.

Runoff Potentiality of a Watershed through SCS and Functional Data Analysis Technique

PubMed Central

Adham, M. I.; Shirazi, S. M.; Othman, F.; Rahman, S.; Yusop, Z.; Ismail, Z.

2014-01-01

Runoff potentiality of a watershed was assessed based on identifying curve number (CN), soil conservation service (SCS), and functional data analysis (FDA) techniques. Daily discrete rainfall data were collected from weather stations in the study area and analyzed through lowess method for smoothing curve. As runoff data represents a periodic pattern in each watershed, Fourier series was introduced to fit the smooth curve of eight watersheds. Seven terms of Fourier series were introduced for the watersheds 5 and 8, while 8 terms of Fourier series were used for the rest of the watersheds for the best fit of data. Bootstrapping smooth curve analysis reveals that watersheds 1, 2, 3, 6, 7, and 8 are with monthly mean runoffs of 29, 24, 22, 23, 26, and 27 mm, respectively, and these watersheds would likely contribute to surface runoff in the study area. The purpose of this study was to transform runoff data into a smooth curve for representing the surface runoff pattern and mean runoff of each watershed through statistical method. This study provides information of runoff potentiality of each watershed and also provides input data for hydrological modeling. PMID:25152911

Spatial-heterodyne interferometry for transmission (SHIFT) measurements

DOEpatents

Bingham, Philip R.; Hanson, Gregory R.; Tobin, Ken W.

2006-10-10

Systems and methods are described for spatial-heterodyne interferometry for transmission (SHIFT) measurements. A method includes digitally recording a spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis using a reference beam, and an object beam that is transmitted through an object that is at least partially translucent; Fourier analyzing the digitally recorded spatially-heterodyned hologram, by shifting an original origin of the digitally recorded spatially-heterodyned hologram to sit on top of a spatial-heterodyne carrier frequency defined by an angle between the reference beam and the object beam, to define an analyzed image; digitally filtering the analyzed image to cut off signals around the original origin to define a result; and performing an inverse Fourier transform on the result.

Simultaneous two-wavelength tri-window common-path digital holography

NASA Astrophysics Data System (ADS)

Liu, Lei; Shan, Mingguang; Zhong, Zhi

2018-06-01

Two-wavelength common-path off-axis digital holography is proposed with a tri-window in a single shot. It is established using a standard 4f optical image system with a 2D Ronchi grating placed outside the Fourier plane. The input plane consists of three windows: one for the object and the other two for reference. Aided by a spatial filter together with two orthogonal linear polarizers in the Fourier plane, the two-wavelength information is encoded into a multiplexed hologram with two orthogonal spatial frequencies that enable full separation of spectral information in the digital Fourier space without resolution loss. Theoretical analysis and experimental results illustrate that our approach can simultaneously perform quantitative phase imaging at two wavelengths.

Radial artery pulse waveform analysis based on curve fitting using discrete Fourier series.

PubMed

Jiang, Zhixing; Zhang, David; Lu, Guangming

2018-04-19

Radial artery pulse diagnosis has been playing an important role in traditional Chinese medicine (TCM). For its non-invasion and convenience, the pulse diagnosis has great significance in diseases analysis of modern medicine. The practitioners sense the pulse waveforms in patients' wrist to make diagnoses based on their non-objective personal experience. With the researches of pulse acquisition platforms and computerized analysis methods, the objective study on pulse diagnosis can help the TCM to keep up with the development of modern medicine. In this paper, we propose a new method to extract feature from pulse waveform based on discrete Fourier series (DFS). It regards the waveform as one kind of signal that consists of a series of sub-components represented by sine and cosine (SC) signals with different frequencies and amplitudes. After the pulse signals are collected and preprocessed, we fit the average waveform for each sample using discrete Fourier series by least squares. The feature vector is comprised by the coefficients of discrete Fourier series function. Compared with the fitting method using Gaussian mixture function, the fitting errors of proposed method are smaller, which indicate that our method can represent the original signal better. The classification performance of proposed feature is superior to the other features extracted from waveform, liking auto-regression model and Gaussian mixture model. The coefficients of optimized DFS function, who is used to fit the arterial pressure waveforms, can obtain better performance in modeling the waveforms and holds more potential information for distinguishing different psychological states. Copyright © 2018 Elsevier B.V. All rights reserved.

Accurate evaluation of sensitivity for calibration between a LiDAR and a panoramic camera used for remote sensing

NASA Astrophysics Data System (ADS)

García-Moreno, Angel-Iván; González-Barbosa, José-Joel; Ramírez-Pedraza, Alfonso; Hurtado-Ramos, Juan B.; Ornelas-Rodriguez, Francisco-Javier

2016-04-01

Computer-based reconstruction models can be used to approximate urban environments. These models are usually based on several mathematical approximations and the usage of different sensors, which implies dependency on many variables. The sensitivity analysis presented in this paper is used to weigh the relative importance of each uncertainty contributor into the calibration of a panoramic camera-LiDAR system. Both sensors are used for three-dimensional urban reconstruction. Simulated and experimental tests were conducted. For the simulated tests we analyze and compare the calibration parameters using the Monte Carlo and Latin hypercube sampling techniques. Sensitivity analysis for each variable involved into the calibration was computed by the Sobol method, which is based on the analysis of the variance breakdown, and the Fourier amplitude sensitivity test method, which is based on Fourier's analysis. Sensitivity analysis is an essential tool in simulation modeling and for performing error propagation assessments.

