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.

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.

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.

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

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.

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.

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.

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.

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.

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.

Unmixing the Materials and Mechanics Contributions in Non-resolved Object Signatures

DTIC Science & Technology

2008-09-01

abundances from hyperspectral or multi-spectral time - resolved signatures. A Fourier analysis of temporal variation of material abundance provides...factorization technique to extract the temporal variation of material abundances from hyperspectral or multi-spectral time - resolved signatures. A Fourier...approximately one hundred wavelengths in the visible spectrum. The frame rate for the instrument was not large enough to collect time resolved data. However

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.

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.

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.

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.

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

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

PubMed

Kim, Jaehee; Ogden, Robert Todd; Kim, Haseong

2013-10-18

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. 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. 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.

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.

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.

Development of the Complex General Linear Model in the Fourier Domain: Application to fMRI Multiple Input-Output Evoked Responses for Single Subjects

PubMed Central

Rio, Daniel E.; Rawlings, Robert R.; Woltz, Lawrence A.; Gilman, Jodi; Hommer, Daniel W.

2013-01-01

A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function. PMID:23840281

Development of the complex general linear model in the Fourier domain: application to fMRI multiple input-output evoked responses for single subjects.

PubMed

Rio, Daniel E; Rawlings, Robert R; Woltz, Lawrence A; Gilman, Jodi; Hommer, Daniel W

2013-01-01

A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function.

Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications

PubMed Central

2013-01-01

Background Time-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications. Methods To accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal. Results The proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods. Conclusions Results show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement. PMID:24274109

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.

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.

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

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.

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.

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.

Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.

PubMed

Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José

2015-12-14

We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.

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

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.

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

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.

Short-time fractional Fourier methods for the time-frequency representation of chirp signals.

PubMed

Capus, Chris; Brown, Keith

2003-06-01

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.

A study of sound generation in subsonic rotors, volume 2

NASA Technical Reports Server (NTRS)

Chalupnik, J. D.; Clark, L. T.

1975-01-01

Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation.

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

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.

Fourier's law of heat conduction: quantum mechanical master equation analysis.

PubMed

Wu, Lian-Ao; Segal, Dvira

2008-06-01

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting of an exchange effect. The pure exchange model directly leads to energy diffusion in a weakly coupled spin- 12 chain.

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.

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.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

PubMed Central

Mobli, Mehdi; Hoch, Jeffrey C.

2017-01-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. PMID:25456315

Methods and Applications of Time Series Analysis. Part I. Regression, Trends, Smoothing, and Differencing.

DTIC Science & Technology

1980-07-01

FUNCTION ( t) CENTERED AT C WITH PERIOD n -nr 0 soTIME t FIGURE 3.4S RECTAPOOLAR PORN )=C FUNCTION g t) CENTERED AT 0 WITH PERIOD n n n 52n tI y I (h...of a typical family in Kabiria (a city in Northern Algeria) over the time period Jan.-Feb. 1975 through Nov.-Dec. 1977. We would like to obtain a...values of y .. .. ... -75- Table 4.2 The Average Bi-Monthly Expenses of a Family in Kabiria and Their Fourier Representation Fourier Coefficients x k

Spectral Analysis of the Effects of Daylight Saving Time on Motor Vehicle Fatal Traffic Accidents

DOT National Transportation Integrated Search

1977-04-01

This report shows that Daylight Saving Time (DST) reduces the number of persons killed in motor vehicle fatal traffic accidents by about one percent. This estimate is based on a spectral (Fourier) analysis of these fatalities which utilizes a filteri...

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

PubMed

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

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.

FPGA-based multi-channel fluorescence lifetime analysis of Fourier multiplexed frequency-sweeping lifetime imaging

PubMed Central

Zhao, Ming; Li, Yu; Peng, Leilei

2014-01-01

We report a fast non-iterative lifetime data analysis method for the Fourier multiplexed frequency-sweeping confocal FLIM (Fm-FLIM) system [ Opt. Express22, 10221 ( 2014)24921725]. The new method, named R-method, allows fast multi-channel lifetime image analysis in the system’s FPGA data processing board. Experimental tests proved that the performance of the R-method is equivalent to that of single-exponential iterative fitting, and its sensitivity is well suited for time-lapse FLIM-FRET imaging of live cells, for example cyclic adenosine monophosphate (cAMP) level imaging with GFP-Epac-mCherry sensors. With the R-method and its FPGA implementation, multi-channel lifetime images can now be generated in real time on the multi-channel frequency-sweeping FLIM system, and live readout of FRET sensors can be performed during time-lapse imaging. PMID:25321778

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.

Dating a tropical ice core by time-frequency analysis of ion concentration depth profiles

NASA Astrophysics Data System (ADS)

Gay, M.; De Angelis, M.; Lacoume, J.-L.

2014-09-01

Ice core dating is a key parameter for the interpretation of the ice archives. However, the relationship between ice depth and ice age generally cannot be easily established and requires the combination of numerous investigations and/or modelling efforts. This paper presents a new approach to ice core dating based on time-frequency analysis of chemical profiles at a site where seasonal patterns may be significantly distorted by sporadic events of regional importance, specifically at the summit area of Nevado Illimani (6350 m a.s.l.), located in the eastern Bolivian Andes (16°37' S, 67°46' W). We used ion concentration depth profiles collected along a 100 m deep ice core. The results of Fourier time-frequency and wavelet transforms were first compared. Both methods were applied to a nitrate concentration depth profile. The resulting chronologies were checked by comparison with the multi-proxy year-by-year dating published by de Angelis et al. (2003) and with volcanic tie points. With this first experiment, we demonstrated the efficiency of Fourier time-frequency analysis when tracking the nitrate natural variability. In addition, we were able to show spectrum aliasing due to under-sampling below 70 m. In this article, we propose a method of de-aliasing which significantly improves the core dating in comparison with annual layer manual counting. Fourier time-frequency analysis was applied to concentration depth profiles of seven other ions, providing information on the suitability of each of them for the dating of tropical Andean ice cores.

Global Data for Ecology and Epidemiology: A Novel Algorithm for Temporal Fourier Processing MODIS Data

PubMed Central

Scharlemann, Jörn P. W.; Benz, David; Hay, Simon I.; Purse, Bethan V.; Tatem, Andrew J.; Wint, G. R. William; Rogers, David J.

2008-01-01

Background Remotely-sensed environmental data from earth-orbiting satellites are increasingly used to model the distribution and abundance of both plant and animal species, especially those of economic or conservation importance. Time series of data from the MODerate-resolution Imaging Spectroradiometer (MODIS) sensors on-board NASA's Terra and Aqua satellites offer the potential to capture environmental thermal and vegetation seasonality, through temporal Fourier analysis, more accurately than was previously possible using the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor data. MODIS data are composited over 8- or 16-day time intervals that pose unique problems for temporal Fourier analysis. Applying standard techniques to MODIS data can introduce errors of up to 30% in the estimation of the amplitudes and phases of the Fourier harmonics. Methodology/Principal Findings We present a novel spline-based algorithm that overcomes the processing problems of composited MODIS data. The algorithm is tested on artificial data generated using randomly selected values of both amplitudes and phases, and provides an accurate estimate of the input variables under all conditions. The algorithm was then applied to produce layers that capture the seasonality in MODIS data for the period from 2001 to 2005. Conclusions/Significance Global temporal Fourier processed images of 1 km MODIS data for Middle Infrared Reflectance, day- and night-time Land Surface Temperature (LST), Normalised Difference Vegetation Index (NDVI), and Enhanced Vegetation Index (EVI) are presented for ecological and epidemiological applications. The finer spatial and temporal resolution, combined with the greater geolocational and spectral accuracy of the MODIS instruments, compared with previous multi-temporal data sets, mean that these data may be used with greater confidence in species' distribution modelling. PMID:18183289

Global data for ecology and epidemiology: a novel algorithm for temporal Fourier processing MODIS data.

PubMed

Scharlemann, Jörn P W; Benz, David; Hay, Simon I; Purse, Bethan V; Tatem, Andrew J; Wint, G R William; Rogers, David J

2008-01-09

Remotely-sensed environmental data from earth-orbiting satellites are increasingly used to model the distribution and abundance of both plant and animal species, especially those of economic or conservation importance. Time series of data from the MODerate-resolution Imaging Spectroradiometer (MODIS) sensors on-board NASA's Terra and Aqua satellites offer the potential to capture environmental thermal and vegetation seasonality, through temporal Fourier analysis, more accurately than was previously possible using the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor data. MODIS data are composited over 8- or 16-day time intervals that pose unique problems for temporal Fourier analysis. Applying standard techniques to MODIS data can introduce errors of up to 30% in the estimation of the amplitudes and phases of the Fourier harmonics. We present a novel spline-based algorithm that overcomes the processing problems of composited MODIS data. The algorithm is tested on artificial data generated using randomly selected values of both amplitudes and phases, and provides an accurate estimate of the input variables under all conditions. The algorithm was then applied to produce layers that capture the seasonality in MODIS data for the period from 2001 to 2005. Global temporal Fourier processed images of 1 km MODIS data for Middle Infrared Reflectance, day- and night-time Land Surface Temperature (LST), Normalised Difference Vegetation Index (NDVI), and Enhanced Vegetation Index (EVI) are presented for ecological and epidemiological applications. The finer spatial and temporal resolution, combined with the greater geolocational and spectral accuracy of the MODIS instruments, compared with previous multi-temporal data sets, mean that these data may be used with greater confidence in species' distribution modelling.

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.

Study on time-frequency analysis method of very fast transient overvoltage

NASA Astrophysics Data System (ADS)

Li, Shuai; Liu, Shiming; Huang, Qiyan; Fu, Chuanshun

2018-04-01

The operation of the disconnector in the gas insulated substation (GIS) may produce very fast transient overvoltage (VFTO), which has the characteristics of short rise time, short duration, high amplitude and rich frequency components. VFTO can cause damage to GIS and secondary equipment, and the frequency components contained in the VFTO can cause resonance overvoltage inside the transformer, so it is necessary to study the spectral characteristics of the VFTO. From the perspective of signal processing, VFTO is a kind of non-stationary signal, the traditional Fourier transform is difficult to describe its frequency which changes with time, so it is necessary to use time-frequency analysis to analyze VFTO spectral characteristics. In this paper, we analyze the performance of short time Fourier transform (STFT), Wigner-Ville distribution (WVD), pseudo Wigner-Ville distribution (PWVD) and smooth pseudo Wigner-Ville distribution (SPWVD). The results show that SPWVD transform is the best. The time-frequency aggregation of SPWVD is higher than STFT, and it does not have cross-interference terms, which can meet the requirements of VFTO spectrum analysis.

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 new fractional wavelet transform

NASA Astrophysics Data System (ADS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

Spectral analysis based on fast Fourier transformation (FFT) of surveillance data: the case of scarlet fever in China.

PubMed

Zhang, T; Yang, M; Xiao, X; Feng, Z; Li, C; Zhou, Z; Ren, Q; Li, X

2014-03-01

Many infectious diseases exhibit repetitive or regular behaviour over time. Time-domain approaches, such as the seasonal autoregressive integrated moving average model, are often utilized to examine the cyclical behaviour of such diseases. The limitations for time-domain approaches include over-differencing and over-fitting; furthermore, the use of these approaches is inappropriate when the assumption of linearity may not hold. In this study, we implemented a simple and efficient procedure based on the fast Fourier transformation (FFT) approach to evaluate the epidemic dynamic of scarlet fever incidence (2004-2010) in China. This method demonstrated good internal and external validities and overcame some shortcomings of time-domain approaches. The procedure also elucidated the cycling behaviour in terms of environmental factors. We concluded that, under appropriate circumstances of data structure, spectral analysis based on the FFT approach may be applicable for the study of oscillating diseases.

Fault detection of gearbox using time-frequency method

NASA Astrophysics Data System (ADS)

Widodo, A.; Satrijo, Dj.; Prahasto, T.; Haryanto, I.

2017-04-01

This research deals with fault detection and diagnosis of gearbox by using vibration signature. In this work, fault detection and diagnosis are approached by employing time-frequency method, and then the results are compared with cepstrum analysis. Experimental work has been conducted for data acquisition of vibration signal thru self-designed gearbox test rig. This test-rig is able to demonstrate normal and faulty gearbox i.e., wears and tooth breakage. Three accelerometers were used for vibration signal acquisition from gearbox, and optical tachometer was used for shaft rotation speed measurement. The results show that frequency domain analysis using fast-fourier transform was less sensitive to wears and tooth breakage condition. However, the method of short-time fourier transform was able to monitor the faults in gearbox. Wavelet Transform (WT) method also showed good performance in gearbox fault detection using vibration signal after employing time synchronous averaging (TSA).

Online frequency estimation with applications to engine and generator sets

NASA Astrophysics Data System (ADS)

Manngård, Mikael; Böling, Jari M.

2017-07-01

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR.

PubMed

Mobli, Mehdi; Hoch, Jeffrey C

2014-11-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. Copyright © 2014 Elsevier B.V. All rights reserved.

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.

Estimation of spectral kurtosis

NASA Astrophysics Data System (ADS)

Sutawanir

2017-03-01

Rolling bearings are the most important elements in rotating machinery. Bearing frequently fall out of service for various reasons: heavy loads, unsuitable lubrications, ineffective sealing. Bearing faults may cause a decrease in performance. Analysis of bearing vibration signals has attracted attention in the field of monitoring and fault diagnosis. Bearing vibration signals give rich information for early detection of bearing failures. Spectral kurtosis, SK, is a parameter in frequency domain indicating how the impulsiveness of a signal varies with frequency. Faults in rolling bearings give rise to a series of short impulse responses as the rolling elements strike faults, SK potentially useful for determining frequency bands dominated by bearing fault signals. SK can provide a measure of the distance of the analyzed bearings from a healthy one. SK provides additional information given by the power spectral density (psd). This paper aims to explore the estimation of spectral kurtosis using short time Fourier transform known as spectrogram. The estimation of SK is similar to the estimation of psd. The estimation falls in model-free estimation and plug-in estimator. Some numerical studies using simulations are discussed to support the methodology. Spectral kurtosis of some stationary signals are analytically obtained and used in simulation study. Kurtosis of time domain has been a popular tool for detecting non-normality. Spectral kurtosis is an extension of kurtosis in frequency domain. The relationship between time domain and frequency domain analysis is establish through power spectrum-autocovariance Fourier transform. Fourier transform is the main tool for estimation in frequency domain. The power spectral density is estimated through periodogram. In this paper, the short time Fourier transform of the spectral kurtosis is reviewed, a bearing fault (inner ring and outer ring) is simulated. The bearing response, power spectrum, and spectral kurtosis are plotted to visualize the pattern of each fault. Keywords: frequency domain Fourier transform, spectral kurtosis, bearing fault

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.

Statistical Evaluation of Time Series Analysis Techniques

NASA Technical Reports Server (NTRS)

Benignus, V. A.

1973-01-01

The performance of a modified version of NASA's multivariate spectrum analysis program is discussed. A multiple regression model was used to make the revisions. Performance improvements were documented and compared to the standard fast Fourier transform by Monte Carlo techniques.

RXTE Observation of Cygnus X-1. Report 2; TIming Analysis

NASA Technical Reports Server (NTRS)

Nowak, Michael A.; Vaughan, Brian A.; Wilms, Joern; Dove, James B.; Begelman, Mitchell C.

1998-01-01

We present timing analysis for a Rossi X-ray Timing Explorer (RXTE) observation of Cygnus X-1 in its hard/low state. This was the first RXTE observation of Cyg X-1 taken after it transited back to this state from its soft/high state. RXTE's large effective area, superior timing capabilities, and ability to obtain long, uninterrupted observations have allowed us to obtain measurements of the power spectral density (PSD), coherence function, and Fourier time lags to a decade lower in frequency and half a decade higher in frequency than typically was achieved with previous instruments. Notable aspects of our observations include a weak 0.005 Hz feature in the PSD coincident with a coherence recovery; a 'hardening' of the high-frequency PSD with increasing energy; a broad frequency range measurement of the coherence function, revealing rollovers from unity coherence at both low and high frequency; and an accurate determination of the Fourier time lags over two and a half decades in frequency. As has been noted in previous similar observations, the time delay is approximately proportional to f(exp -0.7), and at a fixed Fourier frequency the time delay of the hard X-rays compared to the softest energy channel tends to increase logarithmically with energy. Curiously, the 0.01-0.2 Hz coherence between the highest and lowest energy bands is actually slightly greater than the coherence between the second highest and lowest energy bands. We carefully describe all of the analysis techniques used in this paper, and we make comparisons of the data to general theoretical expectations. In a companion paper, we make specific comparisons to a Compton corona model that we have successfully used to describe the energy spectral data from this observation.

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation.

PubMed

Holland, Alexander; Aboy, Mateo

2009-07-01

We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

Extracting oscillation frequencies from sparse spectra: Fourier analysis

NASA Astrophysics Data System (ADS)

Jerzykiewicz, M.

2008-12-01

I begin by explaining the properties of spectral windows of time-series data. Emphasis is on data obtained at a single geographic longitude, but ground-based multi-longitude cam- paigns and space missions such as MOST and Hipparcos are not entirely neglected. In the second section, I consider the Fourier transform of time-series data and the procedure of pre-whitening. Sect. 3 is devoted to the pioneers of the subject. In Sect. 4, I suggest how to avoid pitfalls in the practice of periodogram-analysing variable-stars observations. In the last section, I venture an opinion.

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.

Spectral analysis method and sample generation for real time visualization of speech

NASA Astrophysics Data System (ADS)

Hobohm, Klaus

A method for translating speech signals into optical models, characterized by high sound discrimination and learnability and designed to provide to deaf persons a feedback towards control of their way of speaking, is presented. Important properties of speech production and perception processes and organs involved in these mechanisms are recalled in order to define requirements for speech visualization. It is established that the spectral representation of time, frequency and amplitude resolution of hearing must be fair and continuous variations of acoustic parameters of speech signal must be depicted by a continuous variation of images. A color table was developed for dynamic illustration and sonograms were generated with five spectral analysis methods such as Fourier transformations and linear prediction coding. For evaluating sonogram quality, test persons had to recognize consonant/vocal/consonant words and an optimized analysis method was achieved with a fast Fourier transformation and a postprocessor. A hardware concept of a real time speech visualization system, based on multiprocessor technology in a personal computer, is presented.

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

NASA Technical Reports Server (NTRS)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Research about vibration characteristics of timing chain system based on short-time Fourier transform

NASA Astrophysics Data System (ADS)

Xi, Jiaxin; Liu, Ning

2017-09-01

Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.

Functional feature embedded space mapping of fMRI data.

PubMed

Hu, Jin; Tian, Jie; Yang, Lei

2006-01-01

We have proposed a new method for fMRI data analysis which is called Functional Feature Embedded Space Mapping (FFESM). Our work mainly focuses on the experimental design with periodic stimuli which can be described by a number of Fourier coefficients in the frequency domain. A nonlinear dimension reduction technique Isomap is applied to the high dimensional features obtained from frequency domain of the fMRI data for the first time. Finally, the presence of activated time series is identified by the clustering method in which the information theoretic criterion of minimum description length (MDL) is used to estimate the number of clusters. The feasibility of our algorithm is demonstrated by real human experiments. Although we focus on analyzing periodic fMRI data, the approach can be extended to analyze non-periodic fMRI data (event-related fMRI) by replacing the Fourier analysis with a wavelet analysis.

Photoacoustic detection of blood in dental pulp by using short-time Fourier transform

NASA Astrophysics Data System (ADS)

Yamada, Azusa; Kakino, Satoko; Matsuura, Yuji

2016-03-01

A method based on photoacoustic analysis is proposed to diagnose dental pulp vitality. Photoacoustic analysis enables to get signal from deeper tissues than other optical analyses and therefore, signal detection from root canal of thick dental tissues such as molar teeth is expected. As a light source for excitation of photoacoustic waves, a microchip Q-switched YAG laser with a wavelength of 1064 nm was used and owing to large penetration depth of the near infrared laser, photoacoustic signals from dental root were successfully obtained. It was found that the photoacoustic signals from the teeth containing hemoglobin solution in the pulp cavity provide vibration in high frequency region. It was also shown that the intensities of the high frequency component have correlation with the hemoglobin concentration of solution. We applied short-time Fourier transform for evaluation of photoacoustic signals and this analysis clearly showed photoacoustic signals from dental root.

Adaptive synchrosqueezing based on a quilted short-time Fourier transform

NASA Astrophysics Data System (ADS)

Berrian, Alexander; Saito, Naoki

2017-08-01

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.

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.

Complex-valued time-series correlation increases sensitivity in FMRI analysis.

PubMed

Kociuba, Mary C; Rowe, Daniel B

2016-07-01

To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis. The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel's temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex. The simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing. Including both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in fMRI data sets with high noise variance, and avoid excessive processing induced correlation. Copyright © 2016 Elsevier Inc. All rights reserved.

THE ANALYSIS OF THE TIME-SERIES FLUCTUATION OF WATER DEMAND FOR THE SMALL WATER SUPPLY BLOCK

NASA Astrophysics Data System (ADS)

Koizumi, Akira; Suehiro, Miki; Arai, Yasuhiro; Inakazu, Toyono; Masuko, Atushi; Tamura, Satoshi; Ashida, Hiroshi

The purpose of this study is to define one apartment complex as "the water supply block" and to show the relationship between the amount of water supply for an apartment house and its time series fluctuation. We examined the observation data which were collected from 33 apartment houses. The water meters were installed at individual observation points for about 20 days in Tokyo. This study used Fourier analysis in order to grasp the irregularity in a time series data. As a result, this paper demonstrated that the smaller the amount of water supply became, the larger irregularity the time series fluctuation had. We also found that it was difficult to describe the daily cyclical pattern for a small apartment house using the dominant periodic components which were obtained from a Fourier spectrum. Our research give useful information about the design for a directional water supply system, as to making estimates of the hourly fluctuation and the maximum daily water demand.

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.

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.

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.

Wavelet Analyses and Applications

ERIC Educational Resources Information Center

Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.

2009-01-01

It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…

Pulse analysis of acoustic emission signals

NASA Technical Reports Server (NTRS)

Houghton, J. R.; Packman, P. F.

1977-01-01

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 were examined in the frequency domain analysis and pulse shape deconvolution was developed for use in the time domain analysis. Comparisons of the relative performance of each analysis technique are made for the characterization of acoustic emission pulses recorded by a measuring system. 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 parameter 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 emission associated with (a) crack propagation, (b) ball dropping on a plate, (c) spark discharge, and (d) defective and good ball bearings. Deconvolution of the first few micro-seconds of the pulse train is shown to be the region in which the significant signatures of the acoustic emission event are to be found.

Pulse analysis of acoustic emission signals

NASA Technical Reports Server (NTRS)

Houghton, J. R.; Packman, P. F.

1977-01-01

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 were examined in the frequency domain analysis, and pulse shape deconvolution was developed for use in the time domain analysis. Comparisons of the relative performance of each analysis technique are made for the characterization of acoustic emission pulses recorded by a measuring system. 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. Deconvolution of the first few micro-seconds of the pulse train are shown to be the region in which the significant signatures of the acoustic emission event are to be found.

Cheating Heisenberg: Achieving certainty in wideband spectrography

NASA Astrophysics Data System (ADS)

Fulop, Sean

2003-10-01

The spectrographic analysis of sound has been with us some 58 years, and one of the key properties of the process is the trade-off in resolution between the time and frequency dimensions in the computed graph. While spectrography has greatly advanced the development of phonetics, the uncertainty principle has always been a source of frustration to phoneticians because so many of the interesting features of speech must be observed by computing Fourier spectra over very short time frames-i.e., using a ``wideband'' spectrogram. Since the uncertainty relation between time and frequency is unbreakable, the only option for improvement is to make a new kind of spectrogram that does not graph time and frequency. An algorithm is described and demonstrated which computes a new kind of spectrogram in which Fourier transform frequency is replaced by the channelized instantaneous frequency, and time is adjusted by the local group delay. The theory behind this procedure was clarified in Nelson [J. Acoust. Soc. Am. 110, 2575-2592 (2001)]. The resulting wideband spectrograms show dramatically improved resolution of speech features, which will be demonstrated with sample figures. It is thus suggested that phoneticians should be more interested in the instantaneous frequency spectrum than in the Fourier transform.

On the action of Heisenberg's uncertainty principle in discrete linear methods for calculating the components of the deflection of the vertical

NASA Astrophysics Data System (ADS)

Mazurova, Elena; Lapshin, Aleksey

2013-04-01

The method of discrete linear transformations that can be implemented through the algorithms of the Standard Fourier Transform (SFT), Short-Time Fourier Transform (STFT) or Wavelet transform (WT) is effective for calculating the components of the deflection of the vertical from discrete values of gravity anomaly. The SFT due to the action of Heisenberg's uncertainty principle indicates weak spatial localization that manifests in the following: firstly, it is necessary to know the initial digital signal on the complete number line (in case of one-dimensional transform) or in the whole two-dimensional space (if a two-dimensional transform is performed) in order to find the SFT. Secondly, the localization and values of the "peaks" of the initial function cannot be derived from its Fourier transform as the coefficients of the Fourier transform are formed by taking into account all the values of the initial function. Thus, the SFT gives the global information on all frequencies available in the digital signal throughout the whole time period. To overcome this peculiarity it is necessary to localize the signal in time and apply the Fourier transform only to a small portion of the signal; the STFT that differs from the SFT only by the presence of an additional factor (window) is used for this purpose. A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa. The STFT makes it possible to improve spatial localization, that is, it allows one to define the presence of any frequency in the signal and the interval of its presence. However, owing to Heisenberg's uncertainty principle, it is impossible to tell precisely, what frequency is present in the signal at the current moment of time: it is possible to speak only about the range of frequencies. Besides, it is impossible to specify precisely the time moment of the presence of this or that frequency: it is possible to speak only about the time frame. It is this feature that imposes major constrains on the applicability of the STFT. In spite of the fact that the problems of resolution in time and frequency result from a physical phenomenon (Heisenberg's uncertainty principle) and exist independent of the transform applied, there is a possibility to analyze any signal, using the alternative approach - the multiresolutional analysis (MRA). The wavelet-transform is one of the methods for making a MRA-type analysis. Thanks to it, low frequencies can be shown in a more detailed form with respect to time, and high ones - with respect to frequency. The paper presents the results of calculating of the components of the deflection of the vertical, done by the SFT, STFT and WT. The results are presented in the form of 3-d models that visually show the action of Heisenberg's uncertainty principle in the specified algorithms. The research conducted allows us to recommend the application of wavelet-transform to calculate of the components of the deflection of the vertical in the near-field zone. Keywords: Standard Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, Heisenberg's uncertainty principle.

Sub-Fourier characteristics of a δ-kicked-rotor resonance.

PubMed

Talukdar, I; Shrestha, R; Summy, G S

2010-07-30

We experimentally investigate the sub-Fourier behavior of a δ-kicked-rotor resonance by performing a measurement of the fidelity or overlap of a Bose-Einstein condensate exposed to a periodically pulsed standing wave. The temporal width of the fidelity resonance peak centered at the Talbot time and zero initial momentum exhibits an inverse cube pulse number (1/N3)-dependent scaling compared to a 1/N2 dependence for the mean energy width at the same resonance. A theoretical analysis shows that for an accelerating potential the width of the resonance in acceleration space depends on 1/N3, a property which we also verify experimentally. Such a sub-Fourier effect could be useful for high precision gravity measurements.

SaaS Platform for Time Series Data Handling

NASA Astrophysics Data System (ADS)

Oplachko, Ekaterina; Rykunov, Stanislav; Ustinin, Mikhail

2018-02-01

The paper is devoted to the description of MathBrain, a cloud-based resource, which works as a "Software as a Service" model. It is designed to maximize the efficiency of the current technology and to provide a tool for time series data handling. The resource provides access to the following analysis methods: direct and inverse Fourier transforms, Principal component analysis and Independent component analysis decompositions, quantitative analysis, magnetoencephalography inverse problem solution in a single dipole model based on multichannel spectral data.

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.

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.

Modeling laser-driven electron acceleration using WARP with Fourier decomposition

DOE PAGES

Lee, P.; Audet, T. L.; Lehe, R.; ...

2015-12-31

WARP is used with the recent implementation of the Fourier decomposition algorithm to model laser-driven electron acceleration in plasmas. Simulations were carried out to analyze the experimental results obtained on ionization-induced injection in a gas cell. The simulated results are in good agreement with the experimental ones, confirming the ability of the code to take into account the physics of electron injection and reduce calculation time. We present a detailed analysis of the laser propagation, the plasma wave generation and the electron beam dynamics.

Modeling laser-driven electron acceleration using WARP with Fourier decomposition

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

Lee, P.; Audet, T. L.; Lehe, R.

WARP is used with the recent implementation of the Fourier decomposition algorithm to model laser-driven electron acceleration in plasmas. Simulations were carried out to analyze the experimental results obtained on ionization-induced injection in a gas cell. The simulated results are in good agreement with the experimental ones, confirming the ability of the code to take into account the physics of electron injection and reduce calculation time. We present a detailed analysis of the laser propagation, the plasma wave generation and the electron beam dynamics.

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.

Radar/Sonar and Time Series Analysis

DTIC Science & Technology

1991-04-08

Fourier and Likelihood Analysis in NMR Spectroscopy .......... David Brillinger and Reinhold Kaiser Resampling Techniques for Stationary Time-series... Meyer The parabolic Fock theory foi a convex dielectric Georgia Tech. scatterer Abstract. This talk deals with a high frequency as) mptotic m~thod for...Malesky Inst. of Physics, Moscow Jun 11 - Jun 15 Victor P. Maslov MIEIM, USSR May 29 - Jun 15 Robert P. Meyer University of Wisconsin Jun 11 - Jun 15

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.

Direct Analysis in Real Time (DART) of an Organothiophosphate at Ultrahigh Resolution by Fourier Transform Ion Cyclotron Resonance Mass Spectrometry and Tandem Mass Spectrometry

PubMed Central

Prokai, Laszlo; Stevens, Stanley M.

2016-01-01

Direct analysis in real time (DART) is a recently developed ambient ionization technique for mass spectrometry to enable rapid and sensitive analyses with little or no sample preparation. After swab-based field sampling, the organothiophosphate malathion was analyzed using DART-Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry (MS) and tandem mass spectrometry (MS/MS). Mass resolution was documented to be over 800,000 in full-scan MS mode and over 1,000,000 for an MS/MS product ion produced by collision-induced dissociation of the protonated analyte. Mass measurement accuracy below 1 ppm was obtained for all DART-generated ions that belonged to the test compound in the mass spectra acquired using only external mass calibration. This high mass measurement accuracy, achievable at present only through FTMS, was required for unequivocal identification of the corresponding molecular formulae. PMID:26784186

Direct Analysis in Real Time (DART) of an Organothiophosphate at Ultrahigh Resolution by Fourier Transform Ion Cyclotron Resonance Mass Spectrometry and Tandem Mass Spectrometry.

PubMed

Prokai, Laszlo; Stevens, Stanley M

2016-01-16

Direct analysis in real time (DART) is a recently developed ambient ionization technique for mass spectrometry to enable rapid and sensitive analyses with little or no sample preparation. After swab-based field sampling, the organothiophosphate malathion was analyzed using DART-Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry (MS) and tandem mass spectrometry (MS/MS). Mass resolution was documented to be over 800,000 in full-scan MS mode and over 1,000,000 for an MS/MS product ion produced by collision-induced dissociation of the protonated analyte. Mass measurement accuracy below 1 ppm was obtained for all DART-generated ions that belonged to the test compound in the mass spectra acquired using only external mass calibration. This high mass measurement accuracy, achievable at present only through FTMS, was required for unequivocal identification of the corresponding molecular formulae.

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.

Structure in gamma ray burst time profiles: Statistical Analysis 1

NASA Technical Reports Server (NTRS)

Lestrade, John Patrick

1992-01-01

Since its launch on April 5, 1991, the Burst And Transient Source Experiment (BATSE) has observed and recorded over 500 gamma-ray bursts (GRB). The analysis of the time profiles of these bursts has proven to be difficult. Attempts to find periodicities through Fourier analysis have been fruitless except one celebrated case. Our goal is to be able to qualify the observed time-profiles structure. Before applying this formation to bursts, we have tested it on profiles composed of random Poissonian noise. This paper is a report of those preliminary results.

Time-frequency analysis of acoustic signals in the audio-frequency range generated during Hadfield's steel friction

NASA Astrophysics Data System (ADS)

Dobrynin, S. A.; Kolubaev, E. A.; Smolin, A. Yu.; Dmitriev, A. I.; Psakhie, S. G.

2010-07-01

Time-frequency analysis of sound waves detected by a microphone during the friction of Hadfield’s steel has been performed using wavelet transform and window Fourier transform methods. This approach reveals a relationship between the appearance of quasi-periodic intensity outbursts in the acoustic response signals and the processes responsible for the formation of wear products. It is shown that the time-frequency analysis of acoustic emission in a tribosystem can be applied, along with traditional approaches, to studying features in the wear and friction process.

a Signal-Tuned Gabor Transform with Application to Eeg Analysis

NASA Astrophysics Data System (ADS)

Torreão, José R. A.; Victer, Silvia M. C.; Fernandes, João L.

2013-04-01

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signal's corresponding Fourier component, yielding an analyzing kernel which is a representation of the signal's content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

Fully-automated identification of fish species based on otolith contour: using short-time Fourier transform and discriminant analysis (STFT-DA).

PubMed

Salimi, Nima; Loh, Kar Hoe; Kaur Dhillon, Sarinder; Chong, Ving Ching

2016-01-01

Background. Fish species may be identified based on their unique otolith shape or contour. Several pattern recognition methods have been proposed to classify fish species through morphological features of the otolith contours. However, there has been no fully-automated species identification model with the accuracy higher than 80%. The purpose of the current study is to develop a fully-automated model, based on the otolith contours, to identify the fish species with the high classification accuracy. Methods. Images of the right sagittal otoliths of 14 fish species from three families namely Sciaenidae, Ariidae, and Engraulidae were used to develop the proposed identification model. Short-time Fourier transform (STFT) was used, for the first time in the area of otolith shape analysis, to extract important features of the otolith contours. Discriminant Analysis (DA), as a classification technique, was used to train and test the model based on the extracted features. Results. Performance of the model was demonstrated using species from three families separately, as well as all species combined. Overall classification accuracy of the model was greater than 90% for all cases. In addition, effects of STFT variables on the performance of the identification model were explored in this study. Conclusions. Short-time Fourier transform could determine important features of the otolith outlines. The fully-automated model proposed in this study (STFT-DA) could predict species of an unknown specimen with acceptable identification accuracy. The model codes can be accessed at http://mybiodiversityontologies.um.edu.my/Otolith/ and https://peerj.com/preprints/1517/. The current model has flexibility to be used for more species and families in future studies.

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)

Bilinear Time-frequency Analysis for Lamb Wave Signal Detected by Electromagnetic Acoustic Transducer

NASA Astrophysics Data System (ADS)

Sun, Wenxiu; Liu, Guoqiang; Xia, Hui; Xia, Zhengwu

2018-03-01

Accurate acquisition of the detection signal travel time plays a very important role in cross-hole tomography. The experimental platform of aluminum plate under the perpendicular magnetic field is established and the bilinear time-frequency analysis methods, Wigner-Ville Distribution (WVD) and the pseudo-Wigner-Ville distribution (PWVD), are applied to analyse the Lamb wave signals detected by electromagnetic acoustic transducer (EMAT). By extracting the same frequency component of the time-frequency spectrum as the excitation frequency, the travel time information can be obtained. In comparison with traditional linear time-frequency analysis method such as short-time Fourier transform (STFT), the bilinear time-frequency analysis method PWVD is more appropriate in extracting travel time and recognizing patterns of Lamb wave.

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.

AFIT/AFOSR Workshop on the Role of Wavelets in Signal Processing Applications

DTIC Science & Technology

1992-08-28

Stein and G. Weiss, "Fourier analysis on Eucildean spaces," Princeton University Press, 1971. [V] G. Vitali, Sulla condizione di chiusura di un sistema ...present the more general framework into wavelets fit, suggesting hence companion ways of time-scale analysis for self-similar and 1/f-type processes

A real-time computer for monitoring a rapid-scanning Fourier spectrometer

NASA Technical Reports Server (NTRS)

Michel, G.

1973-01-01

A real-time Fourier computer has been designed and tested as part of the Lunar and Planetary Laboratory's program of airborne infrared astronomy using Fourier spectroscopy. The value and versatility of this device are demonstrated with specific examples of laboratory and in-flight applications.

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…

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.

Time-frequency analysis of electric motors

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

Bentley, C.L.; Dunn, M.E.; Mattingly, J.K.

1995-12-31

Physical signals such as the current of an electric motor become nonstationary as a consequence of degraded operation and broken parts. In this instance, their power spectral densities become time dependent, and time-frequency analysis techniques become the appropriate tools for signal analysis. The first among these techniques, generally called the short-time Fourier transform (STFT) method, is the Gabor transform 2 (GT) of a signal S(t), which decomposes the signal into time-local frequency modes: where the window function, {Phi}(t-{tau}), is a normalized Gaussian. Alternatively, one can decompose the signal into its multi-resolution representation at different levels of magnification. This representation ismore » achieved by the continuous wavelet transform (CWT) where the function g(t) is a kernel of zero average belonging to a family of scaled and shifted wavelet kernels. The CWT can be interpreted as the action of a microscope that locates the signal by the shift parameter b and adjusts its magnification by changing the scale parameter a. The Fourier-transformed CWT, W,{sub g}(a, {omega}), acts as a filter that places the high-frequency content of a signal into the lower end of the scale spectrum and vice versa for the low frequencies. Signals from a motor in three different states were analyzed.« less

Comparison of discrete Fourier transform (DFT) and principal component analysis/DFT as forecasting tools for absorbance time series received by UV-visible probes installed in urban sewer systems.

PubMed

Plazas-Nossa, Leonardo; Torres, Andrés

2014-01-01

The objective of this work is to introduce a forecasting method for UV-Vis spectrometry time series that combines principal component analysis (PCA) and discrete Fourier transform (DFT), and to compare the results obtained with those obtained by using DFT. Three time series for three different study sites were used: (i) Salitre wastewater treatment plant (WWTP) in Bogotá; (ii) Gibraltar pumping station in Bogotá; and (iii) San Fernando WWTP in Itagüí (in the south part of Medellín). Each of these time series had an equal number of samples (1051). In general terms, the results obtained are hardly generalizable, as they seem to be highly dependent on specific water system dynamics; however, some trends can be outlined: (i) for UV range, DFT and PCA/DFT forecasting accuracy were almost the same; (ii) for visible range, the PCA/DFT forecasting procedure proposed gives systematically lower forecasting errors and variability than those obtained with the DFT procedure; and (iii) for short forecasting times the PCA/DFT procedure proposed is more suitable than the DFT procedure, according to processing times obtained.

A computer program for estimating the power-density spectrum of advanced continuous simulation language generated time histories

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1981-01-01

A computer program for performing frequency analysis of time history data is presented. The program uses circular convolution and the fast Fourier transform to calculate power density spectrum (PDS) of time history data. The program interfaces with the advanced continuous simulation language (ACSL) so that a frequency analysis may be performed on ACSL generated simulation variables. An example of the calculation of the PDS of a Van de Pol oscillator is presented.

Fourier-based integration of quasi-periodic gait accelerations for drift-free displacement estimation using inertial sensors.

PubMed

Sabatini, Angelo Maria; Ligorio, Gabriele; Mannini, Andrea

2015-11-23

In biomechanical studies Optical Motion Capture Systems (OMCS) are considered the gold standard for determining the orientation and the position (pose) of an object in a global reference frame. However, the use of OMCS can be difficult, which has prompted research on alternative sensing technologies, such as body-worn inertial sensors. We developed a drift-free method to estimate the three-dimensional (3D) displacement of a body part during cyclical motions using body-worn inertial sensors. We performed the Fourier analysis of the stride-by-stride estimates of the linear acceleration, which were obtained by transposing the specific forces measured by the tri-axial accelerometer into the global frame using a quaternion-based orientation estimation algorithm and detecting when each stride began using a gait-segmentation algorithm. The time integration was performed analytically using the Fourier series coefficients; the inverse Fourier series was then taken for reconstructing the displacement over each single stride. The displacement traces were concatenated and spline-interpolated to obtain the entire trace. The method was applied to estimate the motion of the lower trunk of healthy subjects that walked on a treadmill and it was validated using OMCS reference 3D displacement data; different approaches were tested for transposing the measured specific force into the global frame, segmenting the gait and performing time integration (numerically and analytically). The width of the limits of agreements were computed between each tested method and the OMCS reference method for each anatomical direction: Medio-Lateral (ML), VerTical (VT) and Antero-Posterior (AP); using the proposed method, it was observed that the vertical component of displacement (VT) was within ±4 mm (±1.96 standard deviation) of OMCS data and each component of horizontal displacement (ML and AP) was within ±9 mm of OMCS data. Fourier harmonic analysis was applied to model stride-by-stride linear accelerations during walking and to perform their analytical integration. Our results showed that analytical integration based on Fourier series coefficients was a useful approach to accurately estimate 3D displacement from noisy acceleration data.

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.

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.

Instantaneous lineshape analysis of Fourier domain mode-locked lasers.

PubMed

Todor, Sebastian; Biedermann, Benjamin; Wieser, Wolfgang; Huber, Robert; Jirauschek, Christian

2011-04-25

We present a theoretical and experimental analysis of the instantaneous lineshape of Fourier domain mode-locked (FDML) lasers, yielding good agreement. The simulations are performed employing a recently introduced model for FDML operation. Linewidths around 10 GHz are found, which is significantly below the sweep filter bandwidth. The effect of detuning between the sweep filter drive frequency and cavity roundtrip time is studied revealing features that cannot be resolved in the experiment, and shifting of the instantaneous power spectrum against the sweep filter center frequency is analyzed. We show that, in contrast to most other semiconductor based lasers, the instantaneous linewidth is governed neither by external noise sources nor by amplified spontaneous emission, but it is directly determined by the complex FDML dynamics.

Data characteristic analysis of air conditioning load based on fast Fourier transform

NASA Astrophysics Data System (ADS)

Li, Min; Zhang, Yanchi; Xie, Da

2018-04-01

With the development of economy and the improvement of people's living standards, air conditioning equipment is more and more popular. The influence of air conditioning load for power grid is becoming more and more serious. In this context it is necessary to study the characteristics of air conditioning load. This paper analyzes the data of air conditioning power consumption in an office building. The data is used for Fast Fourier Transform by data analysis software. Then a series of maps are drawn for the transformed data. The characteristics of each map were analyzed separately. The hidden rules of these data are mined from the angle of frequency domain. And these rules are hard to find in the time domain.

FT3D: three-dimensional Fourier analysis on small Unix workstations for electron microscopy and tomographic studies.

PubMed

Lanzavecchia, S; Bellon, P L; Tosoni, L

1993-12-01

FT3D is a self-contained package of tools for three-dimensional Fourier analysis, written in the C language for Unix workstations. It can evaluate direct transforms of three-dimensional real functions, inverse transforms, auto- and cross-correlations and spectra. The library has been developed to support three-dimensional reconstructions of biological structures from projections obtained in the electron microscope. This paper discusses some features of the library, which has been implemented in such a way as to profit from the resources of modern workstations. A table of elapsed times for jobs of different dimensions with different RAM buffers is reported for the particular hardware used in the authors' laboratory.

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.

Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy.

PubMed

Zhao, Ming; Huang, Run; Peng, Leilei

2012-11-19

Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium.

Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy

PubMed Central

Zhao, Ming; Huang, Run; Peng, Leilei

2012-01-01

Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium. PMID:23187535

Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1998-01-01

Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.