All-Fiber, Directly Chirped Laser Source for Chirped-Pulse-Amplification

NASA Astrophysics Data System (ADS)

Xin, Ran

Chirped-pulse-amplification (CPA) technology is widely used to produce ultra-short optical pulses (sub picosecond to femtoseconds) with high pulse energy. A chirped pulse laser source with flexible dispersion control is highly desirable as a CPA seed. This thesis presents an all-fiber, directly chirped laser source (DCLS) that produces nanosecond, linearly-chirped laser pulses at 1053 nm for seeding high energy CPA systems. DCLS produces a frequency chirp on an optical pulse through direct temporal phase modulation. DCLS provides programmable control for the temporal phase of the pulse, high pulse energy and diffraction-limited beam performance, which are beneficial for CPA systems. The DCLS concept is first described. Its key enabling technologies are identified and their experimental demonstration is presented. These include high-precision temporal phase control using an arbitrary waveform generator, multi-pass phase modulation to achieve high modulation depth, regenerative amplification in a fiber ring cavity and a negative feedback system that controls the amplifier cavity dynamics. A few technical challenges that arise from the multi-pass architecture are described and their solutions are presented, such as polarization management and gain-spectrum engineering in the DCLS fiber cavity. A DCLS has been built and its integration into a high energy OPCPA system is demonstrated. DCLS produces a 1-ns chirped pulse with a 3-nm bandwidth. The temporal phase and group delay dispersion on the DCLS output pulse is measured using temporal interferometry. The measured temporal phase has an ˜1000 rad amplitude and is close to a quadratic shape. The chirped pulse is amplified from 0.9 nJ to 76 mJ in an OPCPA system. The amplified pulse is compressed to close to its Fourier transform limit, producing an intensity autocorrelation trace with a 1.5-ps width. Direct compressed-pulse duration control by adjusting the phase modulation drive amplitude is demonstrated. Limitation to pulse compression is investigated using numerical simulation.

Application of otolith shape analysis for stock discrimination and species identification of five goby species (Perciformes: Gobiidae) in the northern Chinese coastal waters

NASA Astrophysics Data System (ADS)

Yu, Xin; Cao, Liang; Liu, Jinhu; Zhao, Bo; Shan, Xiujuan; Dou, Shuozeng

2014-09-01

We tested the use of otolith shape analysis to discriminate between species and stocks of five goby species ( Ctenotrypauchen chinensis, Odontamblyopus lacepedii, Amblychaeturichthys hexanema, Chaeturichthys stigmatias, and Acanthogobius hasta) found in northern Chinese coastal waters. The five species were well differentiated with high overall classification success using shape indices (83.7%), elliptic Fourier coefficients (98.6%), or the combination of both methods (94.9%). However, shape analysis alone was only moderately successful at discriminating among the four stocks (Liaodong Bay, LD; Bohai Bay, BH; Huanghe (Yellow) River estuary HRE, and Jiaozhou Bay, JZ stocks) of A. hasta (50%-54%) and C. stigmatias (65.7%-75.8%). For these two species, shape analysis was moderately successful at discriminating the HRE or JZ stocks from other stocks, but failed to effectively identify the LD and BH stocks. A large number of otoliths were misclassified between the HRE and JZ stocks, which are geographically well separated. The classification success for stock discrimination was higher using elliptic Fourier coefficients alone (70.2%) or in combination with shape indices (75.8%) than using only shape indices (65.7%) in C. stigmatias whereas there was little difference among the three methods for A. hasta. Our results supported the common belief that otolith shape analysis is generally more effective for interspecific identification than intraspecific discrimination. Moreover, compared with shape indices analysis, Fourier analysis improves classification success during inter- and intra-species discrimination by otolith shape analysis, although this did not necessarily always occur in all fish species.

Mapping Landscape Phenology Preference of Yellow-billed Cuckoo with AVHRR data

NASA Astrophysics Data System (ADS)

Wallace, C.; Villarreal, M. L.; Van Riper, C., III

2011-12-01

The yellow-billed cuckoo (Coccycus americanus occidentalis) is a neo-tropical migrant bird that travels north from South America into the southwestern United States during the summer to nest. In Arizona, favored riparian forest and woodland nesting habitat has declined in recent decades, due primarily to human activities and the prolonged drought conditions. As a result, western yellow-billed cuckoos have been petitioned for possible listing under the Endangered Species Act. In this study, we map yellow-billed cuckoo habitat in the state of Arizona using the temporal greenness dynamics of the landscape, or the landscape phenology. Landscape phenometrics were derived from Advanced Very High Resolution Radiometer (AVHRR) satellite Normalized Difference Vegetation Index (NDVI) composite data using Fourier harmonic analysis. Applying Fourier analysis to the waveform composed of the 26 annual composite NDVI values produces phenometrics related to the overall vegetation amount, variability and timing. Field data on Cuckoo presence were obtained from 1998 surveys conducted by Northern Arizona University (NAU), the Arizona Game and Fish Department (AGFD) and the U.S. Geological Survey (USGS). To focus the research within probable landscapes, an AGFD vegetation map (derived from the Arizona GAP program) was used to extract polygons of riparian vegetation and cottonwood-willow riparian vegetation. To create the models, we coupled the satellite phenometrics with field data of cuckoo presence or absence and with points sampling the entirety of mapped riparian and cottonwood-willow vegetation types. Statistical tests reveal that locations with cuckoos present are landscapes with greenness that is significantly more variable and that peaks significantly later than locations in average riparian vegetation, average cottonwood-willow vegetation, or with cuckoos absent. Interestingly, the mean peak greenness date of July 3 for survey locations with cuckoos present coincides with the first day of the 1998 monsoon season recorded for Tucson in southern Arizona. Models developed from the 1998 parameters and applied to 1999 data were effective at predicting cuckoo presence for survey locations visited in 1999, with up to 64 percent of cuckoos located in the highest preference class.

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

PubMed

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

Properties of thermospheric gravity waves on earth, Venus and Mars

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Pesnell, W. D.

1992-01-01

A spectral model with spherical harmonics and Fourier components that can simulate atmospheric perturbations in the global geometry of a multiconstituent atmosphere is presented. The boundaries are the planetary surface where the transport velocities vanish and the exobase where molecular heat conduction and viscosity dominate. The time consuming integration of the conservation equations is reduced to computing the transfer function (TF) which describes the dynamic properties of the medium divorced from the complexities in the temporal and horizontal variations of the excitation source. Given the TF, the atmospheric response to a chosen source distribution is then obtained in short order. Theoretical studies are presented to illuminate some properties of gravity waves on earth, Venus and Mars.