AN INTEGRATED MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS AND QUIESCENT SPECTRA FROM HOMOGENEOUS AND INHOMOGENEOUS BLACK HOLE ACCRETION CORONAE

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

Kroon, John J.; Becker, Peter A., E-mail: jkroon@gmu.edu, E-mail: pbecker@gmu.edu

2016-04-20

Many accreting black holes manifest time lags during outbursts, in which the hard Fourier component typically lags behind the soft component. Despite decades of observations of this phenomenon, the underlying physical explanation for the time lags has remained elusive, although there are suggestions that Compton reverberation plays an important role. However, the lack of analytical solutions has hindered the interpretation of the available data. In this paper, we investigate the generation of X-ray time lags in Compton scattering coronae using a new mathematical approach based on analysis of the Fourier-transformed transport equation. By solving this equation, we obtain the Fouriermore » transform of the radiation Green’s function, which allows us to calculate the exact dependence of the time lags on the Fourier frequency, for both homogeneous and inhomogeneous coronal clouds. We use the new formalism to explore a variety of injection scenarios, including both monochromatic and broadband (bremsstrahlung) seed photon injection. We show that our model can successfully reproduce both the observed time lags and the time-averaged (quiescent) X-ray spectra for Cyg X-1 and GX 339-04, using a single set of coronal parameters for each source. The time lags are the result of impulsive bremsstrahlung injection occurring near the outer edge of the corona, while the time-averaged spectra are the result of continual distributed injection of soft photons throughout the cloud.« less

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.

Analysis of Digital Communication Signals and Extraction of Parameters.

DTIC Science & Technology

1994-12-01

Fast Fourier Transform (FFT). The correlation methods utilize modified time-frequency distributions , where one of these is based on the Wigner - Ville ... Distribution ( WVD ). Gaussian white noise is added to the signal to simulate various signal-to-noise ratios (SNRs).

[Application of Fourier transform attenuated total reflection infrared spectroscopy in analysis of pulp and paper industry].

PubMed

Zhang, Yong; Cao, Chun-yu; Feng, Wen-ying; Xu, Ming; Su, Zhen-hua; Liu, Xiao-meng; Lü, Wei-jun

2011-03-01

As one of the most powerful tools to investigate the compositions of raw materials and the property of pulp and paper, infrared spectroscopy has played an important role in pulp and paper industry. However, the traditional transmission infrared spectroscopy has not met the requirements of the producing processes because of its disadvantages of time consuming and sample destruction. New technique would be needed to be found. Fourier transform attenuated total reflection infrared spectroscopy (ATR-FTIR) is an advanced spectroscopic tool for nondestructive evaluation and could rapidly, accurately estimate the production properties of each process in pulp and paper industry. The present review describes the application of ATR-FTIR in analysis of pulp and paper industry. The analysis processes will include: pulping, papermaking, environmental protecting, special processing and paper identifying.

A comparison of the wavelet and short-time fourier transforms for Doppler spectral analysis.

PubMed

Zhang, Yufeng; Guo, Zhenyu; Wang, Weilian; He, Side; Lee, Ting; Loew, Murray

2003-09-01

Doppler spectrum analysis provides a non-invasive means to measure blood flow velocity and to diagnose arterial occlusive disease. The time-frequency representation of the Doppler blood flow signal is normally computed by using the short-time Fourier transform (STFT). This transform requires stationarity of the signal during a finite time interval, and thus imposes some constraints on the representation estimate. In addition, the STFT has a fixed time-frequency window, making it inaccurate to analyze signals having relatively wide bandwidths that change rapidly with time. In the present study, wavelet transform (WT), having a flexible time-frequency window, was used to investigate its advantages and limitations for the analysis of the Doppler blood flow signal. Representations computed using the WT with a modified Morlet wavelet were investigated and compared with the theoretical representation and those computed using the STFT with a Gaussian window. The time and frequency resolutions of these two approaches were compared. Three indices, the normalized root-mean-squared errors of the minimum, the maximum and the mean frequency waveforms, were used to evaluate the performance of the WT. Results showed that the WT can not only be used as an alternative signal processing tool to the STFT for Doppler blood flow signals, but can also generate a time-frequency representation with better resolution than the STFT. In addition, the WT method can provide both satisfactory mean frequencies and maximum frequencies. This technique is expected to be useful for the analysis of Doppler blood flow signals to quantify arterial stenoses.

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals.

PubMed

Soto-Quiros, Pablo

2015-01-01

This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

Use of the Wigner-Ville distribution in interpreting and identifying ULF waves in triaxial magnetic records

NASA Astrophysics Data System (ADS)

Chi, P. J.; Russell, C. T.

2008-01-01

Magnetospheric ultra-low-frequency (ULF) waves (f = 1 mHz to 1 Hz) exhibit highly time-dependent characteristics due to the dynamic properties of these waves and, for observations in space, the spacecraft motion. These time-dependent features may not be properly resolved by conventional Fourier techniques. In this study we examine how the Wigner-Ville distribution (WVD) can be used to analyze ULF waves. We find that this approach has unique advantages over the conventional Fourier spectrograms and wavelet scalograms. In particular, for Pc1 wave packets, field line/cavity mode resonances in the Pc 3-4 band, and Pi2 pulsations, the start and end times of each wave packet can be well identified and the frequency better defined. In addition, we demonstrate that the Wigner-Ville distribution can be used to calculate the polarization of wave signals in triaxial magnetic field data in a way analogous to Fourier analysis. Motivated by the large amount of ULF wave observations, we have also developed a WVD-based algorithm to identify ULF waves as a way to facilitate the rapid processing of the data collected by satellite missions and the vast network of ground magnetometers.

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.

Fourier spectra of resonant nuclear forward scattering: lineshape dependence on absorber thickness distribution

NASA Astrophysics Data System (ADS)

Rykov, A. I.; Nomura, K.; Wang, J.

2013-08-01

We report on recent developments in the analysis of nuclear forward scattering (NFS) using the Fourier transformation of measured time spectra. In the frequency domain, it is shown that the lineshape is generally described by the convolution of two intensity factors. One of them is Lorentzian related to free decay. We derived the expressions for the second factor related to the Frenkel exciton polariton formed in Mössbauer media. For stray particles of a powder spread over a 2D surface the particle size distribution can be derived from Mössbauer thickness distribution. The thickness-related lineshape is deconvolved through sharpening the Fourier NFS spectra. The lineshapes in these sharpened spectra are theoretically expressed via the parameters of the particle size distributions. Through fitting the lineshapes with our theoretical expressions the particle size distribution parameters were determined.

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

A New Approach in Time-Frequency Analysis with Applications to Experimental High Range Resolution Radar Data

DTIC Science & Technology

2003-11-01

Distributions In contrast to the linear time-frequency transforms such as the short-time Fourier transform, the Wigner - Ville distribution ( WVD ) is...23 9 Results of nine TFDs: (a) Wigner - Ville distribution , (b) Born-Jordan distribution , (c) Choi-Williams distribution , (d) bilinear TFD...are applied in the Wigner - Ville class of time-frequency transforms and the reassignment methods, which are applied to any time-frequency distribution

Mid-Latitude Temperatures at 87 km: Results From Multi-Instrument Fourier Analysis

NASA Technical Reports Server (NTRS)

Drob, Douglas P.; Picone, J. M.; Eckermann, Stephen D.; She, C . Y.; Kafkalidis, J. F.; Ortland, D. A.; Niciejewski, R. J.; Killeen, T. L.

2000-01-01

Using a novel Fourier fitting method we combine two years of mid-latitude temperature measurements at 87 km from the High Resolution Doppler Imager, the Colorado State University lidar, and the Peach Mountain Interferometer. After accounting for calibration bias, significant local-time variations on the order of 10 K were observed. Stationary planetary waves with amplitudes up to 10 K were observed during winter, with weaker wave amplitudes occurring during other seasons. Because of calibration biases among these instruments, we could estimate the annual mean temperature to no better than 193.5 plus or minus 8.5 K.

A Method to Compute the Force Signature of a Body Impacting on a Linear Elastic Structure Using Fourier Analysis

DTIC Science & Technology

1982-09-17

FK * 1PK (2) The convolution of two transforms in time domain is the inverse transform of the product in frequency domain. Thus Rp(s) - Fgc() Ipg(*) (3...its inverse transform by: R,(r)- R,(a.)e’’ do. (5)2w In order to nuke use f a very accurate numerical method to ompute Fourier "ke and coil...taorm. When the inverse transform it tken by using Eq. (15), the cosine transform, because it converges faster than the sine transform refu-ft the

A Constant Percentage Bandwidth Transform for Acoustic Signal Processing

DTIC Science & Technology

1980-01-01

t)eJwt d . 27Th (0) Equation 2.9 is not, however, the most general form for short-time Fourier synthesis, but is in fact a particular case of the...form of the analysis integral. F(Wk? t)eJwkt = f(t) * h( t)’ukt (3.4) Fourier transforming both sides of this equation (and invoking the convolution...properties. In what follows, define 38 f(t) - F(w,t) (3.24) to be an equivalent statement to equation 3.1. 3.6.1 Linearity Property If F1 w,t) and F2 (w

Nycterohemeral eating and ruminating patterns in heifers fed grass or corn silage: analysis by finite Fourier transform.

PubMed

Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C

1993-10-01

Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P < .05) with fewer meals and shorter daily, unitary eating and ruminating times, and smaller number of rumination boli. Analysis of variance of the daily mean of hourly activities and Rhythm Components 1 to 12 indicated effects of (P < .05) silage type (S), animal (A), period (P), and a significant interaction (S x A x P) for each mastication activity. The finite Fourier transform was reparameterized to express the amplitude (as periodograms) and phase of each rhythm component. Rhythm Components 1, 3, and 4 contributed primarily to explaining the total dispersion of the 24-h series of time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)

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.

Electro-Optical Imaging Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

PubMed

Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi

2010-09-01

The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.

Radar signal analysis of ballistic missile with micro-motion based on time-frequency distribution

NASA Astrophysics Data System (ADS)

Wang, Jianming; Liu, Lihua; Yu, Hua

2015-12-01

The micro-motion of ballistic missile targets induces micro-Doppler modulation on the radar return signal, which is a unique feature for the warhead discrimination during flight. In order to extract the micro-Doppler feature of ballistic missile targets, time-frequency analysis is employed to process the micro-Doppler modulated time-varying radar signal. The images of time-frequency distribution (TFD) reveal the micro-Doppler modulation characteristic very well. However, there are many existing time-frequency analysis methods to generate the time-frequency distribution images, including the short-time Fourier transform (STFT), Wigner distribution (WD) and Cohen class distribution, etc. Under the background of ballistic missile defence, the paper aims at working out an effective time-frequency analysis method for ballistic missile warhead discrimination from the decoys.

[Personal long-term reproducibility of the TEOAE time-frequency distributions].

PubMed

Konopka, Wiesław; Grzanka, Antoni; Zalewski, Piotr

2002-01-01

The TEOAE signal is relatively short and content changes in time. Due to the fact that signal is very short (20 ms) a special approach must be applied for the analysis of this nonstationarity. Usually the spectral estimation in TEOAE is based on procedures directly employing the fast Fourier transform (FFT). Because TEOAE signal is non stationary the classical Fourier analysis is not adequate for this signal. The aim of our study was the personal comparison of the TEOAE spectograms by using Wigner-Ville distribution (WVD) before and after one year period. Material consisted of 152 men (304 ears) in the age between 18-19 year with good quality OAE. After one year period the comparison of WVD spectrograms showed the highest similarity in the 274 ears (90%), less in the 24 (8%) and in 6 (2%) similarity was not noticed. Personal similarity of the spectrum TEOAE and differences between individual people's ears despite a long time, give a proof about individual architecture of outer hearing cell and maybe useful in the biometrics as a ear-print.

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.

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.

Homotopic solutions for unsteady second grade liquid utilizing non-Fourier double diffusion concept

NASA Astrophysics Data System (ADS)

Sohail, A.; Khan, W. A.; Khan, M.; Shah, S. I. A.

Main purpose of the current work is to investigate the features of unsteady Cattaneo-Christov heat and mass flux models on the second grade fluid over a stretching surface. The characteristics of unsteady Cattaneo-Christov heat and mass flux models are incorporated in the energy and concentration equations. The unsteady Cattaneo-Christov heat and mass flux models are the generalization of Fourier's and Fick's laws in which the time space upper-convected derivative are utilized to describe the heat conduction and mass diffusion phenomena. The suitable transformations are used to alter the governing partial differential equations into the ordinary differential equations. The resulting problem under consideration is solved analytically by using the homotopy analysis method (HAM). The effect of non-dimensional pertinent parameters on the temperature and concentration distribution are deliberated by using graphs and tables. Results show that the temperature and concentration profiles diminish for augmented values of the thermal and concentration relaxation parameters. Additionally, it is perceived that the temperature and concentration profiles are higher in case of classical Fourier's and Fick's laws as compared to non-Fourier's and non-Fick's laws.

Methodology for processing pressure traces used as inputs for combustion analyses in diesel engines

NASA Astrophysics Data System (ADS)

Rašić, Davor; Vihar, Rok; Žvar Baškovič, Urban; Katrašnik, Tomaž

2017-05-01

This study proposes a novel methodology for designing an optimum equiripple finite impulse response (FIR) filter for processing in-cylinder pressure traces of a diesel internal combustion engine, which serve as inputs for high-precision combustion analyses. The proposed automated workflow is based on an innovative approach of determining the transition band frequencies and optimum filter order. The methodology is based on discrete Fourier transform analysis, which is the first step to estimate the location of the pass-band and stop-band frequencies. The second step uses short-time Fourier transform analysis to refine the estimated aforementioned frequencies. These pass-band and stop-band frequencies are further used to determine the most appropriate FIR filter order. The most widely used existing methods for estimating the FIR filter order are not effective in suppressing the oscillations in the rate- of-heat-release (ROHR) trace, thus hindering the accuracy of combustion analyses. To address this problem, an innovative method for determining the order of an FIR filter is proposed in this study. This method is based on the minimization of the integral of normalized signal-to-noise differences between the stop-band frequency and the Nyquist frequency. Developed filters were validated using spectral analysis and calculation of the ROHR. The validation results showed that the filters designed using the proposed innovative method were superior compared with those using the existing methods for all analyzed cases. Highlights • Pressure traces of a diesel engine were processed by finite impulse response (FIR) filters with different orders • Transition band frequencies were determined with an innovative method based on discrete Fourier transform and short-time Fourier transform • Spectral analyses showed deficiencies of existing methods in determining the FIR filter order • A new method of determining the FIR filter order for processing pressure traces was proposed • The efficiency of the new method was demonstrated by spectral analyses and calculations of rate-of-heat-release traces

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

NASA Astrophysics Data System (ADS)

Pagán Muñoz, Raúl; Hornikx, Maarten

2017-11-01

The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

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

Wollaber, Allan B., E-mail: wollaber@lanl.go; Larsen, Edward W., E-mail: edlarsen@umich.ed

2011-02-20

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, wemore » also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.« less

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

NASA Astrophysics Data System (ADS)

Wollaber, Allan B.; Larsen, Edward W.

2011-02-01

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ⩽ 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.

Fitting the multitemporal curve: a fourier series approach to the missing data problem in remote sensing analysis

Treesearch

Evan Brooks; Valerie Thomas; Wynne Randolph; John Coulston

2012-01-01

With the advent of free Landsat data stretching back decades, there has been a surge of interest in utilizing remotely sensed data in multitemporal analysis for estimation of biophysical parameters. Such analysis is confounded by cloud cover and other image-specific problems, which result in missing data at various aperiodic times of the year. While there is a wealth...

Noise-band factor analysis of cancer Fourier transform infrared evanescent-wave fiber optical (FTIR-FEW) spectra

NASA Astrophysics Data System (ADS)

Sukuta, Sydney; Bruch, Reinhard F.

2002-05-01

The goal of this study is to test the feasibility of using noise factor/eigenvector bands as general clinical analytical tools for diagnoses. We developed a new technique, Noise Band Factor Cluster Analysis (NBFCA), to diagnose benign tumors via their Fourier transform IR fiber optic evanescent wave spectral data for the first time. The middle IR region of human normal skin tissue and benign and melanoma tumors, were analyzed using this new diagnostic technique. Our results are not in full-agreement with pathological classifications hence there is a possibility that our approaches could complement or improve these traditional classification schemes. Moreover, the use of NBFCA make it much easier to delineate class boundaries hence this method provides results with much higher certainty.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Some Applications of Fourier's Great Discovery for Beginners

ERIC Educational Resources Information Center

Kraftmakher, Yaakov

2012-01-01

Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…

Kinetics of lisinopril intramolecular cyclization in solid phase monitored by Fourier transform infrared microscopy.

PubMed

Widjaja, Effendi; Tan, Wei Jian

2008-08-01

The solid-state intramolecular cyclization of lisinopril to diketopiperazine was investigated by in situ Fourier transform infrared (FT-IR) microscopy. Using a controllable heating cell, the isothermal transformation was monitored in situ at 147.5, 150, 152.5, 155, and 157.5 degrees C. The collected time-dependent FT-IR spectra at each isothermal temperature were preprocessed and analyzed using a multivariate chemometric approach. The pure component spectra of the observable component (lisinopril and diketopiperazine) were resolved and their time-dependent relative contributions were also determined. Model-free and various model fitting methods were implemented in the kinetic analysis to estimate the activation energy of the intramolecular cyclization reaction. Arrhenius plots indicate that the activation energy is circa 327 kJ/mol.

The Delicate Analysis of Short-Term Load Forecasting

NASA Astrophysics Data System (ADS)

Song, Changwei; Zheng, Yuan

2017-05-01

This paper proposes a new method for short-term load forecasting based on the similar day method, correlation coefficient and Fast Fourier Transform (FFT) to achieve the precision analysis of load variation from three aspects (typical day, correlation coefficient, spectral analysis) and three dimensions (time dimension, industry dimensions, the main factors influencing the load characteristic such as national policies, regional economic, holidays, electricity and so on). First, the branch algorithm one-class-SVM is adopted to selection the typical day. Second, correlation coefficient method is used to obtain the direction and strength of the linear relationship between two random variables, which can reflect the influence caused by the customer macro policy and the scale of production to the electricity price. Third, Fourier transform residual error correction model is proposed to reflect the nature of load extracting from the residual error. Finally, simulation result indicates the validity and engineering practicability of the proposed method.

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.

An Analytical Time–Domain Expression for the Net Ripple Produced by Parallel Interleaved Converters

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

Johnson, Brian B.; Krein, Philip T.

We apply modular arithmetic and Fourier series to analyze the superposition of N interleaved triangular waveforms with identical amplitudes and duty-ratios. Here, interleaving refers to the condition when a collection of periodic waveforms with identical periods are each uniformly phase-shifted across one period. The main result is a time-domain expression which provides an exact representation of the summed and interleaved triangular waveforms, where the peak amplitude and parameters of the time-periodic component are all specified in closed-form. Analysis is general and can be used to study various applications in multi-converter systems. This model is unique not only in that itmore » reveals a simple and intuitive expression for the net ripple, but its derivation via modular arithmetic and Fourier series is distinct from prior approaches. The analytical framework is experimentally validated with a system of three parallel converters under time-varying operating conditions.« less

Determination of layer ordering using sliding-window Fourier transform of x-ray reflectivity data

NASA Astrophysics Data System (ADS)

Smigiel, E.; Knoll, A.; Broll, N.; Cornet, A.

1998-01-01

X-ray reflectometry allows the determination of the thickness, density and roughness of thin layers on a substrate from several Angstroms to some hundred nanometres. The thickness is determined by simulation with trial-and-error methods after extracting initial values of the layer thicknesses from the result of a classical Fast Fourier Transform (FFT) of the reflectivity data. However, the order information of the layers is lost during classical FFT. The order of the layers has then to be known a priori. In this paper, it will be shown that the order of the layers can be obtained by a sliding-window Fourier transform, the so-called Gabor representation. This joint time-frequency analysis allows the direct determination of the order of the layers and, therefore, the use of a more appropriate starting model for refining simulations. A simulated and a measured example show the interest of this method.

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.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

An optical Fourier transform coprocessor with direct phase determination.

PubMed

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

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.

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

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.

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)

A FOURIER-TRANSFORMED BREMSSTRAHLUNG FLASH MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS IN ACCRETING BLACK HOLE SOURCES

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

Kroon, John J.; Becker, Peter A., E-mail: jkroon@gmu.edu, E-mail: pbecker@gmu.edu

Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resultingmore » Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources.« less

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

Modification of wheat gluten with citric acid to produce superabsorbent materials

USDA-ARS?s Scientific Manuscript database

Wheat gluten was reacted with citric acid to produce natural superabsorbent materials able to absorb up to 78 times its weight in water. The properties of the modified gluten samples were characterized using Fourier Transform Infra-red (FTIR) spectroscopy, thermogravimetric analysis, and water uptak...

Variables that Impact on the Results of Breath-Alcohol Tests

ERIC Educational Resources Information Center

Labianca, Dominick A.

2004-01-01

In a 2003 issue of the "Journal of Chemical Education," Kniesel and Bellamy describe a timely and pedagogically effective experiment involving breath-alcohol analysis using an FTIR (Fourier Transform Infrared Spectroscopy) spectrometer. The present article clarifies some of the information presented in the 2003 article.

Ultrasonic Interferometers Revisited

ERIC Educational Resources Information Center

Greenslade, Thomas B., Jr.

2007-01-01

I have been tinkering with ultrasonic transducers once more. In earlier notes I reported on optics-like experiments performed with ultrasonics, described a number of ultrasonic interferometers, and showed how ultrasonic transducers can be used for Fourier analysis. This time I became interested in trying the technique of using two detectors in…

Accelerated radial Fourier-velocity encoding using compressed sensing.

PubMed

Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert

2014-09-01

Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus, compared to normal Phase Contrast measurements delivering only mean velocities, no additional scan time is necessary to retrieve meaningful velocity spectra in small vessels. Copyright © 2013. Published by Elsevier GmbH.

Investigation of Cyprus thermal tenancy using nine year MODIS LST data and Fourier analysis

NASA Astrophysics Data System (ADS)

Skarlatos, D.; Miliaresis, G.; Georgiou, A.

2013-08-01

Land Surface Temperature (LST) is an extremely important parameter that controls the exchange of long wave radiation between surface and atmosphere. It is a good indicator of the energy balance at the Earth's surface and it is one of the key parameters in the physics of land-surface processes on regional as well as global scale. This paper utilizes monthly night and day averaged LST MODIS imagery over Cyprus for a 9 year period. Fourier analysis and Least squares estimation fitting are implemented to analyze mean daily data over Cyprus in an attempt to investigate possible temperature tenancy over these years and possible differences among areas with different land cover and land use, such as Troodos Mountain and Nicosia, the main city in the center of the island. The analysis of data over a long time period, allows questions such as whether there is a tenancy to temperature increase, to be answered in a statistically better way, provided that `noise' is removed correctly. Dealing with a lot of data, always provides a more accurate estimation, but on the other hand, more noise in implemented on the data, especially when dealing with temperature which is subject to daily and annual cycles. A brief description over semi-automated data acquisition and standardization using object-oriented programming and GIS-based techniques, will be presented. The paper fully describes the time series analysis implemented, the Fourier method and how it was used to analyze and filter mean daily data with high frequency. Comparison of mean monthly daily LST against day and night LSTs is also performed over the 9 year period in order to investigate whether use of the extended data series provide significant advantage over short.

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.

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.

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

Frequency and time-domain inspiral templates for comparable mass compact binaries in eccentric orbits

NASA Astrophysics Data System (ADS)

Tanay, Sashwat; Haney, Maria; Gopakumar, Achamveedu

2016-03-01

Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the postcircular scheme of Yunes et al. [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian amplitude and 2PN-order Fourier phase while incorporating eccentricity effects up to sixth order at each PN order. The importance of incorporating eccentricity evolution contributions to the Fourier phase in a PN-consistent manner is also demonstrated. Second, we present an accurate and efficient prescription to incorporate orbital eccentricity into the quasicircular time-domain TaylorT4 approximant at 2PN order. New features include the use of rational functions in orbital eccentricity to implement the 1.5PN-order tail contributions to the far-zone fluxes. This leads to closed form PN-accurate differential equations for evolving eccentric orbits, and the resulting time-domain approximant is accurate and efficient to handle initial orbital eccentricities ≤0.9 . Preliminary GW data analysis implications are probed using match estimates.

Tradeoffs in manipulator structure and control. Part 4: Flexible manipulator analysis program. [user manual

NASA Technical Reports Server (NTRS)

Book, W. J.

1974-01-01

The Flexible Manipulator Analysis Program (FMAP) is a collection of FORTRAN coding to allow easy analysis of the flexible dynamics of mechanical arms. The user specifies the arm configuration and parameters and any or all of several frequency domain analyses to be performed, while the time domain impulse response is obtained by inverse Fourier transformation of the frequency response. A detailed explanation of how to use FMAP is provided.

A simplified implementation of edge detection in MATLAB is faster and more sensitive than fast fourier transform for actin fiber alignment quantification.

PubMed

Kemeny, Steven Frank; Clyne, Alisa Morss

2011-04-01

Fiber alignment plays a critical role in the structure and function of cells and tissues. While fiber alignment quantification is important to experimental analysis and several different methods for quantifying fiber alignment exist, many studies focus on qualitative rather than quantitative analysis perhaps due to the complexity of current fiber alignment methods. Speed and sensitivity were compared in edge detection and fast Fourier transform (FFT) for measuring actin fiber alignment in cells exposed to shear stress. While edge detection using matrix multiplication was consistently more sensitive than FFT, image processing time was significantly longer. However, when MATLAB functions were used to implement edge detection, MATLAB's efficient element-by-element calculations and fast filtering techniques reduced computation cost 100 times compared to the matrix multiplication edge detection method. The new computation time was comparable to the FFT method, and MATLAB edge detection produced well-distributed fiber angle distributions that statistically distinguished aligned and unaligned fibers in half as many sample images. When the FFT sensitivity was improved by dividing images into smaller subsections, processing time grew larger than the time required for MATLAB edge detection. Implementation of edge detection in MATLAB is simpler, faster, and more sensitive than FFT for fiber alignment quantification.

High-order tail in Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Casals, Marc; Ottewill, Adrian

2015-12-01

We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."

[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.

Radar/Sonar and Time Series Analysis

DTIC Science & Technology

1991-06-27

Davis, William Dunsmuir Fourier and Likelihood Analysis in NMR Spectroscopy .......... David Brillinger and Reinhold Kaiser Resampling Techniques for...Zubelli. 2:30 pm Gunter Meyer The parabolic Fock theory for a convex dielectric Georgia Tech. scatterer Abstract: This talk deals with a high frequency...Lincoln Laboratory, MIT Jun 18 - Jun 29 Gunter Meyer Georgia Institute of Technology Jun 25 - Jun 29 Willard Miller University of Minnesota Ruth Miniowitz

Practical Sub-Nyquist Sampling via Array-Based Compressed Sensing Receiver Architecture

DTIC Science & Technology

2016-07-10

different array ele- ments at different sub-Nyquist sampling rates. Signal processing inspired by the sparse fast Fourier transform allows for signal...reconstruction algorithms can be computationally demanding (REF). The related sparse Fourier transform algorithms aim to reduce the processing time nec- essary to...compute the DFT of frequency-sparse signals [7]. In particular, the sparse fast Fourier transform (sFFT) achieves processing time better than the

Speech Segregation based on Binary Classification

DTIC Science & Technology

2016-07-15

including the IBM, the target binary mask (TBM), the IRM, the short -time Fourier transform spectral magnitude (FFT-MAG) and its corresponding mask (FFT...complementary features and a fixed DNN as the discriminative learning machine. For evaluation metrics, besides SNR, we use the Short -Time Objective...target analysis is a recent successful intelligibility test conducted on both normal-hearing (NH) and hearing-impaired (HI) listeners. The speech

Non-linear Min protein interactions generate harmonics that signal mid-cell division in Escherichia coli

PubMed Central

Walsh, James C.; Angstmann, Christopher N.; Duggin, Iain G.

2017-01-01

The Min protein system creates a dynamic spatial pattern in Escherichia coli cells where the proteins MinD and MinE oscillate from pole to pole. MinD positions MinC, an inhibitor of FtsZ ring formation, contributing to the mid-cell localization of cell division. In this paper, Fourier analysis is used to decompose experimental and model MinD spatial distributions into time-dependent harmonic components. In both experiment and model, the second harmonic component is responsible for producing a mid-cell minimum in MinD concentration. The features of this harmonic are robust in both experiment and model. Fourier analysis reveals a close correspondence between the time-dependent behaviour of the harmonic components in the experimental data and model. Given this, each molecular species in the model was analysed individually. This analysis revealed that membrane-bound MinD dimer shows the mid-cell minimum with the highest contrast when averaged over time, carrying the strongest signal for positioning the cell division ring. This concurs with previous data showing that the MinD dimer binds to MinC inhibiting FtsZ ring formation. These results show that non-linear interactions of Min proteins are essential for producing the mid-cell positioning signal via the generation of second-order harmonic components in the time-dependent spatial protein distribution. PMID:29040283

Entangled Biphoton Virtual-State Spectroscopy of the A(exp 2)Sigma(sup +)-X(exp 2)Pi System of OH

NASA Technical Reports Server (NTRS)

Kojima, Jun; Nguyen, Quang-Viet

2004-01-01

This Letter describes the first application of entanglement-induced virtual-state spectroscopy to a molecular system. Non-classical, non-monotonic behavior in a two-photon absorption cross section of the OH A-X system, induced by an entangled biphoton state is theoretically demonstrated. A Fourier transform analysis of the biphoton cross section permits access to the energy eigenvalues of intermediate rovibronic states with a fixed excitation photon energy. The dependence of the Fourier spectrum on the tuning range of the entanglement time (T(sub e)) and the relative path delay (tau(sub e)) is discussed. Our analysis reveals that the implementation of molecular virtual-state spectroscopy for the OH A-X system requires the tuning of tau(sub e) over a pico-second range with femto-second resolution.

Entangled Biphoton Virtual-State Spectroscopy of the A(exp 2)Sigma(+) - X(exp 2)Pi System of OH

NASA Technical Reports Server (NTRS)

Kojima, Jun; Nguyen, Quang-Viet

2004-01-01

This Letter describes the first application of entanglement-induced virtual-state spectroscopy to a molecular system. Non-classical, non-monotonic behavior in a two-photon absorption cross section of the OH A-X system, induced by an entangled biphoton state is theoretically demonstrated. A Fourier transform analysis of the biphoton cross section permits access to the energy eigenvalues of intermediate rovibronic states with a fixed excitation photon energy. The dependence of the Fourier spectrum on the tuning range of the entanglement time T(sub e), and the relative path delay tau(sub e) is discussed. Our analysis reveals that the implementation of molecular virtual-state spectroscopy for the OH A-X system requires the tuning of tau(sub e) over a pico-second range with femto-second resolution.

Variable mass pendulum behaviour processed by wavelet analysis

NASA Astrophysics Data System (ADS)

Caccamo, M. T.; Magazù, S.

2017-01-01

The present work highlights how, in order to characterize the motion of a variable mass pendulum, wavelet analysis can be an effective tool in furnishing information on the time evolution of the oscillation spectral content. In particular, the wavelet transform is applied to process the motion of a hung funnel that loses fine sand at an exponential rate; it is shown how, in contrast to the Fourier transform which furnishes only an average frequency value for the motion, the wavelet approach makes it possible to perform a joint time-frequency analysis. The work is addressed at undergraduate and graduate students.

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.

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

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.

Modeling of earthquake ground motion in the frequency domain

NASA Astrophysics Data System (ADS)

Thrainsson, Hjortur

In recent years, the utilization of time histories of earthquake ground motion has grown considerably in the design and analysis of civil structures. It is very unlikely, however, that recordings of earthquake ground motion will be available for all sites and conditions of interest. Hence, there is a need for efficient methods for the simulation and spatial interpolation of earthquake ground motion. In addition to providing estimates of the ground motion at a site using data from adjacent recording stations, spatially interpolated ground motions can also be used in design and analysis of long-span structures, such as bridges and pipelines, where differential movement is important. The objective of this research is to develop a methodology for rapid generation of horizontal earthquake ground motion at any site for a given region, based on readily available source, path and site characteristics, or (sparse) recordings. The research includes two main topics: (i) the simulation of earthquake ground motion at a given site, and (ii) the spatial interpolation of earthquake ground motion. In topic (i), models are developed to simulate acceleration time histories using the inverse discrete Fourier transform. The Fourier phase differences, defined as the difference in phase angle between adjacent frequency components, are simulated conditional on the Fourier amplitude. Uniformly processed recordings from recent California earthquakes are used to validate the simulation models, as well as to develop prediction formulas for the model parameters. The models developed in this research provide rapid simulation of earthquake ground motion over a wide range of magnitudes and distances, but they are not intended to replace more robust geophysical models. In topic (ii), a model is developed in which Fourier amplitudes and Fourier phase angles are interpolated separately. A simple dispersion relationship is included in the phase angle interpolation. The accuracy of the interpolation model is assessed using data from the SMART-1 array in Taiwan. The interpolation model provides an effective method to estimate ground motion at a site using recordings from stations located up to several kilometers away. Reliable estimates of differential ground motion are restricted to relatively limited ranges of frequencies and inter-station spacings.

Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method.

PubMed

Li, Zhuoxuan; Pei, Li; Liu, Chao; Ning, Tigang; Yu, Shaowei

2012-10-20

Fourier mode coupling model was first applied to achieve the spectra property of a fiber Bragg grating (FBG)-based longitudinal-acousto-optic modulator. Compared with traditional analysis algorithms, such as the transfer matrix method, the Fourier mode coupling model could improve the computing efficiency up to 100 times with a guarantee of accuracy. In this paper, based on the theoretical analysis of this model, the spectra characteristics of the modulator in different frequencies and acoustically induced strains were numerically simulated. In the experiment, a uniform FBG was modulated by acoustic wave (AW) at 12 different frequencies. In particular, the modulator responses at 563 and 885.5 KHz with three different lead zirconate titanate (PZT) loads applied were plotted for illustration, and the linear fitting of experimental data demonstrated a good match with the simulation result. The acoustic excitation of the longitudinal wave is obtained using a conic silica horn attached to the surface of a shear-mode PZT plate paralleled to the fiber axis. This way of generating longitudinal AW with a transversal PZT may shed light on the optimal structural design for the FBG-based longitudinal-acousto-optic modulator.

Response of Autonomic Nervous System to Body Positions:

NASA Astrophysics Data System (ADS)

Xu, Aiguo; Gonnella, G.; Federici, A.; Stramaglia, S.; Simone, F.; Zenzola, A.; Santostasi, R.

Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1) and the second parts (HD2) of 90° head down tilt, and during recovery (REC). The wavelet transform was performed using the Haar function of period T=2j (j=1,2,...,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frequency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident differences than the R-R intervals. This study suggests a difference in the response of the vessels and the heart to different body positions. The partial dissociation between VLF and LF results is a physiologically relevant finding of this work.

A fractional Fourier transform analysis of the scattering of ultrasonic waves.

PubMed

Tant, Katherine M M; Mulholland, Anthony J; Langer, Matthias; Gachagan, Anthony

2015-03-08

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time-frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time-frequency domain framework to assist in flaw identification and classification.

A Final Approach Trajectory Model for Current Operations

NASA Technical Reports Server (NTRS)

Gong, Chester; Sadovsky, Alexander

2010-01-01

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

RESPONSE OF THE GREEK EARLY WARNING SYSTEM REUTER-STOKES IONIZATION CHAMBERS TO TERRESTRIAL AND COSMIC RADIATION EVALUATED IN COMPARISON WITH SPECTROSCOPIC DATA AND TIME SERIES ANALYSIS.

PubMed

Leontaris, F; Clouvas, A; Xanthos, S; Maltezos, A; Potiriadis, C; Kiriakopoulos, E; Guilhot, J

2018-02-01

The Telemetric Early Warning System Network of the Greek Atomic Energy Commission consists mainly of a network of 24 Reuter-Stokes high-pressure ionization chambers (HPIC) for gamma dose rate measurements and covers all Greece. In the present work, the response of the Reuter-Stokes HPIC to terrestrial and cosmic radiation was evaluated in comparison with spectroscopic data obtained by in situ gamma spectrometry measurements with portable hyper pure Germanium detectors (HPGe), near the Reuter-Stokes detectors and time series analysis. For the HPIC detectors, a conversion factor for the measured absorbed dose rate in air (in nGy h-1) to the total ambient dose equivalent rate Ḣ*(10), due to terrestrial and cosmic component, was deduced by the field measurements. Time series analysis of the mean monthly dose rate (measured by the Reuter-Stokes detector in Thessaloniki, northern Greece, from 2001 to 2016) was performed with advanced statistical methods (Fast Fourier Analysis and Zhao Atlas Marks Transform). Fourier analysis reveals several periodicities (periodogram). The periodogram of the absorbed dose rate in air values was compared with the periodogram of the values measured for the same period (2001-16) and in the same location with a NaI (Tl) detector which in principle is not sensitive to cosmic radiation. The obtained results are presented and discussed. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

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.

Time-Frequency Analysis of Rocket Nozzle Wall Pressures During Start-up Transients

NASA Technical Reports Server (NTRS)

Baars, Woutijn J.; Tinney, Charles E.; Ruf, Joseph H.

2011-01-01

Surveys of the fluctuating wall pressure were conducted on a sub-scale, thrust- optimized parabolic nozzle in order to develop a physical intuition for its Fourier-azimuthal mode behavior during fixed and transient start-up conditions. These unsteady signatures are driven by shock wave turbulent boundary layer interactions which depend on the nozzle pressure ratio and nozzle geometry. The focus however, is on the degree of similarity between the spectral footprints of these modes obtained from transient start-ups as opposed to a sequence of fixed nozzle pressure ratio conditions. For the latter, statistically converged spectra are computed using conventional Fourier analyses techniques, whereas the former are investigated by way of time-frequency analysis. The findings suggest that at low nozzle pressure ratios -- where the flow resides in a Free Shock Separation state -- strong spectral similarities occur between fixed and transient conditions. Conversely, at higher nozzle pressure ratios -- where the flow resides in Restricted Shock Separation -- stark differences are observed between the fixed and transient conditions and depends greatly on the ramping rate of the transient period. And so, it appears that an understanding of the dynamics during transient start-up conditions cannot be furnished by a way of fixed flow analysis.

Probing specific molecular processes and intermediates by time-resolved Fourier transform infrared spectroscopy: application to the bacteriorhodopsin photocycle.

PubMed

Lórenz-Fonfría, Víctor A; Kandori, Hideki; Padrós, Esteve

2011-06-23

We present a general approach for probing the kinetics of specific molecular processes in proteins by time-resolved Fourier transform infrared (IR) spectroscopy. Using bacteriorhodopsin (bR) as a model we demonstrate that by appropriately monitoring some selected IR bands it is possible obtaining the kinetics of the most important events occurring in the photocycle, namely changes in the chromophore and the protein backbone conformation, and changes in the protonation state of the key residues implicated in the proton transfers. Besides confirming widely accepted views of the bR photocycle, our analysis also sheds light into some disputed issues: the degree of retinal torsion in the L intermediate to respect the ground state; the possibility of a proton transfer from Asp85 to Asp212; the relationship between the protonation/deprotonation of Asp85 and the proton release complex; and the timing of the protein backbone dynamics. By providing a direct way to estimate the kinetics of photocycle intermediates the present approach opens new prospects for a robust quantitative kinetic analysis of the bR photocycle, which could also benefit the study of other proteins involved in photosynthesis, in phototaxis, or in respiratory chains.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

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…

Spectral Analysis: From Additive Perspective to Multiplicative Perspective

NASA Astrophysics Data System (ADS)

Wu, Z.

2017-12-01

The early usage of trigonometric functions can be traced back to at least 17th century BC. It was Bhaskara II of the 12th century CE who first proved the mathematical equivalence between the sum of two trigonometric functions of any given angles and the product of two trigonometric functions of related angles, which has been taught these days in middle school classroom. The additive perspective of trigonometric functions led to the development of the Fourier transform that is used to express any functions as the sum of a set of trigonometric functions and opened a new mathematical field called harmonic analysis. Unfortunately, Fourier's sum cannot directly express nonlinear interactions between trigonometric components of different periods, and thereby lacking the capability of quantifying nonlinear interactions in dynamical systems. In this talk, the speaker will introduce the Huang transform and Holo-spectrum which were pioneered by Norden Huang and emphasizes the multiplicative perspective of trigonometric functions in expressing any function. Holo-spectrum is a multi-dimensional spectral expression of a time series that explicitly identifies the interactions among different scales and quantifies nonlinear interactions hidden in a time series. Along with this introduction, the developing concepts of physical, rather than mathematical, analysis of data will be explained. Various enlightening applications of Holo-spectrum analysis in atmospheric and climate studies will also be presented.

Brillouin Scattering Spectrum Analysis Based on Auto-Regressive Spectral Estimation

NASA Astrophysics Data System (ADS)

Huang, Mengyun; Li, Wei; Liu, Zhangyun; Cheng, Linghao; Guan, Bai-Ou

2018-06-01

Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution.

Analysis techniques for residual acceleration data

NASA Technical Reports Server (NTRS)

Rogers, Melissa J. B.; Alexander, J. Iwan D.; Snyder, Robert S.

1990-01-01

Various aspects of residual acceleration data are of interest to low-gravity experimenters. Maximum and mean values and various other statistics can be obtained from data as collected in the time domain. Additional information may be obtained through manipulation of the data. Fourier analysis is discussed as a means of obtaining information about dominant frequency components of a given data window. Transformation of data into different coordinate axes is useful in the analysis of experiments with different orientations and can be achieved by the use of a transformation matrix. Application of such analysis techniques to residual acceleration data provides additional information than what is provided in a time history and increases the effectiveness of post-flight analysis of low-gravity experiments.

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

Phase-shift detection in a Fourier-transform method for temperature sensing using a tapered fiber microknot resonator.

PubMed

Larocque, Hugo; Lu, Ping; Bao, Xiaoyi

2016-04-01

Phase-shift detection in a fast-Fourier-transform (FFT)-based spectrum analysis technique for temperature sensing using a tapered fiber microknot resonator is proposed and demonstrated. Multiple transmission peaks in the FFT spectrum of the device were identified as optical modes having completed different amounts of round trips within the ring structure. Temperature variation induced phase shifts for each set of peaks were characterized, and experimental results show that different peaks have distinct temperature sensitivities reaching values up to -0.542  rad/°C, which is about 10 times greater than that of a regular adiabatic taper Mach-Zehnder interferometer when using similar phase-tracking schemes.

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.

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.

Differentiation of live and dead salmonella cells using fourier transform infrared (FTIR) spectroscopy and principle component analysis (PCA) technique

USDA-ARS?s Scientific Manuscript database

Various technologies have been developed for pathogen detection using optical, electrochemical, biochemical and physical properties. Conventional microbiological methods need time from days to week to get the result. Though this method is very sensitive and accurate, a rapid detection of pathogens i...

Data Mining in Earth System Science (DMESS 2011)

Treesearch

Forrest M. Hoffman; J. Walter Larson; Richard Tran Mills; Bhorn-Gustaf Brooks; Auroop R. Ganguly; William Hargrove; et al

2011-01-01

From field-scale measurements to global climate simulations and remote sensing, the growing body of very large and long time series Earth science data are increasingly difficult to analyze, visualize, and interpret. Data mining, information theoretic, and machine learning techniques—such as cluster analysis, singular value decomposition, block entropy, Fourier and...

Radiometric Short-Term Fourier Transform analysis of photonic Doppler velocimetry recordings and detectivity limit

NASA Astrophysics Data System (ADS)

Prudhomme, G.; Berthe, L.; Bénier, J.; Bozier, O.; Mercier, P.

2017-01-01

Photonic Doppler Velocimetry is a plug-and-play and versatile diagnostic used in dynamic physic experiments to measure velocities. When signals are analyzed using a Short-Time Fourier Transform, multiple velocities can be distinguished: for example, the velocities of moving particle-cloud appear on spectrograms. In order to estimate the back-scattering fluxes of target, we propose an original approach "PDV Radiometric analysis" resulting in an expression of time-velocity spectrograms coded in power units. Experiments involving micron-sized particles raise the issue of detection limit; particle-size limit is very difficult to evaluate. From the quantification of noise sources, we derive an estimation of the spectrogram noise leading to a detectivity limit, which may be compared to the fraction of the incoming power which has been back-scattered by the particle and then collected by the probe. This fraction increases with their size. At last, some results from laser-shock accelerated particles using two different PDV systems are compared: it shows the improvement of detectivity with respect to the Effective Number of Bits (ENOB) of the digitizer.

[On-line monitoring of biomass in 1,3-propanediol fermentation by Fourier-transformed near-infrared spectra analysis].