Fourier Transform Infrared Spectroscopy (FTIR) and Multivariate Analysis for Identification of Different Vegetable Oils Used in Biodiesel Production

PubMed Central

Mueller, Daniela; Ferrão, Marco Flôres; Marder, Luciano; da Costa, Adilson Ben; de Cássia de Souza Schneider, Rosana

2013-01-01

The main objective of this study was to use infrared spectroscopy to identify vegetable oils used as raw material for biodiesel production and apply multivariate analysis to the data. Six different vegetable oil sources—canola, cotton, corn, palm, sunflower and soybeans—were used to produce biodiesel batches. The spectra were acquired by Fourier transform infrared spectroscopy using a universal attenuated total reflectance sensor (FTIR-UATR). For the multivariate analysis principal component analysis (PCA), hierarchical cluster analysis (HCA), interval principal component analysis (iPCA) and soft independent modeling of class analogy (SIMCA) were used. The results indicate that is possible to develop a methodology to identify vegetable oils used as raw material in the production of biodiesel by FTIR-UATR applying multivariate analysis. It was also observed that the iPCA found the best spectral range for separation of biodiesel batches using FTIR-UATR data, and with this result, the SIMCA method classified 100% of the soybean biodiesel samples. PMID:23539030

Transitions between Central and Peripheral Vision Create Spatial/Temporal Distortions: A Hypothesis Concerning the Perceived Break of the Curveball

PubMed Central

Shapiro, Arthur; Lu, Zhong-Lin; Huang, Chang-Bing; Knight, Emily; Ennis, Robert

2010-01-01

Background The human visual system does not treat all parts of an image equally: the central segments of an image, which fall on the fovea, are processed with a higher resolution than the segments that fall in the visual periphery. Even though the differences between foveal and peripheral resolution are large, these differences do not usually disrupt our perception of seamless visual space. Here we examine a motion stimulus in which the shift from foveal to peripheral viewing creates a dramatic spatial/temporal discontinuity. Methodology/Principal Findings The stimulus consists of a descending disk (global motion) with an internal moving grating (local motion). When observers view the disk centrally, they perceive both global and local motion (i.e., observers see the disk's vertical descent and the internal spinning). When observers view the disk peripherally, the internal portion appears stationary, and the disk appears to descend at an angle. The angle of perceived descent increases as the observer views the stimulus from further in the periphery. We examine the first- and second-order information content in the display with the use of a three-dimensional Fourier analysis and show how our results can be used to describe perceived spatial/temporal discontinuities in real-world situations. Conclusions/Significance The perceived shift of the disk's direction in the periphery is consistent with a model in which foveal processing separates first- and second-order motion information while peripheral processing integrates first- and second-order motion information. We argue that the perceived distortion may influence real-world visual observations. To this end, we present a hypothesis and analysis of the perception of the curveball and rising fastball in the sport of baseball. The curveball is a physically measurable phenomenon: the imbalance of forces created by the ball's spin causes the ball to deviate from a straight line and to follow a smooth parabolic path. However, the curveball is also a perceptual puzzle because batters often report that the flight of the ball undergoes a dramatic and nearly discontinuous shift in position as the ball nears home plate. We suggest that the perception of a discontinuous shift in position results from differences between foveal and peripheral processing. PMID:20967247

Partial Fourier techniques in single-shot cross-term spatiotemporal encoded MRI.

PubMed

Zhang, Zhiyong; Frydman, Lucio

2018-03-01

Cross-term spatiotemporal encoding (xSPEN) is a single-shot approach with exceptional immunity to field heterogeneities, the images of which faithfully deliver 2D spatial distributions without requiring a priori information or using postacquisition corrections. xSPEN, however, suffers from signal-to-noise ratio penalties due to its non-Fourier nature and due to diffusion losses-especially when seeking high resolution. This study explores partial Fourier transform approaches that, acting along either the readout or the spatiotemporally encoded dimensions, reduce these penalties. xSPEN uses an orthogonal (e.g., z) gradient to read, in direct space, the low-bandwidth (e.g., y) dimension. This substantially changes the nature of partial Fourier acquisitions vis-à-vis conventional imaging counterparts. A suitable theoretical analysis is derived to implement these procedures, along either the spatiotemporally or readout axes. Partial Fourier single-shot xSPEN images were recorded on preclinical and human scanners. Owing to their reduction in the experiments' acquisition times, this approach provided substantial sensitivity gains vis-à-vis previous implementations for a given targeted in-plane resolution. The physical origins of these gains are explained. Partial Fourier approaches, particularly when implemented along the low-bandwidth spatiotemporal dimension, provide several-fold sensitivity advantages at minimal costs to the execution and processing of the single-shot experiments. Magn Reson Med 79:1506-1514, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Clustering of change patterns using Fourier coefficients.

PubMed

Kim, Jaehee; Kim, Haseong

2008-01-15

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a time period because biologically related gene groups can share the same change patterns. Many clustering algorithms have been proposed to group observation data. However, because of the complexity of the underlying functions there have not been many studies on grouping data based on change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. The sample Fourier coefficients not only provide information about the underlying functions, but also reduce the dimension. In addition, as their limiting distribution is a multivariate normal, a model-based clustering method incorporating statistical properties would be appropriate. This work is aimed at discovering gene groups with similar change patterns that share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. The model-based method is advantageous over other methods in our proposed model because the sample Fourier coefficients asymptotically follow the multivariate normal distribution. Change patterns are automatically estimated with the Fourier representation in our model. Our model was tested in simulations and on real gene data sets. The simulation results showed that the model-based clustering method with the sample Fourier coefficients has a lower clustering error rate than K-means clustering. Even when the number of repeated time points was small, the same results were obtained. We also applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns. The R program is available upon the request.

ON THE VARIATION OF SOLAR RADIUS IN ROTATION CYCLES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qu, Z. N.; Kong, D. F.; Xiang, N. B.