PubMed

Wang, Lu; Liu, Tao; Chen, Yang; Sun, Yaqin; Xiu, Zhilong

2017-01-25

Biomass is an important parameter reflecting the fermentation dynamics. Real-time monitoring of biomass can be used to control and optimize a fermentation process. To overcome the deficiencies of measurement delay and manual errors from offline measurement, we designed an experimental platform for online monitoring the biomass during a 1,3-propanediol fermentation process, based on using the fourier-transformed near-infrared (FT-NIR) spectra analysis. By pre-processing the real-time sampled spectra and analyzing the sensitive spectra bands, a partial least-squares algorithm was proposed to establish a dynamic prediction model for the biomass change during a 1,3-propanediol fermentation process. The fermentation processes with substrate glycerol concentrations of 60 g/L and 40 g/L were used as the external validation experiments. The root mean square error of prediction (RMSEP) obtained by analyzing experimental data was 0.341 6 and 0.274 3, respectively. These results showed that the established model gave good prediction and could be effectively used for on-line monitoring the biomass during a 1,3-propanediol fermentation process.

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)

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…

Improvements of the two-dimensional FDTD method for the simulation of normal- and superconducting planar waveguides using time series analysis

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

Hofschen, S.; Wolff, I.

1996-08-01

Time-domain simulation results of two-dimensional (2-D) planar waveguide finite-difference time-domain (FDTD) analysis are normally analyzed using Fourier transform. The introduced method of time series analysis to extract propagation and attenuation constants reduces the desired computation time drastically. Additionally, a nonequidistant discretization together with an adequate excitation technique is used to reduce the number of spatial grid points. Therefore, it is possible to reduce the number of spatial grid points. Therefore, it is possible to simulate normal- and superconducting planar waveguide structures with very thin conductors and small dimensions, as they are used in MMIC technology. The simulation results are comparedmore » with measurements and show good agreement.« less

Real-Time and Memory Correlation via Acousto-Optic Processing,

DTIC Science & Technology

1978-06-01

acousto - optic technology as an answer to these requirements appears very attractive. Three fundamental signal-processing schemes using the acousto ... optic interaction have been investigated: (i) real-time correlation and convolution, (ii) Fourier and discrete Fourier transformation, and (iii

Picosecond imaging of sprays

NASA Technical Reports Server (NTRS)

Breisacher, Kevin; Liou, Larry; Wang, L.; Liang, X.; Galland, P.; Ho, P. P.; Alfano, R. R.

1994-01-01

Preliminary results from applying a Kerr-Fourier imaging system to a water/air spray produced by a shear coaxial element are presented. The physics behind ultrafast time-gated optical techniques is discussed briefly. A typical setup of a Kerr-Fourier time gating system is presented.

Stokes polarimetry using analysis of the nonlinear voltage-retardance relationship for liquid-crystal variable retarders

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

López-Téllez, J. M., E-mail: jmlopez@comunidad.unam.mx; Bruce, N. C.

2014-03-15

We present a method for using liquid-crystal variable retarders (LCVR’s) with continually varying voltage to measure the Stokes vector of a light beam. The LCVR's are usually employed with fixed retardance values due to the nonlinear voltage-retardance behavior that they show. The nonlinear voltage-retardance relationship is first measured and then a linear fit of the known retardance terms to the detected signal is performed. We use known waveplates (half-wave and quarter-wave) as devices to provide controlled polarization states to the Stokes polarimeter and we use the measured Stokes parameters as functions of the orientation of the axes of the waveplatesmore » as an indication of the quality of the polarimeter. Results are compared to a Fourier analysis method that does not take into account the nonlinear voltage-retardance relationship and also to a Fourier analysis method that uses experimental voltage values to give a linear retardance function with time. Also, we present results of simulations for comparison.« less

Time history solution program, L225 (TEV126). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Kroll, R. I.; Tornallyay, A.; Clemmons, R. E.

1979-01-01

Volume 1 of a two volume document is presented. The usage of the convolution program L225 (TEV 126) is described. The program calculates the time response of a linear system by convoluting the impulsive response function with the time-dependent excitation function. The convolution is performed as a multiplication in the frequency domain. Fast Fourier transform techniques are used to transform the product back into the time domain to obtain response time histories. A brief description of the analysis used is presented.

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.

A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.

PubMed

Barlow, Euan; Mulholland, Anthony J

2011-11-01

The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.

Capillary waves' dynamics at the nanoscale

NASA Astrophysics Data System (ADS)

Delgado-Buscalioni, Rafael; Chacón, Enrique; Tarazona, Pedro

2008-12-01

We study the dynamics of thermally excited capillary waves (CW) at molecular scales, using molecular dynamics simulations of simple liquid slabs. The analysis is based on the Fourier modes of the liquid surface, constructed via the intrinsic sampling method (Chacón and Tarazona 2003 Phys. Rev. Lett. 91 166103). We obtain the time autocorrelation of the Fourier modes to get the frequency and damping rate Γd(q) of each mode, with wavenumber q. Continuum hydrodynamics predicts \\Gamma (q) \\propto q\\gamma (q) and thus provides a dynamic measure of the q-dependent surface tension, γd(q). The dynamical estimation is much more robust than the structural prediction based on the amplitude of the Fourier mode, γs(q). Using the optimal estimation of the intrinsic surface, we obtain quantitative agreement between the structural and dynamic pictures. Quite surprisingly, the hydrodynamic prediction for CW remains valid up to wavelengths of about four molecular diameters. Surface tension hydrodynamics break down at shorter scales, whereby a transition to a molecular diffusion regime is observed.

Glaucoma diagnosis by mapping macula with Fourier domain optical coherence tomography

NASA Astrophysics Data System (ADS)

Tan, Ou; Lu, Ake; Chopra, Vik; Varma, Rohit; Hiroshi, Ishikawa; Schuman, Joel; Huang, David

2008-03-01

A new image segmentation method was developed to detect macular retinal sub-layers boundary on newly-developed Fourier-Domain Optical Coherence Tomography (FD-OCT) with macular grid scan pattern. The segmentation results were used to create thickness map of macular ganglion cell complex (GCC), which contains the ganglion cell dendrites, cell bodies and axons. Overall average and several pattern analysis parameters were defined on the GCC thickness map and compared for the diagnosis of glaucoma. Intraclass correlation (ICC) is used to compare the reproducibility of the parameters. Area under receiving operative characteristic curve (AROC) was calculated to compare the diagnostic power. The result is also compared to the output of clinical time-domain OCT (TD-OCT). We found that GCC based parameters had good repeatability and comparable diagnostic power with circumpapillary nerve fiber layer (cpNFL) thickness. Parameters based on pattern analysis can increase the diagnostic power of GCC macular mapping.

Monitoring of the degradation in the rat's articular cartilage inducing osteoarthritis using common-path Fourier-domain optical coherence tomography

NASA Astrophysics Data System (ADS)

Shin, D. H.; Park, S. H.; Kim, B. Y.; Lee, M. Y.; Baik, H. K.; Seo, J. H.; Kang, J. U.; Song, C. G.

2013-03-01

The objective of this experiment is to evaluate the utility and limitations of optical coherence tomography (OCT) for real-time, high-resolution structural analysis. We monitored the degradation of the rat's articular cartilage inducing osteoarthritis (OA) and the change of the rat's articular cartilage recovery by treatment medication, using our developed common-path Fourier-domain (CP-FD) OCT. Also, we have done a comparative analysis the rat's articular cartilage and OA grade. To observe the progression of OA, we induced OA by injecting the monosodium iodoacetate (MIA) into the right knee joint. After the injection of MIA, we sacrificed the rats at intervals of 3 days and obtained OCT and histological images. OCT and histological images showed the OA progress of similar pattern. These results illustrated the potential for non-invasive diagnosis about the grade of OA using CP-FD OCT.

Discrimination of healthy and osteoarthritic articular cartilages by Fourier transform infrared imaging and partial least squares-discriminant analysis

PubMed Central

Zhang, Xue-Xi; Yin, Jian-Hua; Mao, Zhi-Hua; Xia, Yang

2015-01-01

Abstract. Fourier transform infrared imaging (FTIRI) combined with chemometrics algorithm has strong potential to obtain complex chemical information from biology tissues. FTIRI and partial least squares-discriminant analysis (PLS-DA) were used to differentiate healthy and osteoarthritic (OA) cartilages for the first time. A PLS model was built on the calibration matrix of spectra that was randomly selected from the FTIRI spectral datasets of healthy and lesioned cartilage. Leave-one-out cross-validation was performed in the PLS model, and the fitting coefficient between actual and predicted categorical values of the calibration matrix reached 0.95. In the calibration and prediction matrices, the successful identifying percentages of healthy and lesioned cartilage spectra were 100% and 90.24%, respectively. These results demonstrated that FTIRI combined with PLS-DA could provide a promising approach for the categorical identification of healthy and OA cartilage specimens. PMID:26057029

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

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

Levnajić, Zoran; Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106; Mezić, Igor

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone,more » and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.« less

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.

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

PubMed

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

Discrimination of healthy and osteoarthritic articular cartilages by Fourier transform infrared imaging and partial least squares-discriminant analysis.

PubMed

Zhang, Xue-Xi; Yin, Jian-Hua; Mao, Zhi-Hua; Xia, Yang

2015-06-01

Fourier transform infrared imaging (FTIRI) combined with chemometrics algorithm has strong potential to obtain complex chemical information from biology tissues. FTIRI and partial least squares-discriminant analysis (PLS-DA) were used to differentiate healthy and osteoarthritic (OA) cartilages for the first time. A PLS model was built on the calibration matrix of spectra that was randomly selected from the FTIRI spectral datasets of healthy and lesioned cartilage. Leave-one-out cross-validation was performed in the PLS model, and the fitting coefficient between actual and predicted categorical values of the calibration matrix reached 0.95. In the calibration and prediction matrices, the successful identifying percentages of healthy and lesioned cartilage spectra were 100% and 90.24%, respectively. These results demonstrated that FTIRI combined with PLS-DA could provide a promising approach for the categorical identification of healthy and OA cartilage specimens.

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.

Establishing a direct connection between detrended fluctuation analysis and Fourier analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken

2015-10-01

To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the single-frequency response of the DFA, the following facts are shown analytically: (1) in the analysis of stochastic processes exhibiting a power-law scaling of the power spectral density (PSD), S (f ) ˜f-β , a higher-order detrending in the DFA has no adverse effect in the estimation of the DFA scaling exponent α , which satisfies the scaling relation α =(β +1 )/2 ; (2) the upper limit of the scaling exponents detectable by the DFA depends on the order of polynomial fit used in the DFA, and is bounded by m +1 , where m is the order of the polynomial fit; (3) the relation between the time scale in the DFA and the corresponding frequency in the PSD are distorted depending on both the order of the DFA and the frequency dependence of the PSD. We can improve the scale distortion by introducing the corrected time scale in the DFA corresponding to the inverse of the frequency scale in the PSD. In addition, our analytical approach makes it possible to characterize variants of the DFA using different types of detrending. As an application, properties of the detrending moving average algorithm are discussed.

The short time Fourier transform and local signals

NASA Astrophysics Data System (ADS)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

Analytical properties of time-of-flight PET data.

PubMed

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M

2008-06-07

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Analytical properties of time-of-flight PET data

NASA Astrophysics Data System (ADS)

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2008-06-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Modeling and Simulation of a Signal Processor Implementing the Winograd Fourier Transform.

DTIC Science & Technology

1985-12-01

advisor, Captain Richard Linderman, for the gui- dance and timely remotivation needed to ensure successful completion of this research . The members...of the WFT research group, Captains Paul Coutee, Paul Rosssbach, and Kent Taylor provided a much needed source of answers to the many questions I had... research is directed toward analysis of VHDL as a tool useful in VLSI design. This analysis covered learning the language syntax, development of a

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.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

[Continuum based fast Fourier transform processing of infrared spectrum].

PubMed

Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai

2009-12-01

To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.

Screening retinal transplants with Fourier-domain OCT

NASA Astrophysics Data System (ADS)

Rao, Bin

2009-02-01

Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.

Remote monitoring of parental incubation conditions in the greater sandhill crane

USGS Publications Warehouse

Gee, G.F.; Hatfield, J.; Howey, P.J.

1995-01-01

To monitor incubation conditions in nests of greater sandhill cranes, a radiotransmitting egg was built using six temperature sensors, a position sensor, and a light sensor. Sensor readings were received, along with time of observations, and stored in a computer. The egg was used to monitor incubation in nests of six pairs of cranes during 1987 and 1988. Ambient temperature was also measured. Analysis of covariance (ANCOVA) was used to relate highest egg temperature, core egg temperature, and lowest egg temperature to ambient temperature, time since the egg was last turned, and time since the beginning of incubation. Ambient temperature had the greatest effect on egg temperature (P 0.0001), followed by the time since the beginning of incubation and time since the egg was last turned. Pair effect, the class variable in the ANCOVA. was also very significant (P < 0.0001). A nine-term Fourier series was used to estimate the average core egg temperature versus time of day and was found to fit the data well (r2 = 0.94). The Fourier series will be used to run a mechanical incubator to simulate natural incubation conditions for cranes.

Accuracy evaluation of Fourier series analysis and singular spectrum analysis for predicting the volume of motorcycle sales in Indonesia

NASA Astrophysics Data System (ADS)

Sasmita, Yoga; Darmawan, Gumgum

2017-08-01

This research aims to evaluate the performance of forecasting by Fourier Series Analysis (FSA) and Singular Spectrum Analysis (SSA) which are more explorative and not requiring parametric assumption. Those methods are applied to predicting the volume of motorcycle sales in Indonesia from January 2005 to December 2016 (monthly). Both models are suitable for seasonal and trend component data. Technically, FSA defines time domain as the result of trend and seasonal component in different frequencies which is difficult to identify in the time domain analysis. With the hidden period is 2,918 ≈ 3 and significant model order is 3, FSA model is used to predict testing data. Meanwhile, SSA has two main processes, decomposition and reconstruction. SSA decomposes the time series data into different components. The reconstruction process starts with grouping the decomposition result based on similarity period of each component in trajectory matrix. With the optimum of window length (L = 53) and grouping effect (r = 4), SSA predicting testing data. Forecasting accuracy evaluation is done based on Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The result shows that in the next 12 month, SSA has MAPE = 13.54 percent, MAE = 61,168.43 and RMSE = 75,244.92 and FSA has MAPE = 28.19 percent, MAE = 119,718.43 and RMSE = 142,511.17. Therefore, to predict volume of motorcycle sales in the next period should use SSA method which has better performance based on its accuracy.

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

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.

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.

Interactive digital signal processor

NASA Technical Reports Server (NTRS)

Mish, W. H.; Wenger, R. M.; Behannon, K. W.; Byrnes, J. B.

1982-01-01

The Interactive Digital Signal Processor (IDSP) is examined. It consists of a set of time series analysis Operators each of which operates on an input file to produce an output file. The operators can be executed in any order that makes sense and recursively, if desired. The operators are the various algorithms used in digital time series analysis work. User written operators can be easily interfaced to the sysatem. The system can be operated both interactively and in batch mode. In IDSP a file can consist of up to n (currently n=8) simultaneous time series. IDSP currently includes over thirty standard operators that range from Fourier transform operations, design and application of digital filters, eigenvalue analysis, to operators that provide graphical output, allow batch operation, editing and display information.

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

Flow transition with 2-D roughness elements in a 3-D channel

NASA Technical Reports Server (NTRS)

Liu, Zhining; Liu, Chaoquin; Mccormick, Stephen F.

1993-01-01

We develop a new numerical approach to study the spatially evolving instability of the streamwise dominant flow in the presence of roughness elements. The difficulty in handling the flow over the boundary surface with general geometry is removed by using a new conservative form of the governing equations and an analytical mapping. The numerical scheme uses second-order backward Euler in time, fourth-order central differences in all three spatial directions, and boundary-fitted staggered grids. A three-dimensional channel with multiple two-dimensional-type roughness elements is employed as the test case. Fourier analysis is used to decompose different Fourier modes of the disturbance. The results show that surface roughness leads to transition at lower Reynolds number than for smooth channels.

Reference ultraviolet wavelengths of CrIII measured by Fourier transform spectrometry

NASA Astrophysics Data System (ADS)

Smillie, D. G.; Pickering, J. C.; Smith, P. L.

2008-10-01

We report CrIII ultraviolet (UV) transition wavelengths measured using a high-resolution Fourier transform spectrometer (FTS), for the first time, available for use as wavelength standards. The doubly ionized iron group element spectra dominate the observed opacity of hot B stars in the UV, and improved, accurate, wavelengths are required for the analysis of astronomical spectra. The spectrum was excited using a chromium-neon Penning discharge lamp and measured with the Imperial College vacuum ultraviolet FTS. 140 classified 3d34s-3d34p CrIII transition lines, in the spectral range 38000 to 49000 cm-1 (2632 to 2041 Å), the strongest having wavelength uncertainties less than one part in 107, are presented.

Ramanujan sums for signal processing of low-frequency noise.

PubMed

Planat, Michel; Rosu, Haret; Perrine, Serge

2002-11-01

An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums c(q)(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals.

Ramanujan sums for signal processing of low-frequency noise

NASA Astrophysics Data System (ADS)

Planat, Michel; Rosu, Haret; Perrine, Serge

2002-11-01

An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums cq(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals.

Critical assessment of von Mises distribution and an infinite series ansatz for self-propelled particles

NASA Astrophysics Data System (ADS)

Kürsten, Rüdiger; Ihle, Thomas

2017-03-01

We consider a Vicsek model of self-propelled particles with bounded confidence, where each particle interacts only with neighbors that have a similar direction. Depending on parameters, the system exhibits a continuous or discontinuous polar phase transition from the isotropic phase to a phase with a preferred direction. In a recent paper (Lam, Schindler and Dauchot 2015 J. Stat. Mech. P10017) the von Mises distribution was proposed as an ansatz for polar ordering. In the present system the time evolution of the angular distribution can be solved in Fourier space. We compare the results of the Fourier analysis with the ones obtained by using the von Mises distribution ansatz. In the latter case the qualitative behavior of the system is recovered correctly. However, quantitatively there are serious deviations. We introduce an extended von Mises distribution ansatz such that a second term takes care of the next two Fourier modes. With the extended ansatz we find much better quantitative agreement. As an alternative approach we also use a Gaussian and a geometric series ansatz in Fourier space. The geometric series ansatz is analytically handable but fails for very weak noise, the Gaussian ansatz yields better results but it is not analytically treatable.

An Efficient Implementation For Real Time Applications Of The Wigner-Ville Distribution

NASA Astrophysics Data System (ADS)

Boashash, Boualem; Black, Peter; Whitehouse, Harper J.

1986-03-01

The Wigner-Ville Distribution (WVD) is a valuable tool for time-frequency signal analysis. In order to implement the WVD in real time an efficient algorithm and architecture have been developed which may be implemented with commercial components. This algorithm successively computes the analytic signal corresponding to the input signal, forms a weighted kernel function and analyses the kernel via a Discrete Fourier Transform (DFT). To evaluate the analytic signal required by the algorithm it is shown that the time domain definition implemented as a finite impulse response (FIR) filter is practical and more efficient than the frequency domain definition of the analytic signal. The windowed resolution of the WVD in the frequency domain is shown to be similar to the resolution of a windowed Fourier Transform. A real time signal processsor has been designed for evaluation of the WVD analysis system. The system is easily paralleled and can be configured to meet a variety of frequency and time resolutions. The arithmetic unit is based on a pair of high speed VLSI floating-point multiplier and adder chips. Dual operand buses and an independent result bus maximize data transfer rates. The system is horizontally microprogrammed and utilizes a full instruction pipeline. Each microinstruction specifies two operand addresses, a result location, the type of arithmetic and the memory configuration. input and output is via shared memory blocks with front-end processors to handle data transfers during the non access periods of the analyzer.

Ultra-Wideband Radar Transient Detection using Time-Frequency and Wavelet Transforms.

DTIC Science & Technology

1992-12-01

if p==2, mesh(flipud(abs(spdatamatrix).A2)) end 2. Wigner - Ville Distribution function P = wvd (data,winlenstep,begintheendp) % Filename: wvd.m % Title...short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution , and time-scale methods, such as the a trous...such as the short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution [1], and time-scale methods, such

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

[Fast determination of induction period of motor gasoline using Fourier transform attenuated total reflection infrared spectroscopy].

PubMed

Liu, Ya-Fei; Yuan, Hong-Fu; Song, Chun-Feng; Xie, Jin-Chun; Li, Xiao-Yu; Yan, De-Lin

2014-11-01

A new method is proposed for the fast determination of the induction period of gasoline using Fourier transform attenuated total reflection infrared spectroscopy (ATR-FTIR). A dedicated analysis system with the function of spectral measurement, data processing, display and storage was designed and integrated using a Fourier transform infrared spectrometer module and chemometric software. The sample presentation accessory designed which has advantages of constant optical path, convenient sample injection and cleaning is composed of a nine times reflection attenuated total reflectance (ATR) crystal of zinc selenide (ZnSe) coated with a diamond film and a stainless steel lid with sealing device. The influence of spectral scanning number and repeated sample loading times on the spectral signal-to-noise ratio was studied. The optimum spectral scanning number is 15 times and the optimum sample loading number is 4 times. Sixty four different gasoline samples were collected from the Beijing-Tianjin area and the induction period values were determined as reference data by standard method GB/T 8018-87. The infrared spectra of these samples were collected in the operating condition mentioned above using the dedicated fast analysis system. Spectra were pretreated using mean centering and 1st derivative to reduce the influence of spectral noise and baseline shift A PLS calibration model for the induction period was established by correlating the known induction period values of the samples with their spectra. The correlation coefficient (R2), standard error of calibration (SEC) and standard error of prediction (SEP) of the model are 0.897, 68.3 and 91.9 minutes, respectively. The relative deviation of the model for gasoline induction period prediction is less than 5%, which meets the requirements of repeatability tolerance in GB method. The new method is simple and fast. It takes no more than 3 minutes to detect one sample. Therefore, the method is feasible for implementing fast determination of gasoline induction period, and of a positive meaning in the evaluation of fuel quality.

Analytical Properties of Time-of-Flight PET Data

PubMed Central

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2015-01-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the “bow-tie” property of the 2D Radon transform to the time of flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data. PMID:18460746

A Short-Segment Fourier Transform Methodology

DTIC Science & Technology

2009-03-01

defined sampling of the continuous-valued discrete-time Fourier transform, superresolution in the frequency domain and allowance of Dirac delta functions associated with pure sinusoidal input data components.

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform

PubMed Central

Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

2018-01-01

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm. PMID:29438317

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

PubMed

Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

2018-02-13

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

PubMed

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

A crash course on data analysis in asteroseismology

NASA Astrophysics Data System (ADS)

Appourchaux, Thierry

2014-02-01

In this course, I try to provide a few basics required for performing data analysis in asteroseismology. First, I address how one can properly treat times series: the sampling, the filtering effect, the use of Fourier transform, the associated statistics. Second, I address how one can apply statistics for decision making and for parameter estimation either in a frequentist of a Bayesian framework. Last, I review how these basic principle have been applied (or not) in asteroseismology.

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.

Nonlinear Analysis of Motor Activity Shows Differences between Schizophrenia and Depression: A Study Using Fourier Analysis and Sample Entropy

PubMed Central

Hauge, Erik R.; Berle, Jan Øystein; Oedegaard, Ketil J.; Holsten, Fred; Fasmer, Ole Bernt

2011-01-01

The purpose of this study has been to describe motor activity data obtained by using wrist-worn actigraphs in patients with schizophrenia and major depression by the use of linear and non-linear methods of analysis. Different time frames were investigated, i.e., activity counts measured every minute for up to five hours and activity counts made hourly for up to two weeks. The results show that motor activity was lower in the schizophrenic patients and in patients with major depression, compared to controls. Using one minute intervals the depressed patients had a higher standard deviation (SD) compared to both the schizophrenic patients and the controls. The ratio between the root mean square successive differences (RMSSD) and SD was higher in the schizophrenic patients compared to controls. The Fourier analysis of the activity counts measured every minute showed that the relation between variance in the low and the high frequency range was lower in the schizophrenic patients compared to the controls. The sample entropy was higher in the schizophrenic patients compared to controls in the time series from the activity counts made every minute. The main conclusions of the study are that schizophrenic and depressive patients have distinctly different profiles of motor activity and that the results differ according to period length analysed. PMID:21297977

Carotid MR angiography with traditional bolus timing: clinical observations and Fourier-based modelling of contrast kinetics.

PubMed

Menke, Jan

2009-11-01

This study analyses the relation between image quality and contrast kinetics in bolus-timed carotid magnetic resonance angiography (MRA) and interprets the findings by Fourier-based numerical modelling. One hundred patients prone to carotid stenosis were studied using contrast-enhanced carotid MRA with bolus timing. The carotid MRAs were timed to start relatively early without accounting for the injection time of the contrast medium. For interpretation different starting times were modelled, utilising the spectral information of the test bolus series. In the test bolus series the arterial time-to-peak showed a large 95% confidence interval of 12-27 s, indicating the need for individual MRA timing. All bolus-timed MRAs were of good diagnostic quality. The mean (+/-SD) arterial contrast-to-noise ratio was 53.0 (+/-12.8) and thus high, and 95% of the MRAs showed a slight venous contamination of 11.8% or less (median 5.6%). According to the Fourier-based modelling the central k-space may be acquired about 2 s before the arterial contrast peak. This results in carotid MRAs with sufficiently high arterial enhancement and little venous contamination. In conclusion, in bolus-timed carotid MRA a relatively short timing provides good arterial contrast with little venous contamination, which can be explained by Fourier-based numerical modelling of the contrast kinetics.

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.

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

A class of Fourier integrals based on the electric potential of an elongated dipole.

PubMed

Skianis, Georgios Aim

2014-01-01

In the present paper the closed expressions of a class of non tabulated Fourier integrals are derived. These integrals are associated with a group of functions at space domain, which represent the electric potential of a distribution of elongated dipoles which are perpendicular to a flat surface. It is shown that the Fourier integrals are produced by the Fourier transform of the Green's function of the potential of the dipole distribution, times a definite integral in which the distribution of the polarization is involved. Therefore the form of this distribution controls the expression of the Fourier integral. Introducing various dipole distributions, the respective Fourier integrals are derived. These integrals may be useful in the quantitative interpretation of electric potential anomalies produced by elongated dipole distributions, at spatial frequency domain.

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.

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.

Quantum Entanglement Molecular Absorption Spectrum Simulator

NASA Technical Reports Server (NTRS)

Nguyen, Quang-Viet; Kojima, Jun

2006-01-01

Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.

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.

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

Real-Time Stability Margin Measurements for X-38 Robustness Analysis

NASA Technical Reports Server (NTRS)

Bosworth, John T.; Stachowiak, Susan J.

2005-01-01

A method has been developed for real-time stability margin measurement calculations. The method relies on a tailored-forced excitation targeted to a specific frequency range. Computation of the frequency response is matched to the specific frequencies contained in the excitation. A recursive Fourier transformation is used to make the method compatible with real-time calculation. The method was incorporated into the X-38 nonlinear simulation and applied to an X-38 robustness test. X-38 stability margins were calculated for different variations in aerodynamic and mass properties over the vehicle flight trajectory. The new method showed results comparable to more traditional stability analysis techniques, and at the same time, this new method provided coverage that is more complete and increased efficiency.

Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures.

PubMed

Costa, Madalena D; Peng, Chung-Kang; Goldberger, Ary L

2008-06-01

Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools--multiscale entropy and multiscale time irreversibility--are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs.

Endoplasmic motility spectral characteristics in plasmodium of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Avsievich, T. I.; Ghaleb, K. E. S.; Frolov, S. V.; Proskurin, S. G.

2015-03-01

Spectral Fourier analysis of experimentally acquired velocity time dependencies, V(t), of shuttle endoplasmic motility in an isolated strand of plasmodium of slime mold Physarum Polycephalum has been realized. V(t) registration was performed in normal conditions and after the treatment by respiration inhibitors, which lead to a complete cessation of endoplasmic motion in the strand. Spectral analysis of the velocity time dependences of the endoplasm allows obtaining two distinct harmonic components in the spectra. Their ratio appeared to be constant in all cases, ν2/ν1=1.97±0.17. After the inhibitors are washed out respiratory system becomes normal, gradually restoring the activity of both harmonic oscillatory sources with time. Simulated velocity time dependences correspond to experimental data with good accuracy.

Multiscale Analysis of Heart Rate Dynamics: Entropy and Time Irreversibility Measures

PubMed Central

Peng, Chung-Kang; Goldberger, Ary L.

2016-01-01

Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and nonequilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools— multiscale entropy and multiscale time irreversibility—are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs. PMID:18172763

Fourier and Wavelet Analysis of Coronal Time Series

NASA Astrophysics Data System (ADS)

Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.

2016-10-01

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.

Real-time and high accuracy frequency measurements for intermediate frequency narrowband signals

NASA Astrophysics Data System (ADS)

Tian, Jing; Meng, Xiaofeng; Nie, Jing; Lin, Liwei

2018-01-01

Real-time and accurate measurements of intermediate frequency signals based on microprocessors are difficult due to the computational complexity and limited time constraints. In this paper, a fast and precise methodology based on the sigma-delta modulator is designed and implemented by first generating the twiddle factors using the designed recursive scheme. This scheme requires zero times of multiplications and only half amounts of addition operations by using the discrete Fourier transform (DFT) and the combination of the Rife algorithm and Fourier coefficient interpolation as compared with conventional methods such as DFT and Fast Fourier Transform. Experimentally, when the sampling frequency is 10 MHz, the real-time frequency measurements with intermediate frequency and narrowband signals have a measurement mean squared error of ±2.4 Hz. Furthermore, a single measurement of the whole system only requires approximately 0.3 s to achieve fast iteration, high precision, and less calculation time.

In Situ Analysis of a High-Temperature Cure Reaction in Real Time Using Modulated Fiber-Optic FT-Raman Spectroscopy

NASA Technical Reports Server (NTRS)

Aust, Jeffrey F.; Cooper, John B.; Wise, Kent L.; Jensen, Brian J.

1999-01-01

The vibrational spectrum of a high-temperature (330 C) polymerization reaction was successfully monitored in real time with the use of a modulated fiber-optic Fourier transform (FT)-Raman spectrometer. A phenylethynyl-terminated monomer was cured, and spectral evidence for two different reaction products was acquired. The products are a conjugated polyene chain and a cyclized trimer. This is the first report describing the use of FT-Raman spectroscopy to monitor a high temperature (greater than 250 C) reaction in real time.

Time series analysis of ozone data in Isfahan

NASA Astrophysics Data System (ADS)

Omidvari, M.; Hassanzadeh, S.; Hosseinibalam, F.

2008-07-01

Time series analysis used to investigate the stratospheric ozone formation and decomposition processes. Different time series methods are applied to detect the reason for extreme high ozone concentrations for each season. Data was convert into seasonal component and frequency domain, the latter has been evaluated by using the Fast Fourier Transform (FFT), spectral analysis. The power density spectrum estimated from the ozone data showed peaks at cycle duration of 22, 20, 36, 186, 365 and 40 days. According to seasonal component analysis most fluctuation was in 1999 and 2000, but the least fluctuation was in 2003. The best correlation between ozone and sun radiation was found in 2000. Other variables which are not available cause to this fluctuation in the 1999 and 2001. The trend of ozone is increasing in 1999 and is decreasing in other years.

Aqueous contaminant detection via UiO-66 thin film optical fiber sensor platform with fast Fourier transform based spectrum analysis

NASA Astrophysics Data System (ADS)

Nazari, Marziyeh; Rubio-Martinez, Marta; Babarao, Ravichandar; Ayad Younis, Adel; Collins, Stephen F.; Hill, Matthew R.; Duke, Mikel C.

2018-01-01

Routine water quality monitoring is required in drinking and waste water management. A particular interest is to measure concentrations of a range of diverse contaminants on-site or remotely in real time. Here we present metal organic framework (MOF) integrated optical fiber sensor that allows for rapid optical measurement based on fast Fourier transform (FFT) spectrum analysis. The end-face of these glass optical fibers was modified with UiO-66(Zr) MOF thin film by in situ hydrothermal synthesis for the detection of the model contaminants, Rhodamine-B and 4-Aminopyridine, in water. The sensing mechanism is based on the change in the optical path length of the thin film induced by the adsorption of chemical molecules by UiO-66. Using FFT analysis, various modes of interaction (physical and chemical) became apparent, showing both irreversible changes upon contact with the contaminant, as well as reversible changes according to actual concentration. This was indicated by the second harmonic elevation to a certain level translating to high sensitivity detection.

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).

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

Synthesis and characterization of some metal oxide nanocrystals by microwave irradiation

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

Rashad, M.; Gaber, A.; Abdelrahim, M. A.

2013-12-16

Copper oxide and cobalt oxide (CuO, Co3O4) nanocrystals (NCs) have been successfully prepared in a short time using microwave irradiation. The resulted powders of nanocrystals (NCs) were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Thermogravimetric analysis (TGA) measurements are also studied. Fourier-transform infrared (FT-IR) and UV–visible absorption spectroscopy of both kind of nanoparticels are illustrated. Optical absorption analysis indicated the direct band gap for both kinds of nanocrystals.

An efficient solution procedure for the thermoelastic analysis of truss space structures

NASA Technical Reports Server (NTRS)

Givoli, D.; Rand, O.

1992-01-01

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

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…

Analysis and correction of ground reflection effects in measured narrowband sound spectra using cepstral techniques

NASA Technical Reports Server (NTRS)

Miles, J. H.; Stevens, G. H.; Leininger, G. G.

1975-01-01

Ground reflections generate undesirable effects on acoustic measurements such as those conducted outdoors for jet noise research, aircraft certification, and motor vehicle regulation. Cepstral techniques developed in speech processing are adapted to identify echo delay time and to correct for ground reflection effects. A sample result is presented using an actual narrowband sound pressure level spectrum. The technique can readily be adapted to existing fast Fourier transform type spectrum measurement instrumentation to provide field measurements/of echo time delays.

Reference Ultraviolet Wavelengths of Cr III Measured by Fourier Transform Spectrometry

NASA Technical Reports Server (NTRS)

Smillie, D.G.; Pickering, J.C.; Smith, P.L.

2008-01-01

We report Cr III ultraviolet (UV) transition wavelengths measured using a high-resolution Fourier transform spectrometer (FTS), for the first time, available for use as wavelength standards. The doubly ionized iron group element spectra dominate the observed opacity of hot B stars in the UV, and improved, accurate, wavelengths are required for the analysis of astronomical spectra. The spectrum was excited using a chromium-neon Penning discharge lamp and measured with the Imperial College vacuum ultraviolet FTS. 140 classified 3d(exp 3)4s- 3d(exp 3)4p Cr III transition lines, in the spectral range 38,000 to 49,000 cm(exp -1) (2632 to 2041 A), the strongest having wavelength uncertainties less than one part in 10(exp 7), are presented.

In-situ chemical analyses of trans-polyisoprene by histochemical staining and Fourier transform infrared microspectroscopy in a rubber-producing plant, Eucommia ulmoides Oliver.

PubMed

Bamba, Takeshi; Fukusaki, Ei-Ichiro; Nakazawa, Yoshihisa; Kobayashi, Akio

2002-10-01

The localization of polyisoprene in young stem tissues of Eucommia ulmoides Oliver was investigated by histochemical staining and Fourier transform infrared (FT-IR) microspectroscopy. The fibrous structures were stained with Oil Red O. FT-IR microspectroscopic analysis proved that the fibrous structures were trans-polyisoprene. Granular structures stained with the dye, and characteristic absorptions at 2,960 cm(-1) and 1,430 cm(-1) in FT-IR suggested that trans-polyisoprene accumulated in the vicinity of the cambium layer. We have thus successfully shown for the first time the localization of trans-polyisoprene in plant tissues, and our histological investigation allowed us to presume the main sites of biosynthesis and accumulation of trans-rubber. Furthermore, a new technical approach, the preparation of sections using an electronic freezing unit and the in situ analysis of polyisoprene using FT-IR microspectroscopy, is demonstrated to be a promising method for determining the accumulation of polyisoprene as well as other metabolites.

Stepwise Iterative Fourier Transform: The SIFT

NASA Technical Reports Server (NTRS)

Benignus, V. A.; Benignus, G.

1975-01-01

A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.

Time-localized frequency analysis of ultrasonic guided waves for nondestructive testing

NASA Astrophysics Data System (ADS)

Shin, Hyeon Jae; Song, Sung-Jin

2000-05-01

A time-localized frequency (TLF) analysis is employed for the guided wave mode identification and improved guided wave applications. For the analysis of time-localized frequency contents of digitized ultrasonic signals, TLF analysis consists of splitting the time domain signal into overlapping segments, weighting each with the hanning window, and forming the columns of discrete Fourier transforms. The result is presented by a frequency versus time domain diagram showing frequency variation along the signal arrival time. For the demonstration of the utility of TLF analysis, an experimental group velocity dispersion pattern obtained by TLF analysis is compared with the dispersion diagram obtained by theory of elasticity. Sample piping is carbon steel piping that is used for the transportation of natural gas underground. Guided wave propagation characteristic on the piping is considered with TLF analysis and wave structure concepts. TLF analysis is used for the detection of simulated corrosion defects and the assessment of weld joint using ultrasonic guided waves. TLF analysis has revealed that the difficulty of mode identification in multi-mode propagation could be overcome. Group velocity dispersion pattern obtained by TLF analysis agrees well with theoretical results.

Dissipative structure and global existence in critical space for Timoshenko system of memory type

NASA Astrophysics Data System (ADS)

Mori, Naofumi

2018-08-01

In this paper, we consider the initial value problem for the Timoshenko system with a memory term in one dimensional whole space. In the first place, we consider the linearized system: applying the energy method in the Fourier space, we derive the pointwise estimate of the solution in the Fourier space, which first gives the optimal decay estimate of the solution. Next, we give a characterization of the dissipative structure of the system by using the spectral analysis, which confirms our pointwise estimate is optimal. In the second place, we consider the nonlinear system: we show that the global-in-time existence and uniqueness result could be proved in the minimal regularity assumption in the critical Sobolev space H2. In the proof we don't need any time-weighted norm as recent works; we use just an energy method, which is improved to overcome the difficulties caused by regularity-loss property of Timoshenko system.

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.

Predictive searching algorithm for Fourier ptychography

NASA Astrophysics Data System (ADS)

Li, Shunkai; Wang, Yifan; Wu, Weichen; Liang, Yanmei

2017-12-01

By capturing a set of low-resolution images under different illumination angles and stitching them together in the Fourier domain, Fourier ptychography (FP) is capable of providing high-resolution image with large field of view. Despite its validity, long acquisition time limits its real-time application. We proposed an incomplete sampling scheme in this paper, termed the predictive searching algorithm to shorten the acquisition and recovery time. Informative sub-regions of the sample’s spectrum are searched and the corresponding images of the most informative directions are captured for spectrum expansion. Its effectiveness is validated by both simulated and experimental results, whose data requirement is reduced by ˜64% to ˜90% without sacrificing image reconstruction quality compared with the conventional FP method.

A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials

NASA Astrophysics Data System (ADS)

Lu, Tiao; Cai, Wei

2008-10-01

In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger-Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method.

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.

Classification of electroencephalograph signals using time-frequency decomposition and linear discriminant analysis

NASA Astrophysics Data System (ADS)

Szuflitowska, B.; Orlowski, P.

2017-08-01

Automated detection system consists of two key steps: extraction of features from EEG signals and classification for detection of pathology activity. The EEG sequences were analyzed using Short-Time Fourier Transform and the classification was performed using Linear Discriminant Analysis. The accuracy of the technique was tested on three sets of EEG signals: epilepsy, healthy and Alzheimer's Disease. The classification error below 10% has been considered a success. The higher accuracy are obtained for new data of unknown classes than testing data. The methodology can be helpful in differentiation epilepsy seizure and disturbances in the EEG signal in Alzheimer's Disease.

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.

Identification of chemical components in Baidianling Capsule based on gas chromatography-mass spectrometry and high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Wu, Wenying; Chen, Yu; Wang, Binjie; Sun, Xiaoyang; Guo, Ping; Chen, Xiaohui

2017-08-01

Baidianling Capsule, which is made from 16 Chinese herbs, has been widely used for treating vitiligo clinically. In this study, the sensitive and rapid method has been developed for the analysis of chemical components in Baidianling Capsule by gas chromatography-mass spectrometry in combination with retention indices and high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry. Firstly, a total of 110 potential volatile compounds obtained from different extraction procedures including alkanes, alkenes, alkynes, ketones, ethers, aldehydes, alcohols, phenols, organic acids, esters, furans, pyrrole, acid amides, heterocycles, and oxides were detected from Baidianling Capsule by gas chromatography-mass spectrometry, of which 75 were identified by mass spectrometry in combination with the retention index. Then, a total of 124 components were tentatively identified by high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry. Fifteen constituents from Baidianling Capsule were accurately identified by comparing the retention times with those of reference compounds, others were identified by comparing the retention times and mass spectrometry data, as well as retrieving the reference literature. This study provides a practical strategy for rapidly screening and identifying the multiple constituents of a complex traditional Chinese medicine. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

Development of Imaging Fourier-Transform Spectroscopy for the Characterization of Turbulent Jet Flames

DTIC Science & Technology

2014-09-18

Spatially resolved infrared spectra of jet exhaust from an F109 turbofan engine...Appendix E contains a conference proceeding in its entirety [32]. This proceeding summarizes analysis of a turbofan engine exhaust via the Hyper-Cam and...demonstrated in a separate experiment. Recently, exhaust from an F109 turbofan engine was imaged with the IFTS[32]. Examination of the time-averaged

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...

Temporal Fourier analysis applied to equilibrium radionuclide cineangiography. Importance in the study of global and regional left ventricular wall motion.

PubMed

Cardot, J C; Berthout, P; Verdenet, J; Bidet, A; Faivre, R; Bassand, J P; Bidet, R; Maurat, J P

1982-01-01

Regional and global left ventricular wall motion was assessed in 120 patients using radionuclide cineangiography (RCA) and contrast angiography. Functional imaging procedures based on a temporal Fourier analysis of dynamic image sequences were applied to the study of cardiac contractility. Two images were constructed by taking the phase and amplitude values of the first harmonic in the Fourier transform for each pixel. These two images aided in determining the perimeter of the left ventricle to calculate the global ejection fraction. Regional left ventricular wall motion was studied by analyzing the phase value and by examining the distribution histogram of these values. The accuracy of global ejection fraction calculation was improved by the Fourier technique. This technique increased the sensitivity of RCA for determining segmental abnormalities especially in the left anterior oblique view (LAO).

Fourier rebinning and consistency equations for time-of-flight PET planograms

PubMed Central

Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

2016-01-01

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give numerical examples of implementation of a fast 2D TOF planogram projector and Fourier-based rebinning for a 2D TOF planograms using the FORCEs to show the efficacy of the Fourier-based solutions. PMID:28255191

Fourier rebinning and consistency equations for time-of-flight PET planograms.

PubMed

Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

2016-01-01

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give numerical examples of implementation of a fast 2D TOF planogram projector and Fourier-based rebinning for a 2D TOF planograms using the FORCEs to show the efficacy of the Fourier-based solutions.

Imaging through ground-level turbulence by Fourier telescopy: Simulations and preliminary experiments

NASA Astrophysics Data System (ADS)

Randunu Pathirannehelage, Nishantha

Fourier telescopy imaging is a recently-developed imaging method that relies on active structured-light illumination of the object. Reflected/scattered light is measured by a large "light bucket" detector; processing of the detected signal yields the magnitude and phase of spatial frequency components of the object reflectance or transmittance function. An inverse Fourier transform results in the image. In 2012 a novel method, known as time-average Fourier telescopy (TAFT), was introduced by William T. Rhodes as a means for diffraction-limited imaging through ground-level atmospheric turbulence. This method, which can be applied to long horizontal-path terrestrial imaging, addresses a need that is not solved by the adaptive optics methods being used in astronomical imaging. Field-experiment verification of the TAFT concept requires instrumentation that is not available at Florida Atlantic University. The objective of this doctoral research program is thus to demonstrate, in the absence of full-scale experimentation, the feasibility of time-average Fourier telescopy through (a) the design, construction, and testing of small-scale laboratory instrumentation capable of exploring basic Fourier telescopy data-gathering operations, and (b) the development of MATLAB-based software capable of demonstrating the effect of kilometer-scale passage of laser beams through ground-level turbulence in a numerical simulation of TAFT.

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).

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.

Using time-frequency analysis to determine time-resolved detonation velocity with microwave interferometry.