2015-01-10

The Date Compensated Discrete Fourier Transform and CLEANest algorithm are used to study the temporal variations of the solar radius observed at Rio de Janeiro Observatory from 1998 March 2 to 2009 November 6. The CLEANest spectra show several significant periodicities around 400, 312, 93.5, 86.2, 79.4, 70.9, 53.2, and 26.3 days. Then, combining the data on the daily solar radius measured at Calern Observatory and Rio de Janeiro Observatory and the corresponding daily sunspot areas, we study the short-term periodicity of the solar radius and the role of magnetic field in the variation of the solar radius. The rotation periodmore » of the daily solar radius is determined to be statistically significant. Moreover, its temporal evolution is anti-phase with that of sunspot activity, and it is found anti-phase with solar activity. Generally, the stronger solar activity is, the more obvious is the anti-phase relation of radius with solar activity. This indicates that strong magnetic fields have a greater inhibitive effect than weak magnetic fields on the variation of the radius.« less

Time sequence analysis of flickering auroras. I - Application of Fourier analysis. [in atmosphere

NASA Technical Reports Server (NTRS)

Berkey, F. T.; Silevitch, M. B.; Parsons, N. R.

1980-01-01

Using a technique that enables one to digitize the brightness of auroral displays from individual fields of a video signal, we have analyzed the frequency content of flickering aurora. Through the application of Fourier analysis to our data, we have found that flickering aurora contains a wide range of enhanced frequencies, although the dominant frequency enhancement generally occurs in the range 6-12 Hz. Each incidence of flickering that we observed was associated with increased radio wave absorption. Furthermore, we have found that flickering occurs in bright auroral surges, the occurrence of which is not limited to the 'breakup' phase of auroral substorms. Our results are interpreted in terms of a recently proposed theory of fluctuating double layers that accounts for a number of the observational features.

Study of lignification by noninvasive techniques in growing maize internodes. An investigation by Fourier transform infrared cross-polarization-magic angle spinning 13C-nuclear magnetic resonance spectroscopy and immunocytochemical transmission electron microscopy.

PubMed Central

Joseleau, J P; Ruel, K

1997-01-01

Noninvasive techniques were used for the study in situ of lignification in the maturing cell walls of the maize (Zea mays L.) stem. Within the longitudinal axis of a developing internode all of the stages of lignification can be found. The synthesis of the three types of lignins, p-hydroxyphenylpropane (H), guaiacyl (G), and syringyl (S), was investigated in situ by cross-polarization-magic angle spinning 13C-solid-state nuclear magnetic resonance, Fourier transform infrared spectroscopy, and immunocytochemical electron microscopy. The first lignin appearing in the parenchyma is of the G-type preceeding the incorporation of S nuclei in the later stages. However, in vascular bundles, typical absorption bands of S nuclei are visible in the Fourier transform infrared spectra at the earliest stage of lignification. Immunocytochemical determination of the three types of lignin in transmission electron microscopy was possible thanks to the use of antisera prepared against synthetic H, G, and the mixed GS dehydrogenative polymers (K. Ruel, O. Faix, J.P. Joseleau [1994] J Trace Microprobe Tech 12: 247-265). The specificity of the immunological probes demonstrated that there are differences in the relative temporal synthesis of the H, G, and GS lignins in the different tissues undergoing lignification. Considering the intermonomeric linkages predominating in the antigens used for the preparation of the immunological probes, the relative intensities of the labeling obtained provided, for the first time to our knowledge, information about the macromolecular nature of lignins (condensed versus noncondensed) in relation to their ultrastructural localization and development stage. PMID:9232887

Multidecadal Atlantic climate variability and its impact on marine pelagic communities

NASA Astrophysics Data System (ADS)

Harris, Victoria; Edwards, Martin; Olhede, Sofia C.

2014-05-01

A large scale analysis of sea surface temperature (SST) and climate variability over the North Atlantic and its interactions with plankton over the North East Atlantic was carried out to better understand what drives both temperature and species abundance. The spatio-temporal pattern of SST was found to correspond to known climate indices, namely the Atlantic Multidecadal Oscillation (AMO), the East Atlantic Pattern (EAP) and the North Atlantic Oscillation (NAO). The spatial influence of these indices is heterogeneous. Although the AMO is present across all regions, it is most strongly represented in the SST signal in the subpolar gyre region. The NAO instead is strongly weighted in the North Sea and the pattern of its influence is oscillatory in space with a wavelength of approximately 6000 km. Natural oscillations might obscure the influence of climate change effects, making it difficult to determine how much of the variation is attributable to longer term trends. In order to separate the influences of different climate signals the SST signals were decomposed in to spatial and temporal components using principal component analysis (PCA). A similar analysis is carried out on various indicator species of plankton: Calanus finmarchicus, Phytoplankton Colour Index and total copepod abundance, as well as phytoplankton and zooplankton communities. By comparing the two outputs it is apparent that the dominant driver is the recent warming trend, which has a negative influence on C. finmarchicus and total copepods, but has a positive one on phytoplankton colour. However natural oscillations also influence the abundance of plankton, in particular the AMO is a driver of diatom abundance. Fourier principal component analysis, an approach which is novel in terms of the ecological data, was used to analyse the behaviour of various communities averaged over space. The zooplankton community is found to be primarily influenced by climate warming trends. The analysis provides compelling evidence for the hypothesis that cold water species are gradually being replaced by more temperate species in the North Atlantic. This may have detrimental effects for the entire marine ecosystem, by affecting on organisms such as fish larva for example. The second group, a phytoplankton subset consisting primarily of diatom species, is primarily influenced by the AMO rather than the average temperature trend. This result highlights the importance of natural oscillations to certain functional groups, in particular those subgroups which are less directly metabolically affected by changes in temperature.

Face recognition system using multiple face model of hybrid Fourier feature under uncontrolled illumination variation.