PubMed

Kittell, David E; Mares, Jesus O; Son, Steven F

2015-04-01

Two time-frequency analysis methods based on the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used to determine time-resolved detonation velocities with microwave interferometry (MI). The results were directly compared to well-established analysis techniques consisting of a peak-picking routine as well as a phase unwrapping method (i.e., quadrature analysis). The comparison is conducted on experimental data consisting of transient detonation phenomena observed in triaminotrinitrobenzene and ammonium nitrate-urea explosives, representing high and low quality MI signals, respectively. Time-frequency analysis proved much more capable of extracting useful and highly resolved velocity information from low quality signals than the phase unwrapping and peak-picking methods. Additionally, control of the time-frequency methods is mainly constrained to a single parameter which allows for a highly unbiased analysis method to extract velocity information. In contrast, the phase unwrapping technique introduces user based variability while the peak-picking technique does not achieve a highly resolved velocity result. Both STFT and CWT methods are proposed as improved additions to the analysis methods applied to MI detonation experiments, and may be useful in similar applications.

Diffusion tensor MRI shows progressive changes in the hippocampus and dentate gyrus after status epilepticus in rat - histological validation with Fourier-based analysis.

PubMed

Salo, Raimo A; Miettinen, Tuukka; Laitinen, Teemu; Gröhn, Olli; Sierra, Alejandra

2017-05-15

Imaging markers for monitoring disease progression, recovery, and treatment efficacy are a major unmet need for many neurological diseases, including epilepsy. Recent evidence suggests that diffusion tensor imaging (DTI) provides high microstructural contrast even outside major white matter tracts. We hypothesized that in vivo DTI could detect progressive microstructural changes in the dentate gyrus and the hippocampal CA3bc in the rat brain after status epilepticus (SE). To test this hypothesis, we induced SE with systemic kainic acid or pilocarpine in adult male Wistar rats and subsequently scanned them using in vivo DTI at five time-points: prior to SE, and 10, 20, 34, and 79 days post SE. In order to tie the DTI findings to changes in the tissue microstructure, myelin- and glial fibrillary acidic protein (GFAP)-stained sections from the same animals underwent Fourier analysis. We compared the Fourier analysis parameters, anisotropy index and angle of myelinated axons or astrocyte processes, to corresponding DTI parameters, fractional anisotropy (FA) and the orientation angle of the principal eigenvector. We found progressive detectable changes in DTI parameters in both the dentate gyrus (FA, axial diffusivity [D || ], linear anisotropy [CL] and spherical anisotropy [CS], p<0.001, linear mixed-effects model [LMEM]) and the CA3bc (FA, D || , CS, and angle, p<0.001, LMEM; CL and planar anisotropy [CP], p<0.01, LMEM) post SE. The Fourier analysis revealed that both myelinated axons and astrocyte processes played a role in the water diffusion anisotropy changes detected by DTI in individual portions of the dentate gyrus (suprapyramidal blade, mid-portion, and infrapyramidal blade). In the whole dentate gyrus, myelinated axons markedly contributed to the water diffusion changes. In CA3bc as well as in CA3b and CA3c, both myelinated axons and astrocyte processes contributed to water diffusion anisotropy and orientation. Our study revealed that DTI is a promising method for noninvasive detection of microstructural alterations in the hippocampus proper. These alterations may be potential imaging markers for epileptogenesis. Copyright © 2017 Elsevier Inc. All rights reserved.

A Smoothing Technique for the Multifractal Analysis of a Medium Voltage Feeders Electric Current

NASA Astrophysics Data System (ADS)

de Santis, Enrico; Sadeghian, Alireza; Rizzi, Antonello

2017-12-01

The current paper presents a data-driven detrending technique allowing to smooth complex sinusoidal trends from a real-world electric load time series before applying the Detrended Multifractal Fluctuation Analysis (MFDFA). The algorithm we call Smoothed Sort and Cut Fourier Detrending (SSC-FD) is based on a suitable smoothing of high power periodicities operating directly in the Fourier spectrum through a polynomial fitting technique of the DFT. The main aim consists of disambiguating the characteristic slow varying periodicities, that can impair the MFDFA analysis, from the residual signal in order to study its correlation properties. The algorithm performances are evaluated on a simple benchmark test consisting of a persistent series where the Hurst exponent is known, with superimposed ten sinusoidal harmonics. Moreover, the behavior of the algorithm parameters is assessed computing the MFDFA on the well-known sunspot data, whose correlation characteristics are reported in literature. In both cases, the SSC-FD method eliminates the apparent crossover induced by the synthetic and natural periodicities. Results are compared with some existing detrending methods within the MFDFA paradigm. Finally, a study of the multifractal characteristics of the electric load time series detrendended by the SSC-FD algorithm is provided, showing a strong persistent behavior and an appreciable amplitude of the multifractal spectrum that allows to conclude that the series at hand has multifractal characteristics.

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.

On the Hilbert-Huang Transform Data Processing System Development

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Flatley, Thomas P.; Huang, Norden E.; Cornwell, Evette; Smith, Darell

2003-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

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.

Self spectrum window method in wigner-ville distribution.

PubMed

Liu, Zhongguo; Liu, Changchun; Liu, Boqiang; Lv, Yangsheng; Lei, Yinsheng; Yu, Mengsun

2005-01-01

Wigner-Ville distribution (WVD) is an important type of time-frequency analysis in biomedical signal processing. The cross-term interference in WVD has a disadvantageous influence on its application. In this research, the Self Spectrum Window (SSW) method was put forward to suppress the cross-term interference, based on the fact that the cross-term and auto-WVD- terms in integral kernel function are orthogonal. With the Self Spectrum Window (SSW) algorithm, a real auto-WVD function was used as a template to cross-correlate with the integral kernel function, and the Short Time Fourier Transform (STFT) spectrum of the signal was used as window function to process the WVD in time-frequency plane. The SSW method was confirmed by computer simulation with good analysis results. Satisfactory time- frequency distribution was obtained.

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.

Target Identification Using Harmonic Wavelet Based ISAR Imaging

NASA Astrophysics Data System (ADS)

Shreyamsha Kumar, B. K.; Prabhakar, B.; Suryanarayana, K.; Thilagavathi, V.; Rajagopal, R.

2006-12-01

A new approach has been proposed to reduce the computations involved in the ISAR imaging, which uses harmonic wavelet-(HW) based time-frequency representation (TFR). Since the HW-based TFR falls into a category of nonparametric time-frequency (T-F) analysis tool, it is computationally efficient compared to parametric T-F analysis tools such as adaptive joint time-frequency transform (AJTFT), adaptive wavelet transform (AWT), and evolutionary AWT (EAWT). Further, the performance of the proposed method of ISAR imaging is compared with the ISAR imaging by other nonparametric T-F analysis tools such as short-time Fourier transform (STFT) and Choi-Williams distribution (CWD). In the ISAR imaging, the use of HW-based TFR provides similar/better results with significant (92%) computational advantage compared to that obtained by CWD. The ISAR images thus obtained are identified using a neural network-based classification scheme with feature set invariant to translation, rotation, and scaling.

Early-type galaxies in the Antlia cluster: catalogue and isophotal analysis

NASA Astrophysics Data System (ADS)

Calderón, Juan P.; Bassino, Lilia P.; Cellone, Sergio A.; Gómez, Matías

2018-06-01

We present a statistical isophotal analysis of 138 early-type galaxies in the Antlia cluster, located at a distance of ˜ 35 Mpc. The observational material consists of CCD images of four 36 × 36 arcmin2 fields obtained with the MOSAIC II camera at the Blanco 4-m telescope at Cerro Tololo Interamerican Observatory. Our present work supersedes previous Antlia studies in the sense that the covered area is four times larger, the limiting magnitude is MB ˜ -9.6 mag, and the surface photometry parameters of each galaxy are derived from Sérsic model fits extrapolated to infinity. In a companion previous study we focused on the scaling relations obtained by means of surface photometry, and now we present the data, on which the previous paper is based, the parameters of the isophotal fits as well as an isophotal analysis. For each galaxy, we derive isophotal shape parameters along the semimajor axis and search for correlations within different radial bins. Through extensive statistical tests, we also analyse the behaviour of these values against photometric and global parameters of the galaxies themselves. While some galaxies do display radial gradients in their ellipticity (ɛ) and/or their Fourier coefficients, differences in mean values between adjacent regions are not statistically significant. Regarding Fourier coefficients, dwarf galaxies usually display gradients between all adjacent regions, while non-dwarfs tend to show this behaviour just between the two outermost regions. Globally, there is no obvious correlation between Fourier coefficients and luminosity for the whole magnitude range (-12 ≳ MV ≳ -22); however, dwarfs display much higher dispersions at all radii.

Fourier Collocation Approach With Mesh Refinement Method for Simulating Transit-Time Ultrasonic Flowmeters Under Multiphase Flow Conditions.

PubMed

Simurda, Matej; Duggen, Lars; Basse, Nils T; Lassen, Benny

2018-02-01

A numerical model for transit-time ultrasonic flowmeters operating under multiphase flow conditions previously presented by us is extended by mesh refinement and grid point redistribution. The method solves modified first-order stress-velocity equations of elastodynamics with additional terms to account for the effect of the background flow. Spatial derivatives are calculated by a Fourier collocation scheme allowing the use of the fast Fourier transform, while the time integration is realized by the explicit third-order Runge-Kutta finite-difference scheme. The method is compared against analytical solutions and experimental measurements to verify the benefit of using mapped grids. Additionally, a study of clamp-on and in-line ultrasonic flowmeters operating under multiphase flow conditions is carried out.

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.

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.

Detection of Fast Moving and Accelerating Targets Compensating Range and Doppler Migration

DTIC Science & Technology

2014-06-01

Radon -Fourier transform has been introduced to realize long- term coherent integration of the moving targets with range migration [8, 9]. Radon ...2010) Long-time coherent integration for radar target detection base on Radon -Fourier transform, in Proceedings of the IEEE Radar Conference, pp...432–436. 9. Xu, J., Yu, J., Peng, Y. & Xia, X. (2011) Radon -Fourier transform for radar target detection, I: Generalized Doppler filter bank, IEEE

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.…

AN OPTIMIZED 64X64 POINT TWO-DIMENSIONAL FAST FOURIER TRANSFORM

NASA Technical Reports Server (NTRS)

Miko, J.

1994-01-01

Scientists at Goddard have developed an efficient and powerful program-- An Optimized 64x64 Point Two-Dimensional Fast Fourier Transform-- which combines the performance of real and complex valued one-dimensional Fast Fourier Transforms (FFT's) to execute a two-dimensional FFT and its power spectrum coefficients. These coefficients can be used in many applications, including spectrum analysis, convolution, digital filtering, image processing, and data compression. The program's efficiency results from its technique of expanding all arithmetic operations within one 64-point FFT; its high processing rate results from its operation on a high-speed digital signal processor. For non-real-time analysis, the program requires as input an ASCII data file of 64x64 (4096) real valued data points. As output, this analysis produces an ASCII data file of 64x64 power spectrum coefficients. To generate these coefficients, the program employs a row-column decomposition technique. First, it performs a radix-4 one-dimensional FFT on each row of input, producing complex valued results. Then, it performs a one-dimensional FFT on each column of these results to produce complex valued two-dimensional FFT results. Finally, the program sums the squares of the real and imaginary values to generate the power spectrum coefficients. The program requires a Banshee accelerator board with 128K bytes of memory from Atlanta Signal Processors (404/892-7265) installed on an IBM PC/AT compatible computer (DOS ver. 3.0 or higher) with at least one 16-bit expansion slot. For real-time operation, an ASPI daughter board is also needed. The real-time configuration reads 16-bit integer input data directly into the accelerator board, operating on 64x64 point frames of data. The program's memory management also allows accumulation of the coefficient results. The real-time processing rate to calculate and accumulate the 64x64 power spectrum output coefficients is less than 17.0 mSec. Documentation is included in the price of the program. Source code is written in C, 8086 Assembly, and Texas Instruments TMS320C30 Assembly Languages. This program is available on a 5.25 inch 360K MS-DOS format diskette. IBM and IBM PC are registered trademarks of International Business Machines. MS-DOS is a registered trademark of Microsoft Corporation.

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

Rocketdyne automated dynamics data analysis and management system

NASA Technical Reports Server (NTRS)

Tarn, Robert B.

1988-01-01

An automated dynamics data analysis and management systems implemented on a DEC VAX minicomputer cluster is described. Multichannel acquisition, Fast Fourier Transformation analysis, and an online database have significantly improved the analysis of wideband transducer responses from Space Shuttle Main Engine testing. Leakage error correction to recover sinusoid amplitudes and correct for frequency slewing is described. The phase errors caused by FM recorder/playback head misalignment are automatically measured and used to correct the data. Data compression methods are described and compared. The system hardware is described. Applications using the data base are introduced, including software for power spectral density, instantaneous time history, amplitude histogram, fatigue analysis, and rotordynamics expert system analysis.

Discrete Fourier transforms of nonuniformly spaced data

NASA Technical Reports Server (NTRS)

Swan, P. R.

1982-01-01

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

Wavelet Filter Banks for Super-Resolution SAR Imaging

NASA Technical Reports Server (NTRS)

Sheybani, Ehsan O.; Deshpande, Manohar; Memarsadeghi, Nargess

2011-01-01

This paper discusses Innovative wavelet-based filter banks designed to enhance the analysis of super resolution Synthetic Aperture Radar (SAR) images using parametric spectral methods and signal classification algorithms, SAR finds applications In many of NASA's earth science fields such as deformation, ecosystem structure, and dynamics of Ice, snow and cold land processes, and surface water and ocean topography. Traditionally, standard methods such as Fast-Fourier Transform (FFT) and Inverse Fast-Fourier Transform (IFFT) have been used to extract Images from SAR radar data, Due to non-parametric features of these methods and their resolution limitations and observation time dependence, use of spectral estimation and signal pre- and post-processing techniques based on wavelets to process SAR radar data has been proposed. Multi-resolution wavelet transforms and advanced spectral estimation techniques have proven to offer efficient solutions to this problem.

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 New View of Earthquake Ground Motion Data: The Hilbert Spectral Analysis

NASA Technical Reports Server (NTRS)

Huang, Norden; Busalacchi, Antonio J. (Technical Monitor)

2000-01-01

A brief description of the newly developed Empirical Mode Decomposition (ENID) and Hilbert Spectral Analysis (HSA) method will be given. The decomposition is adaptive and can be applied to both nonlinear and nonstationary data. Example of the method applied to a sample earthquake record 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.

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

ON THE FOURIER AND WAVELET ANALYSIS OF CORONAL TIME SERIES

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

Auchère, F.; Froment, C.; Bocchialini, K.

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence and Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causingmore » false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence and Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.« less

On the Fourier and Wavelet Analysis of Coronal Time Series

NASA Astrophysics Data System (ADS)

Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.

2016-07-01

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.

Proteolytically-induced changes of secondary structural protein conformation of bovine serum albumin monitored by Fourier transform infrared (FT-IR) and UV-circular dichroism spectroscopy

NASA Astrophysics Data System (ADS)

Güler, Günnur; Vorob'ev, Mikhail M.; Vogel, Vitali; Mäntele, Werner

2016-05-01

Enzymatically-induced degradation of bovine serum albumin (BSA) by serine proteases (trypsin and α-chymotrypsin) in various concentrations was monitored by means of Fourier transform infrared (FT-IR) and ultraviolet circular dichroism (UV-CD) spectroscopy. In this study, the applicability of both spectroscopies to monitor the proteolysis process in real time has been proven, by tracking the spectral changes together with secondary structure analysis of BSA as proteolysis proceeds. On the basis of the FTIR spectra and the changes in the amide I band region, we suggest the progression of proteolysis process via conversion of α-helices (1654 cm- 1) into unordered structures and an increase in the concentration of free carboxylates (absorption of 1593 and 1402 cm- 1). For the first time, the correlation between the degree of hydrolysis and the concentration of carboxylic groups measured by FTIR spectroscopy was revealed as well. The far UV-CD spectra together with their secondary structure analysis suggest that the α-helical content decreases concomitant with an increase in the unordered structure. Both spectroscopic techniques also demonstrate that there are similar but less spectral changes of BSA for the trypsin attack than for α-chymotrypsin although the substrate/enzyme ratio is taken the same.

Comparative of signal processing techniques for micro-Doppler signature extraction with automotive radar systems

NASA Astrophysics Data System (ADS)

Rodriguez-Hervas, Berta; Maile, Michael; Flores, Benjamin C.

2014-05-01

In recent years, the automotive industry has experienced an evolution toward more powerful driver assistance systems that provide enhanced vehicle safety. These systems typically operate in the optical and microwave regions of the electromagnetic spectrum and have demonstrated high efficiency in collision and risk avoidance. Microwave radar systems are particularly relevant due to their operational robustness under adverse weather or illumination conditions. Our objective is to study different signal processing techniques suitable for extraction of accurate micro-Doppler signatures of slow moving objects in dense urban environments. Selection of the appropriate signal processing technique is crucial for the extraction of accurate micro-Doppler signatures that will lead to better results in a radar classifier system. For this purpose, we perform simulations of typical radar detection responses in common driving situations and conduct the analysis with several signal processing algorithms, including short time Fourier Transform, continuous wavelet or Kernel based analysis methods. We take into account factors such as the relative movement between the host vehicle and the target, and the non-stationary nature of the target's movement. A comparison of results reveals that short time Fourier Transform would be the best approach for detection and tracking purposes, while the continuous wavelet would be the best suited for classification purposes.

Wavelet Statistical Analysis of Low-Latitude Geomagnetic Measurements

NASA Astrophysics Data System (ADS)

Papa, A. R.; Akel, A. F.

2009-05-01

Following previous works by our group (Papa et al., JASTP, 2006), where we analyzed a series of records acquired at the Vassouras National Geomagnetic Observatory in Brazil for the month of October 2000, we introduced a wavelet analysis for the same type of data and for other periods. It is well known that wavelets allow a more detailed study in several senses: the time window for analysis can be drastically reduced if compared to other traditional methods (Fourier, for example) and at the same time allow an almost continuous accompaniment of both amplitude and frequency of signals as time goes by. This advantage brings some possibilities for potentially useful forecasting methods of the type also advanced by our group in previous works (see for example, Papa and Sosman, JASTP, 2008). However, the simultaneous statistical analysis of both time series (in our case amplitude and frequency) is a challenging matter and is in this sense that we have found what we consider our main goal. Some possible trends for future works are advanced.

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...

Gastric Emptying Assessment in Frequency and Time Domain Using Bio-impedance: Preliminary Results

NASA Astrophysics Data System (ADS)

Huerta-Franco, R.; Vargas-Luna, M.; Hernández, E.; Córdova, T.; Sosa, M.; Gutiérrez, G.; Reyes, P.; Mendiola, C.

2006-09-01

The impedance assessment to measure gastric emptying and in general gastric activity has been reported since 1985. The physiological interpretation of these measurements, is still under research. This technique usually uses a single frequency, and the conductivity parameter. The frequency domain and the Fourier analysis of the time domain behavior of the gastric impedance in different gastric conditions (fasting state, and after food administration) has not been explored in detail. This work presents some insights of the potentiality of these alternative methodologies to measure gastric activity.

A new phase encoding approach for a compact head-up display

NASA Astrophysics Data System (ADS)

Suszek, Jaroslaw; Makowski, Michal; Sypek, Maciej; Siemion, Andrzej; Kolodziejczyk, Andrzej; Bartosz, Andrzej

2008-12-01

The possibility of encoding multiple asymmetric symbols into a single thin binary Fourier hologram would have a practical application in the design of simple translucent holographic head-up displays. A Fourier hologram displays the encoded images at the infinity so this enables an observation without a time-consuming eye accommodation. Presenting a set of the most crucial signs for a driver in this way is desired, especially by older people with various eyesight disabilities. In this paper a method of holographic design is presented that assumes a combination of a spatial segmentation and carrier frequencies. It allows to achieve multiple reconstructed images selectable by the angle of the incident laser beam. In order to encode several binary symbols into a single Fourier hologram, the chessboard shaped segmentation function is used. An optimized sequence of phase encoding steps and a final direct phase binarization enables recording of asymmetric symbols into a binary hologram. The theoretical analysis is presented, verified numerically and confirmed in the optical experiment. We suggest and describe a practical and highly useful application of such holograms in an inexpensive HUD device for the use of the automotive industry. We present two alternative propositions of car viewing setups.

Fourier transform infrared evanescent wave (FTIR-FEW) spectroscopy of tissue

NASA Astrophysics Data System (ADS)

Bruch, Reinhard F.; Sukuta, Sydney; Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Butvina, Leonid N.

1997-05-01

A new Fourier transform infrared fiberoptic evanescent wave (FTIR-FEW) spectroscopy method has been developed for tissue diagnostics in the middle infrared (MIR) wavelength range (3 to 20 micrometers). Specific novel fiberoptical chemical and biological sensors have been studied and used for spectroscopic diagnostic purposes. These nontoxic and nonhygroscopic fiber sensors are characterized by (1) low optical losses (0.05 to 0.2 dB/m at about 10 micrometer) and (2) high flexibility. Our new fiber optical devices can be utilized with standard commercially available Fourier transform spectrometers including attenuated total reflection (ATR) techniques. They are in particular ideally suited for noninvasive, fast, direct, sensitive investigations of in vivo and ex vivo medical diagnostics applications. Here we present data on IR spectra of skin tissue in vivo for various cases of melanoma and nevus in the range of 1480 - 1800 cm-1. The interpretation of the spectra of healthy and different stages of tumor and cancer skin tissue clearly indicates that this technique can be used for precancer and cancer diagnostics. This technique can be designed for real-time and on-line computer modeling and analysis of tissue changes.

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC

NASA Technical Reports Server (NTRS)

White, Michael J.

2006-01-01

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

High-resolution retinal imaging using adaptive optics and Fourier-domain optical coherence tomography

DOEpatents

Olivier, Scot S.; Werner, John S.; Zawadzki, Robert J.; Laut, Sophie P.; Jones, Steven M.

2010-09-07

This invention permits retinal images to be acquired at high speed and with unprecedented resolution in three dimensions (4.times.4.times.6 .mu.m). The instrument achieves high lateral resolution by using adaptive optics to correct optical aberrations of the human eye in real time. High axial resolution and high speed are made possible by the use of Fourier-domain optical coherence tomography. Using this system, we have demonstrated the ability to image microscopic blood vessels and the cone photoreceptor mosaic.