PubMed

Hwang, Wonjun; Wang, Haitao; Kim, Hyunwoo; Kee, Seok-Cheol; Kim, Junmo

2011-04-01

The authors present a robust face recognition system for large-scale data sets taken under uncontrolled illumination variations. The proposed face recognition system consists of a novel illumination-insensitive preprocessing method, a hybrid Fourier-based facial feature extraction, and a score fusion scheme. First, in the preprocessing stage, a face image is transformed into an illumination-insensitive image, called an "integral normalized gradient image," by normalizing and integrating the smoothed gradients of a facial image. Then, for feature extraction of complementary classifiers, multiple face models based upon hybrid Fourier features are applied. The hybrid Fourier features are extracted from different Fourier domains in different frequency bandwidths, and then each feature is individually classified by linear discriminant analysis. In addition, multiple face models are generated by plural normalized face images that have different eye distances. Finally, to combine scores from multiple complementary classifiers, a log likelihood ratio-based score fusion scheme is applied. The proposed system using the face recognition grand challenge (FRGC) experimental protocols is evaluated; FRGC is a large available data set. Experimental results on the FRGC version 2.0 data sets have shown that the proposed method shows an average of 81.49% verification rate on 2-D face images under various environmental variations such as illumination changes, expression changes, and time elapses.

In vivo MRS and MRSI: Performance analysis, measurement considerations and evaluation of metabolite concentration images

NASA Astrophysics Data System (ADS)

Vikhoff-Baaz, Barbro

2000-10-01

The doctoral thesis concerns development, evaluation and performance of quality assessment methods for volume- selection methods in 31P and 1H MR spectroscopy (MRS). It also contains different aspects of the measurement procedure for 1H MR spectroscopic imaging (MRSI) with application on the human brain, image reconstruction of the MRSI images and evaluation methods for lateralization of temporal lobe epilepsy (TLE). Two complementary two-compartment phantoms and evaluation methods for quality assessment of 31P MRS in small-bore MR systems were presented. The first phantom consisted of an inner cube inside a sphere phantom where measurements with and without volume selection where compared for various VOI sizes. The multi-centre showed that the evaluated parameters provide useful information of the performance of volume-selective MRS at the MR system. The second phantom consisted of two compartments divided by a very thin wall and was found useful for measurements of the appearance and position of the VOI profile in specific gradient directions. The second part concerned 1H MRS and MRSI of whole-body MR systems. Different factors that may degrade or complicate the measurement procedure like for MRSI were evaluated, e.g. the volume selection performance, contamination, susceptibility and motion. Two interpolation methods for reconstruction of MRSI images were compared. Measurements and computer simulations showed that Fourier interpolation correctly visualizes the information inherent in the data set, while the results were dependent on the position of the object relative the original matrix using Cubic spline interpolation. Application of spatial filtering may improve the image representation of the data. Finally, 1H MRSI was performed on healthy volunteers and patients with temporal lobe epilepsy (TLE). Metabolite concentration images were used for lateralization of TLE, where the signal intensity in the two hemispheres were compared. Visual analysis of the metabolite concentration images can, with high accuracy, be used for lateralization in routine examinations. Analysis from measurements with region-of-interests (ROI) in different locations gives quantitative information about the degree of signal loss and the spatial distribution.

Multichannel Dynamic Fourier-Transform IR Spectrometer

NASA Astrophysics Data System (ADS)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

Nonlinear Propagation of Alfven Waves Driven by Observed Photospheric Motions: Application to the Coronal Heating and Spicule Formation

NASA Astrophysics Data System (ADS)

Matsumoto, Takuma; Shibata, Kazunari

We have performed MHD simulations of Alfven wave propagation along an open ux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photo-spheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy ux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave gener-ator. This difference can be explained by the Alfven wave resonance between the photosphere and the transition region. After performing Fourier analysis on our numerical results, we have found that the region between the photosphere and the transition region becomes an Alfven wave resonant cavity. We have conrmed that there are at least three resonant frequencies, 1, 3 and 5 mHz, in our numerical model. Alfven wave resonance is one of the most effective mechanisms to explain the dynamics of the spicules and the sufficient energy ux to heat the corona.

Small-scale structure of the midlatitude storm enhanced density plume during the 17 March 2015 St. Patrick's Day storm

NASA Astrophysics Data System (ADS)

Heine, Thomas R. P.; Moldwin, Mark B.; Zou, Shasha

2017-03-01

Kilometer-scale density irregularities in the ionosphere can cause ionospheric scintillation—a phenomenon that degrades space-based navigation and communication signals. During strong geomagnetic storms, the midlatitude ionosphere is primed to produce these ˜1-10 km small-scale irregularities along the steep gradients between midlatitude storm enhanced density (SED) plumes and the adjacent low-density trough. The length scales of irregularities on the order of 1-10 km are determined from a combination of spatial, temporal, and frequency analyses using single-station ground-based Global Positioning System total electron content (TEC) combined with radar plasma velocity measurements. Kilometer-scale irregularities are detected along the boundaries of the SED plume and depleted density trough during the 17 March 2015 geomagnetic storm, but not equatorward of the plume or within the plume itself. Analysis using the fast Fourier transform of high-pass filtered slant TEC suggests that the kilometer-scale irregularities formed near the poleward gradients of SED plumes can have similar intensity and length scales to those typically found in the aurora but are shown to be distinct phenomena in spacecraft electron precipitation measurements.

Scale size-dependent characteristics of the nightside aurora

NASA Astrophysics Data System (ADS)

Humberset, B. K.; Gjerloev, J. W.; Samara, M.; Michell, R. G.

2017-02-01

We have determined the spatiotemporal characteristics of the magnetosphere-ionosphere (M-I) coupling using auroral imaging. Observations at fixed positions for an extended period of time are provided by a ground-based all-sky imager measuring the 557.7 nm auroral emissions. We report on a single event of nightside aurora (˜22 magnetic local time) preceding a substorm onset. To determine the spatiotemporal characteristics, we perform an innovative analysis of an all-sky imager movie (19 min duration, images at 3.31 Hz) that combines a two-dimensional spatial fast Fourier transform with a temporal correlation. We find a scale size-dependent variability where the largest scale sizes are stable on timescales of minutes while the small scale sizes are more variable. When comparing two smaller time intervals of different types of auroral displays, we find a variation in their characteristics. The characteristics averaged over the event are in remarkable agreement with the spatiotemporal characteristics of the nightside field-aligned currents during moderately disturbed times. Thus, two different electrodynamical parameters of the M-I coupling show similar behavior. This gives independent support to the claim of a system behavior that uses repeatable solutions to transfer energy and momentum from the magnetosphere to the ionosphere.

Terahertz parametric sources and imaging applications

NASA Astrophysics Data System (ADS)

Yamashita, M.; Ogawa, Y.; Otani, C.; Kawase, K.

2005-12-01

We have studied the generation of terahertz (THz) waves by optical parametric processes based on laser light scattering from the polariton mode of nonlinear crystals. Using parametric oscillation of LiNbO 3 or MgO-doped LiNbO 3 crystal pumped by a nano-second Q-switched Nd:YAG laser, we have realized a widely tunable coherent THz-wave sources with a simple configuration. We report the detailed characteristics of the oscillation and the radiation including tunability, spatial and temporal coherency, uni directivity, and efficiency. A Fourier transform limited THz-wave spectrum narrowing was achieved by introducing the injection seeding method. Further, we have developed a spectroscopic THz imaging system using a TPO, which allows detection and identification of drugs concealed in envelopes, by introducing the component spatial pattern analysis. Several images of the envelope are recorded at different THz frequencies and then processed. The final result is an image that reveals what substances are present in the envelope, in what quantity, and how they are distributed across the envelope area. The example presented here shows the identification of three drugs, two of which illegal, while one is an over-the-counter drug.

Terahertz parametric sources and imaging applications

NASA Astrophysics Data System (ADS)

Kawase, Kodo; Ogawa, Yuichi; Minamide, Hiroaki; Ito, Hiromasa

2005-07-01

We have studied the generation of terahertz (THz) waves by optical parametric processes based on laser light scattering from the polariton mode of nonlinear crystals. Using parametric oscillation of LiNbO3 or MgO-doped LiNbO3 crystal pumped by a nano-second Q-switched Nd:YAG laser, we have realized a widely tunable coherent THz-wave source with a simple configuration. We report the detailed characteristics of the oscillation and the radiation including tunability, spatial and temporal coherency, uni-directivity, and efficiency. A Fourier transform limited THz-wave spectrum narrowing was achieved by introducing the injection seeding method. Further, we have developed a spectroscopic THz imaging system using a THz-wave parametric oscillator, which allows detection and identification of drugs concealed in envelopes, by introducing the component spatial pattern analysis. Several images of the envelope are recorded at different THz frequencies and then processed. The final result is an image that reveals what substances are present in the envelope, in what quantity, and how they are distributed across the envelope area. The example presented here shows the identification of three drugs, two of which are illegal, while one is an over-the-counter drug.

Automatic food intake detection based on swallowing sounds.

PubMed

Makeyev, Oleksandr; Lopez-Meyer, Paulo; Schuckers, Stephanie; Besio, Walter; Sazonov, Edward

2012-11-01

This paper presents a novel fully automatic food intake detection methodology, an important step toward objective monitoring of ingestive behavior. The aim of such monitoring is to improve our understanding of eating behaviors associated with obesity and eating disorders. The proposed methodology consists of two stages. First, acoustic detection of swallowing instances based on mel-scale Fourier spectrum features and classification using support vector machines is performed. Principal component analysis and a smoothing algorithm are used to improve swallowing detection accuracy. Second, the frequency of swallowing is used as a predictor for detection of food intake episodes. The proposed methodology was tested on data collected from 12 subjects with various degrees of adiposity. Average accuracies of >80% and >75% were obtained for intra-subject and inter-subject models correspondingly with a temporal resolution of 30s. Results obtained on 44.1 hours of data with a total of 7305 swallows show that detection accuracies are comparable for obese and lean subjects. They also suggest feasibility of food intake detection based on swallowing sounds and potential of the proposed methodology for automatic monitoring of ingestive behavior. Based on a wearable non-invasive acoustic sensor the proposed methodology may potentially be used in free-living conditions.

Automatic food intake detection based on swallowing sounds

PubMed Central

Makeyev, Oleksandr; Lopez-Meyer, Paulo; Schuckers, Stephanie; Besio, Walter; Sazonov, Edward

2012-01-01

This paper presents a novel fully automatic food intake detection methodology, an important step toward objective monitoring of ingestive behavior. The aim of such monitoring is to improve our understanding of eating behaviors associated with obesity and eating disorders. The proposed methodology consists of two stages. First, acoustic detection of swallowing instances based on mel-scale Fourier spectrum features and classification using support vector machines is performed. Principal component analysis and a smoothing algorithm are used to improve swallowing detection accuracy. Second, the frequency of swallowing is used as a predictor for detection of food intake episodes. The proposed methodology was tested on data collected from 12 subjects with various degrees of adiposity. Average accuracies of >80% and >75% were obtained for intra-subject and inter-subject models correspondingly with a temporal resolution of 30s. Results obtained on 44.1 hours of data with a total of 7305 swallows show that detection accuracies are comparable for obese and lean subjects. They also suggest feasibility of food intake detection based on swallowing sounds and potential of the proposed methodology for automatic monitoring of ingestive behavior. Based on a wearable non-invasive acoustic sensor the proposed methodology may potentially be used in free-living conditions. PMID:23125873

Rod- versus cone-driven ERGs at different stimulus sizes in normal subjects and retinitis pigmentosa patients.

PubMed

Aher, Avinash J; McKeefry, Declan J; Parry, Neil R A; Maguire, John; Murray, I J; Tsai, Tina I; Huchzermeyer, Cord; Kremers, Jan

2018-02-01

To study how rod- and cone-driven responses depend on stimulus size in normal subjects and patients with retinitis pigmentosa (RP), and to show that comparisons between responses to full-field (FF) and smaller stimuli can be useful in diagnosing and monitoring disorders of the peripheral retina without the need for lengthy dark adaptation periods. The triple silent substitution technique was used to isolate L-cone-, M-cone- and rod-driven ERGs with 19, 18 and 33% photoreceptor contrasts, respectively, under identical mean luminance conditions. Experiments were conducted on five normal subjects and three RP patients. ERGs on control subjects were recorded at nine different temporal frequencies (between 2 and 60 Hz) for five different stimulus sizes: FF, 70°, 60°, 50° and 40° diameter circular stimuli. Experiments on RP patients involved rod- and L-cone-driven ERG measurements with FF and 40° stimuli at 8 and 48 Hz. Response amplitudes were defined as those of the first harmonic component after Fourier analysis. In normal subjects, rod-driven responses displayed a fundamentally different behavior than cone-driven responses, particularly at low temporal frequencies. At low and intermediate temporal frequencies (≤ 12 Hz), rod-driven signals increased by a factor of about four when measured with smaller stimuli. In contrast, L- and M-cone-driven responses in this frequency region did not change substantially with stimulus size. At high temporal frequencies (≥ 24 Hz), both rod- and cone-driven response amplitudes decreased with decreasing stimulus size. Signals obtained from rod-isolating stimuli under these conditions are likely artefactual. Interestingly, in RP patients, both rod-driven and L-cone-driven ERGs were similar using 40° and FF stimuli. The increased responses with smaller stimuli in normal subjects to rod-isolating stimuli indicate that a fundamentally different mechanism drives the ERGs in comparison with the cone-driven responses. We propose that the increased responses are caused by stray light stimulating the peripheral retina, thereby allowing peripheral rod-driven function to be studied using the triple silent substitution technique at photopic luminances. The method is effective in studying impaired peripheral rod- and cone- function in RP patients.

Differentiation and detection of microorganisms using Fourier transform infrared photoacoustic spectroscopy

NASA Astrophysics Data System (ADS)

Irudayaraj, Joseph; Yang, Hong; Sakhamuri, Sivakesava

2002-03-01

Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) was used to differentiate and identify microorganisms on a food (apple) surface. Microorganisms considered include bacteria (Lactobacillus casei, Bacillus cereus, and Escherichia coli), yeast (Saccharomyces cerevisiae), and fungi (Aspergillus niger and Fusarium verticilliodes). Discriminant analysis was used to differentiate apples contaminated with the different microorganisms from uncontaminated apple. Mahalanobis distances were calculated to quantify the differences. The higher the value of the Mahalanobis distance metric between different microorganisms, the greater is their difference. Additionally, pathogenic (O157:H7) E. coli was successfully differentiated from non-pathogenic strains. Results demonstrate that FTIR-PAS spectroscopy has the potential to become a non-destructive analysis tool in food safety related research.

Structural, spectral and birefringence studies of semiorganic nonlinear optical single crystal: Calcium5-sulfosalicylate

NASA Astrophysics Data System (ADS)

Shalini, D.; Kalainathan, S.; Ambika, V. Revathi; Hema, N.; Jayalakshmi, D.

2017-11-01

Semi-organic nonlinear optical crystal Calcium5-Sulfosalicylate (CA5SS) was grown by slow evaporation solution growth technique. The cell parameters and molecular structure of the grown crystal were studied by single crystal x-ray diffraction analysis. The presence of various functional groups of the grown crystal was confirmed using Fourier transform infrared (FT-IR), Fourier transform Raman (FT-Raman) analysis. UV-Visible spectrum shows that CA5SS crystals have high transmittance in the range of 330-900 nm. The refractive index, birefringence and transient photoluminescence properties of the grown crystal were analyzed. The frequency doubling of the grown crystal (CA5SS) were studied and compared with that of KDP.

Antenna pattern correction for the Nimbus-7 SMMR

NASA Technical Reports Server (NTRS)

Milman, A. S.

1986-01-01

This paper describes the philosophy and method used to develop the antenna pattern correction (APC) algorithm that was used on the data from the Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus-7. There are limitations on what can be accomplished with such a procedure; these limitations are explored with the aid of Fourier analysis, even though the algorithm used on the SMMR data does not perform any Fourier transforms. The resulting analysis showed that, for the SMMR instrument, no useful improvement could be made in the data in terms of reduction of side lobes, but the quality of the sea surface temperature retrievals could be improved considerably by matching the antenna beamwidths at the different frequencies.

Machine learning for the automatic localisation of foetal body parts in cine-MRI scans

NASA Astrophysics Data System (ADS)

Bowles, Christopher; Nowlan, Niamh C.; Hayat, Tayyib T. A.; Malamateniou, Christina; Rutherford, Mary; Hajnal, Joseph V.; Rueckert, Daniel; Kainz, Bernhard

2015-03-01

Being able to automate the location of individual foetal body parts has the potential to dramatically reduce the work required to analyse time resolved foetal Magnetic Resonance Imaging (cine-MRI) scans, for example, for use in the automatic evaluation of the foetal development. Currently, manual preprocessing of every scan is required to locate body parts before analysis can be performed, leading to a significant time overhead. With the volume of scans becoming available set to increase as cine-MRI scans become more prevalent in clinical practice, this stage of manual preprocessing is a bottleneck, limiting the data available for further analysis. Any tools which can automate this process will therefore save many hours of research time and increase the rate of new discoveries in what is a key area in understanding early human development. Here we present a series of techniques which can be applied to foetal cine-MRI scans in order to first locate and then differentiate between individual body parts. A novel approach to maternal movement suppression and segmentation using Fourier transforms is put forward as a preprocessing step, allowing for easy extraction of short movements of individual foetal body parts via the clustering of optical flow vector fields. These body part movements are compared to a labelled database and probabilistically classified before being spatially and temporally combined to give a final estimate for the location of each body part.

Applications of Self-Organizing Maps for Ecomorphological Investigations through Early Ontogeny of Fish

PubMed Central

Russo, Tommaso; Scardi, Michele; Cataudella, Stefano

2014-01-01

We propose a new graphical approach to the analysis of multi-temporal morphological and ecological data concerning the life history of fish, which can typically serves models in ecomorphological investigations because they often undergo significant ontogenetic changes. These changes can be very complex and difficult to describe, so that visualization, abstraction and interpretation of the underlying relationships are often impeded. Therefore, classic ecomorphological analyses of covariation between morphology and ecology, performed by means of multivariate techniques, may result in non-exhaustive models. The Self Organizing map (SOM) is a new, effective approach for pursuing this aim. In this paper, lateral outlines of larval stages of gilthead sea bream (Sparus aurata) and dusky grouper (Epinephelus marginatus) were recorded and broken down using by means of Elliptic Fourier Analysis (EFA). Gut contents of the same specimens were also collected and analyzed. Then, shape and trophic habits data were examined by SOM, which allows both a powerful visualization of shape changes and an easy comparison with trophic habit data, via their superimposition onto the trained SOM. Thus, the SOM provides a direct visual approach for matching morphological and ecological changes during fish ontogenesis. This method could be used as a tool to extract and investigate relationships between shape and other sinecological or environmental variables, which cannot be taken into account simultaneously using conventional statistical methods. PMID:24466185

Applying spectral data analysis techniques to aquifer monitoring data in Belvoir Ranch, Wyoming

NASA Astrophysics Data System (ADS)

Gao, F.; He, S.; Zhang, Y.

2017-12-01

This study uses spectral data analysis techniques to estimate the hydraulic parameters from water level fluctuation due to tide effect and barometric effect. All water level data used in this study are collected in Belvoir Ranch, Wyoming. Tide effect can be not only observed in coastal areas, but also in inland confined aquifers. The force caused by changing positions of sun and moon affects not only ocean but also solid earth. The tide effect has an oscillatory pumping or injection sequence to the aquifer, and can be observed from dense water level monitoring. Belvoir Ranch data are collected once per hour, thus is dense enough to capture the tide effect. First, transforming de-trended data from temporal domain to frequency domain with Fourier transform method. Then, the storage coefficient can be estimated using Bredehoeft-Jacob model. After this, analyze the gain function, which expresses the amplification and attenuation of the output signal, and derive barometric efficiency. Next, find effective porosity with storage coefficient and barometric efficiency with Jacob's model. Finally, estimate aquifer transmissivity and hydraulic conductivity using Paul Hsieh's method. The estimated hydraulic parameters are compared with those from traditional pumping data estimation. This study proves that hydraulic parameter can be estimated by only analyze water level data in frequency domain. It has the advantages of low cost and environmental friendly, thus should be considered for future use of hydraulic parameter estimations.

Comparison of detrending methods for fluctuation analysis in hydrology

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Zhou, Yu; Singh, Vijay P.; Chen, Yongqin David

2011-03-01

SummaryTrends within a hydrologic time series can significantly influence the scaling results of fluctuation analysis, such as rescaled range (RS) analysis and (multifractal) detrended fluctuation analysis (MF-DFA). Therefore, removal of trends is important in the study of scaling properties of the time series. In this study, three detrending methods, including adaptive detrending algorithm (ADA), Fourier-based method, and average removing technique, were evaluated by analyzing numerically generated series and observed streamflow series with obvious relative regular periodic trend. Results indicated that: (1) the Fourier-based detrending method and ADA were similar in detrending practices, and given proper parameters, these two methods can produce similarly satisfactory results; (2) detrended series by Fourier-based detrending method and ADA lose the fluctuation information at larger time scales, and the location of crossover points is heavily impacted by the chosen parameters of these two methods; and (3) the average removing method has an advantage over the other two methods, i.e., the fluctuation information at larger time scales is kept well-an indication of relatively reliable performance in detrending. In addition, the average removing method performed reasonably well in detrending a time series with regular periods or trends. In this sense, the average removing method should be preferred in the study of scaling properties of the hydrometeorolgical series with relative regular periodic trend using MF-DFA.

Fractal and Fourier analysis of the hepatic sinusoidal network in normal and cirrhotic rat liver

PubMed Central

Gaudio, Eugenio; Chaberek, Slawomir; Montella, Andrea; Pannarale, Luigi; Morini, Sergio; Novelli, Gilnardo; Borghese, Federica; Conte, Davide; Ostrowski, Kazimierz

2005-01-01

The organization of the hepatic microvascular network has been widely studied in recent years, especially with regard to cirrhosis. This research has enabled us to recognize the distinctive vascular patterns in the cirrhotic liver, compared with the normal liver, which may explain the cause of liver dysfunction and failure. The aim of this study was to compare normal and cirrhotic rat livers by means of a quantitative mathematical approach based on fractal and Fourier analyses performed on photomicrographs and therefore on discriminant analysis. Vascular corrosion casts of livers belonging to the following three experimental groups were studied by scanning electron microscopy: normal rats, CCl4-induced cirrhotic rats and cirrhotic rats after ligation of the bile duct. Photomicrographs were taken at a standard magnification; these images were used for the mathematical analysis. Our experimental design found that use of these different analyses reaches an efficiency of over 94%. Our analyses demonstrated a higher complexity of the normal hepatic sinusoidal network in comparison with the cirrhotic network. In particular, the morphological changes were more marked in the animals with bile duct-ligation cirrhosis compared with animals with CCl4-induced cirrhosis. The present findings based on fractal and Fourier analysis could increase our understanding of the pathophysiological alterations of the liver, and may have a diagnostic value in future clinical research. PMID:16050897

Novel applications of photonic signal processing: Temporal cloaking and biphoton pulse shaping

NASA Astrophysics Data System (ADS)

Lukens, Joseph M.

We experimentally demonstrate two innovative applications of photonic technologies previously solidified in the field of classical optical communications. In the first application, we exploit electro-optic modulator technology to develop a novel "time cloak,'' a device which hides events in time by manipulating the flow of a probing light beam. Our temporal cloak is capable of masking high-speed optical data from a receiver, greatly improving the feasibility of time cloaking and bringing such exotic concepts to the verge of practical application. In the second specialization, high-resolution Fourier-transform pulse shaping---perfected for multi-wavelength telecom networks---is applied to shape the correlations of entangled photon pairs, states which have received considerable attention in nonlocal tests of quantum theory and in quantum key distribution. Using nonlinear waveguides fabricated out of periodically poled lithium niobate, we are able to demonstrate ultrafast coincidence detection with record-high efficiency, which coupled with our pulse shaper allows us to realize for the first time several capabilities in biphoton control, including high-order dispersion cancellation, orthogonal spectral coding, correlation train generation, and tunable delay control. Each of these experiments represents an important advance in quantum state manipulation, with the potential to impact developments in quantum information. And more generally, our work introducing telecommunication technology into both temporal cloaking and biphoton control highlights the potential of such tools in more nascent outgrowths of classical and quantum optics.

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.