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

Supply of avocado starch (Persea americana mill) as bioplastic material

NASA Astrophysics Data System (ADS)

Ginting, M. H. S.; Hasibuan, R.; Lubis, M.; Alanjani, F.; Winoto, F. A.; Siregar, R. C.

2018-02-01

The purpose of this study was to determine the effect of time precipitation of avocado slurry seed to yield of starch. Starch analysis included starch content, moisture content, amylose content, amylopectin content, ash content, protein content, fat content, Fourier transform infra red analysis and rapid visco analyzer. Supply of starch from avocado seeds was used by extraction method. Every one hundred grams of avocado slurry was precipitated by gravity with variations for 4 hours, 8 hours, 12 hours, 16 hours, 20 hours and 24 hours. The Starch yield was washed, and dried using oven at 70°C for 30 minutes. Starch yield was the highest as 24.20 gram at 24 hours. The result of starch characterization was 73.62%, water content 16.6%, amylose 0.07%, amylopectin 73.55%, ash content 0.23%, protein content 2.16%, fat content 1.09%. Rapid visco analyzer obtained at 91.33°C of gelatinization temperature. Scanning electron microscopy analyzes obtained 20 μm oval-shaped starch granules. Fourier Transform Infra Red analysis of starch obtained the peak spectrum of O-H group of alcohols, C-H alkanes and C-O ether.

Signal Coherence Recovery Using Acousto-Optic Fourier Transform Architectures

DTIC Science & Technology

1990-06-14

processing of data in ground- and space-based applications. We have implemented a prototype one-dimensional time-integrating acousto - optic (AO) Fourier...theory of optimum coherence recovery (CR) applicable in computation-limited environments. We have demonstrated direct acousto - optic implementation of CR

Automatic Between-Pulse Analysis of DIII-D Experimental Data Performed Remotely on a Supercomputer at Argonne Leadership Computing Facility

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

Kostuk, M.; Uram, T. D.; Evans, T.

For the first time, an automatically triggered, between-pulse fusion science analysis code was run on-demand at a remotely located supercomputer at Argonne Leadership Computing Facility (ALCF, Lemont, IL) in support of in-process experiments being performed at DIII-D (San Diego, CA). This represents a new paradigm for combining geographically distant experimental and high performance computing (HPC) facilities to provide enhanced data analysis that is quickly available to researchers. Enhanced analysis improves the understanding of the current pulse, translating into a more efficient use of experimental resources, and to the quality of the resultant science. The analysis code used here, called SURFMN,more » calculates the magnetic structure of the plasma using Fourier transform. Increasing the number of Fourier components provides a more accurate determination of the stochastic boundary layer near the plasma edge by better resolving magnetic islands, but requires 26 minutes to complete using local DIII-D resources, putting it well outside the useful time range for between pulse analysis. These islands relate to confinement and edge localized mode (ELM) suppression, and may be controlled by adjusting coil currents for the next pulse. Argonne has ensured on-demand execution of SURFMN by providing a reserved queue, a specialized service that launches the code after receiving an automatic trigger, and with network access from the worker nodes for data transfer. Runs are executed on 252 cores of ALCF’s Cooley cluster and the data is available locally at DIII-D within three minutes of triggering. The original SURFMN design limits additional improvements with more cores, however our work shows a path forward where codes that benefit from thousands of processors can run between pulses.« less

Automatic Between-Pulse Analysis of DIII-D Experimental Data Performed Remotely on a Supercomputer at Argonne Leadership Computing Facility

DOE PAGES

Kostuk, M.; Uram, T. D.; Evans, T.; ...

2018-02-01

For the first time, an automatically triggered, between-pulse fusion science analysis code was run on-demand at a remotely located supercomputer at Argonne Leadership Computing Facility (ALCF, Lemont, IL) in support of in-process experiments being performed at DIII-D (San Diego, CA). This represents a new paradigm for combining geographically distant experimental and high performance computing (HPC) facilities to provide enhanced data analysis that is quickly available to researchers. Enhanced analysis improves the understanding of the current pulse, translating into a more efficient use of experimental resources, and to the quality of the resultant science. The analysis code used here, called SURFMN,more » calculates the magnetic structure of the plasma using Fourier transform. Increasing the number of Fourier components provides a more accurate determination of the stochastic boundary layer near the plasma edge by better resolving magnetic islands, but requires 26 minutes to complete using local DIII-D resources, putting it well outside the useful time range for between pulse analysis. These islands relate to confinement and edge localized mode (ELM) suppression, and may be controlled by adjusting coil currents for the next pulse. Argonne has ensured on-demand execution of SURFMN by providing a reserved queue, a specialized service that launches the code after receiving an automatic trigger, and with network access from the worker nodes for data transfer. Runs are executed on 252 cores of ALCF’s Cooley cluster and the data is available locally at DIII-D within three minutes of triggering. The original SURFMN design limits additional improvements with more cores, however our work shows a path forward where codes that benefit from thousands of processors can run between pulses.« less

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.

A unified Fourier theory for time-of-flight PET data

PubMed Central

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-01

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D X-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions—the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D X-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions. PMID:26689836

A unified Fourier theory for time-of-flight PET data.

PubMed

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-21

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions--the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D x-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions.

Quasi-periodic oscillations in short recurring bursts of magnetars SGR 1806–20 and SGR 1900+14 observed with RXTE

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

Huppenkothen, D.; Heil, L. M.; Watts, A. L.

2014-11-10

Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars are of particular interest due to their potential to open up a window into the neutron star interior via neutron star asteroseismology. However, only three giant flares have been observed. We therefore make use of the much larger data set of shorter, less energetic recurrent bursts. Here, we report on a search for QPOs in a large data set of bursts from the two most burst-active magnetars, SGR 1806-20 and SGR 1900+14, observed with Rossi X-ray Timing Explorer. We find a single detection in an averaged periodogram comprising 30 burstsmore » from SGR 1806–20, with a frequency of 57 Hz and a width of 5 Hz, remarkably similar to a giant flare QPO observed from SGR 1900+14. This QPO fits naturally within the framework of global magneto-elastic torsional oscillations employed to explain giant flare QPOs. Additionally, we uncover a limit on the applicability of Fourier analysis for light curves with low background count rates and strong variability on short timescales. In this regime, standard Fourier methodology and more sophisticated Fourier analyses fail in equal parts by yielding an unacceptably large number of false-positive detections. This problem is not straightforward to solve in the Fourier domain. Instead, we show how simulations of light curves can offer a viable solution for QPO searches in these light curves.« less

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.

Industrial realization of a direct Fourier transform in automated experimental data processing systems

NASA Technical Reports Server (NTRS)

Lyubashevskiy, G. S.

1973-01-01

Fourier processing of automatic signals transforms direct current voltage into a numerical form through bandpass filtration in time-pulse multiplying devices. It is shown that the ratio of the interference energy to the useful signal energy is inversely proportional to the square of the product of the depth of the width modulation and the ratio of the time constant averaging to the cross-multiplied signals.

Fourier Transform Infrared Spectroscopy (FT-IR) and Simple Algorithm Analysis for Rapid and Non-Destructive Assessment of Developmental Cotton Fibers.

PubMed

Liu, Yongliang; Kim, Hee-Jin

2017-06-22

With cotton fiber growth or maturation, cellulose content in cotton fibers markedly increases. Traditional chemical methods have been developed to determine cellulose content, but it is time-consuming and labor-intensive, mostly owing to the slow hydrolysis process of fiber cellulose components. As one approach, the attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy technique has also been utilized to monitor cotton cellulose formation, by implementing various spectral interpretation strategies of both multivariate principal component analysis (PCA) and 1-, 2- or 3-band/-variable intensity or intensity ratios. The main objective of this study was to compare the correlations between cellulose content determined by chemical analysis and ATR FT-IR spectral indices acquired by the reported procedures, among developmental Texas Marker-1 (TM-1) and immature fiber ( im ) mutant cotton fibers. It was observed that the R value, CI IR , and the integrated intensity of the 895 cm -1 band exhibited strong and linear relationships with cellulose content. The results have demonstrated the suitability and utility of ATR FT-IR spectroscopy, combined with a simple algorithm analysis, in assessing cotton fiber cellulose content, maturity, and crystallinity in a manner which is rapid, routine, and non-destructive.

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.

Analysis of photonic Doppler velocimetry data based on the continuous wavelet transform

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

Liu Shouxian; Wang Detian; Li Tao

2011-02-15

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated bymore » a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.« less

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

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

NASA Astrophysics Data System (ADS)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

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 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.

An introduction to wavelet analysis in oceanography and meteorology - With application to the dispersion of Yanai waves

NASA Technical Reports Server (NTRS)

Meyers, Steven D.; Kelly, B. G.; O'Brien, J. J.

1993-01-01

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an instantaneous estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumbers, possibly due to interaction with the basin boundaries.

Synthetic wind speed scenarios generation for probabilistic analysis of hybrid energy systems

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

Chen, Jun; Rabiti, Cristian

Hybrid energy systems consisting of multiple energy inputs and multiple energy outputs have been proposed to be an effective element to enable ever increasing penetration of clean energy. In order to better understand the dynamic and probabilistic behavior of hybrid energy systems, this paper proposes a model combining Fourier series and autoregressive moving average (ARMA) to characterize historical weather measurements and to generate synthetic weather (e.g., wind speed) data. In particular, Fourier series is used to characterize the seasonal trend in historical data, while ARMA is applied to capture the autocorrelation in residue time series (e.g., measurements minus seasonal trends).more » The generated synthetic wind speed data is then utilized to perform probabilistic analysis of a particular hybrid energy system con guration, which consists of nuclear power plant, wind farm, battery storage, natural gas boiler, and chemical plant. As a result, requirements on component ramping rate, economic and environmental impacts of hybrid energy systems, and the effects of deploying different sizes of batteries in smoothing renewable variability, are all investigated.« less

Analysis of structural transformation in wool fiber resulting from oxygen plasma treatment using vibrational spectroscopy

NASA Astrophysics Data System (ADS)

Barani, Hossein; Haji, Aminoddin

2015-01-01

The aim of this study was to investigate the influence of oxygen plasma procedure at different time treatments on wool fiber using the micro-Raman spectroscopy as a non-destructive vibrational spectroscopic technique and Fourier transform infrared spectroscopy. The amide I and III regions, Csbnd C skeletal vibration region, and Ssbnd S and Csbnd S bonds vibration regions were analyzed with the Raman microscope. The Fourier transform infrared spectroscope analysis was employed to find out the effect of oxygen plasma treatment on the cysteic acid residues content of the wool fiber sample. The results indicated that the α-helix structure was the highest component content of wool fiber. Moreover, the protein secondary structure of wool fibers was transformed from α-helical arrangement to the β-pleated sheet configuration during the oxygen plasma treatment. Also, the disulphide bonds content in the treated wool fiber reduced because they were fractured and oxidized during oxygen plasma treatment. The oxygen plasma treated samples presented higher cysteic acid compared to the untreated wool samples due to produce more cleavage of disulfide linkages.

Synthetic wind speed scenarios generation for probabilistic analysis of hybrid energy systems

DOE PAGES

Chen, Jun; Rabiti, Cristian

2016-11-25

Hybrid energy systems consisting of multiple energy inputs and multiple energy outputs have been proposed to be an effective element to enable ever increasing penetration of clean energy. In order to better understand the dynamic and probabilistic behavior of hybrid energy systems, this paper proposes a model combining Fourier series and autoregressive moving average (ARMA) to characterize historical weather measurements and to generate synthetic weather (e.g., wind speed) data. In particular, Fourier series is used to characterize the seasonal trend in historical data, while ARMA is applied to capture the autocorrelation in residue time series (e.g., measurements minus seasonal trends).more » The generated synthetic wind speed data is then utilized to perform probabilistic analysis of a particular hybrid energy system con guration, which consists of nuclear power plant, wind farm, battery storage, natural gas boiler, and chemical plant. As a result, requirements on component ramping rate, economic and environmental impacts of hybrid energy systems, and the effects of deploying different sizes of batteries in smoothing renewable variability, are all investigated.« less

Fourier-domain angle-resolved low coherence interferometry for clinical detection of dysplasia

NASA Astrophysics Data System (ADS)

Terry, Neil G.; Zhu, Yizheng; Wax, Adam

2010-02-01

Improved methods for detecting dysplasia, or pre-cancerous growth are a current clinical need, particularly in the esophagus. The currently accepted method of random biopsy and histological analysis provides only a limited examination of tissue in question while being coupled with a long time delay for diagnosis. Light scattering spectroscopy, in contrast, allows for inspection of the cellular structure and organization of tissue in vivo. Fourier-domain angle-resolved low-coherence interferometry (a/LCI) is a novel light scattering spectroscopy technique that provides quantitative depth-resolved morphological measurements of the size and optical density of the examined cell nuclei, which are characteristic biomarkers of dysplasia. Previously, clinical viability of the a/LCI system was demonstrated through analysis of ex vivo human esophageal tissue in Barrett's esophagus patients using a portable a/LCI, as was the development of a clinical a/LCI system. Data indicating the feasibility of the technique in other organ sites (colon, oral cavity) will be presented. We present an adaptation of the a/LCI system that will be used to investigate the presence of dysplasia in vivo in Barrett's esophagus patients.

Nonlinear effects in the time measurement device based on surface acoustic wave filter excitation.

PubMed

Prochazka, Ivan; Panek, Petr

2009-07-01

A transversal surface acoustic wave filter has been used as a time interpolator in a time interval measurement device. We are presenting the experiments and results of an analysis of the nonlinear effects in such a time interpolator. The analysis shows that the nonlinear distortion in the time interpolator circuits causes a deterministic measurement error which can be understood as the time interpolation nonlinearity. The dependence of this error on time of the measured events can be expressed as a sparse Fourier series thus it usually oscillates very quickly in comparison to the clock period. The theoretical model is in good agreement with experiments carried out on an experimental two-channel timing system. Using highly linear amplifiers in the time interpolator and adjusting the filter excitation level to the optimum, we have achieved the interpolation nonlinearity below 0.2 ps. The overall single-shot precision of the experimental timing device is 0.9 ps rms in each channel.

Analysis of HD 73045 light curve data

NASA Astrophysics Data System (ADS)

Das, Mrinal Kanti; Bhatraju, Naveen Kumar; Joshi, Santosh

2018-04-01

In this work we analyzed the Kepler light curve data of HD 73045. The raw data has been smoothened using standard filters. The power spectrum has been obtained by using a fast Fourier transform routine. It shows the presence of more than one period. In order to take care of any non-stationary behavior, we carried out a wavelet analysis to obtain the wavelet power spectrum. In addition, to identify the scale invariant structure, the data has been analyzed using a multifractal detrended fluctuation analysis. Further to characterize the diversity of embedded patterns in the HD 73045 flux time series, we computed various entropy-based complexity measures e.g. sample entropy, spectral entropy and permutation entropy. The presence of periodic structure in the time series was further analyzed using the visibility network and horizontal visibility network model of the time series. The degree distributions in the two network models confirm such structures.

Weak Fault Feature Extraction of Rolling Bearings Based on an Improved Kurtogram.

PubMed

Chen, Xianglong; Feng, Fuzhou; Zhang, Bingzhi

2016-09-13

Kurtograms have been verified to be an efficient tool in bearing fault detection and diagnosis because of their superiority in extracting transient features. However, the short-time Fourier Transform is insufficient in time-frequency analysis and kurtosis is deficient in detecting cyclic transients. Those factors weaken the performance of the original kurtogram in extracting weak fault features. Correlated Kurtosis (CK) is then designed, as a more effective solution, in detecting cyclic transients. Redundant Second Generation Wavelet Packet Transform (RSGWPT) is deemed to be effective in capturing more detailed local time-frequency description of the signal, and restricting the frequency aliasing components of the analysis results. The authors in this manuscript, combining the CK with the RSGWPT, propose an improved kurtogram to extract weak fault features from bearing vibration signals. The analysis of simulation signals and real application cases demonstrate that the proposed method is relatively more accurate and effective in extracting weak fault features.

Algorithms for computing the time-corrected instantaneous frequency (reassigned) spectrogram, with applications.

PubMed

Fulop, Sean A; Fitz, Kelly

2006-01-01

A modification of the spectrogram (log magnitude of the short-time Fourier transform) to more accurately show the instantaneous frequencies of signal components was first proposed in 1976 [Kodera et al., Phys. Earth Planet. Inter. 12, 142-150 (1976)], and has been considered or reinvented a few times since but never widely adopted. This paper presents a unified theoretical picture of this time-frequency analysis method, the time-corrected instantaneous frequency spectrogram, together with detailed implementable algorithms comparing three published techniques for its computation. The new representation is evaluated against the conventional spectrogram for its superior ability to track signal components. The lack of a uniform framework for either mathematics or implementation details which has characterized the disparate literature on the schemes has been remedied here. Fruitful application of the method is shown in the realms of speech phonation analysis, whale song pitch tracking, and additive sound modeling.

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...

Analysis of Gravitational Signals from Core-Collapse Supernovae (CCSNe) using MatLab

NASA Astrophysics Data System (ADS)

Frere, Noah; Mezzacappa, Anthony; Yakunin, Konstantin

2017-01-01

When a massive star runs out of fuel, it collapses under its own weight and rebounds in a powerful supernova explosion, sending, among other things, ripples through space-time, known as gravitational waves (GWs). GWs can be detected by earth-based observatories, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO). Observers must compare the data from GW detectors with theoretical waveforms in order to confirm that the detection of a GW signal from a particular source has occurred. GW predictions for core collapse supernovae (CCSNe) rely on computer simulations. The UTK/ORNL astrophysics group has performed such simulations. Here, I analyze the resulting waveforms, using Matlab, to generate their Fourier transforms, short-time Fourier transforms, energy spectra, evolution of frequencies, and frequency maxima. One product will be a Matlab interface for analyzing and comparing GW predictions based on data from future simulations. This interface will make it easier to analyze waveforms and to share the results with the GW astrophysics community. Funding provided by Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA.

Passive Fourier-transform infrared spectroscopy of chemical plumes: an algorithm for quantitative interpretation and real-time background removal

NASA Astrophysics Data System (ADS)

Polak, Mark L.; Hall, Jeffrey L.; Herr, Kenneth C.

1995-08-01

We present a ratioing algorithm for quantitative analysis of the passive Fourier-transform infrared spectrum of a chemical plume. We show that the transmission of a near-field plume is given by tau plume = (Lobsd - Lbb-plume)/(Lbkgd - Lbb-plume), where tau _{plume is the frequency-dependent transmission of the plume, L obsd is the spectral radiance of the scene that contains the plume, Lbkgd is the spectral radiance of the same scene without the plume, and Lbb-plume is the spectral radiance of a blackbody at the plume temperature. The algorithm simultaneously achieves background removal, elimination of the spectrometer internal signature, and quantification of the plume spectral transmission. It has applications to both real-time processing for plume visualization and quantitative measurements of plume column densities. The plume temperature (Lbb-plume ), which is not always precisely known, can have a profound effect on the quantitative interpretation of the algorithm and is discussed in detail. Finally, we provide an illustrative example of the use of the algorithm on a trichloroethylene and acetone plume.}

Hyperfine structure measurements of neutral iodine atom (127I) using Fourier Transform Spectrometry

NASA Astrophysics Data System (ADS)

Ashok, Chilukoti; Vishwakarma, S. R.; Bhatt, Himal; Ankush, B. K.; Deo, M. N.

2018-01-01

We report the hyperfine Structure (hfs) splitting observations of neutral iodine atom (II) in the 6000 - 10,000 cm-1 near infrared spectral region. The measurements were carried out using a high-resolution Fourier Transform Spectrometer (FTS), where an electrodeless discharge lamp (EDL), excited using microwaves, was employed as the light source and InGaAs as the light detector. A specially designed setup was used to lower the plasma temperature of the medium so as to reduce the Doppler width and consequently to increase the spectral resolution of hfs components. A total of 183 lines with hfs splitting have been observed, out of which hfs in 53 spectral lines are reported for the first time. On the basis of hfs analysis, we derived the magnetic dipole and electric quadrupole coupling constants, A and B respectively for 30 even and 30 odd energy levels and are compared with the values available in the literature. New hfs values for 5 even and 4 odd levels are also reported here for the first time.

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.

Differences between time domain and Fourier domain optical coherence tomography in imaging tissues.

PubMed

Gao, W; Wu, X

2017-11-01

It has been numerously demonstrated that both time domain and Fourier domain optical coherence tomography (OCT) can generate high-resolution depth-resolved images of living tissues and cells. In this work, we compare the common points and differences between two methods when the continuous and random properties of live tissue are taken into account. It is found that when relationships that exist between the scattered light and tissue structures are taken into account, spectral interference measurements in Fourier domain OCT (FDOCT) is more advantageous than interference fringe envelope measurements in time domain OCT (TDOCT) in the cases where continuous property of tissue is taken into account. It is also demonstrated that when random property of tissue is taken into account FDOCT measures the Fourier transform of the spatial correlation function of the refractive index and speckle phenomena will limit the effective limiting imaging resolution in both TDOCT and FDOCT. Finally, the effective limiting resolution of both TDOCT and FDOCT are given which can be used to estimate the effective limiting resolution in various practical applications. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

PubMed

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

A simple filter circuit for denoising biomechanical impact signals.

PubMed

Subramaniam, Suba R; Georgakis, Apostolos

2009-01-01

We present a simple scheme for denoising non-stationary biomechanical signals with the aim of accurately estimating their second derivative (acceleration). The method is based on filtering in fractional Fourier domains using well-known low-pass filters in a way that amounts to a time-varying cut-off threshold. The resulting algorithm is linear and its design is facilitated by the relationship between the fractional Fourier transform and joint time-frequency representations. The implemented filter circuit employs only three low-order filters while its efficiency is further supported by the low computational complexity of the fractional Fourier transform. The results demonstrate that the proposed method can denoise the signals effectively and is more robust against noise as compared to conventional low-pass filters.

Applications of charge-coupled device transversal filters to communication

NASA Technical Reports Server (NTRS)

Buss, D. D.; Bailey, W. H.; Brodersen, R. W.; Hewes, C. R.; Tasch, A. F., Jr.

1975-01-01

The paper discusses the computational power of state-of-the-art charged-coupled device (CCD) transversal filters in communications applications. Some of the performance limitations of CCD transversal filters are discussed, with attention given to time delay and bandwidth, imperfect charge transfer efficiency, weighting coefficient error, noise, and linearity. The application of CCD transversal filters to matched filtering, spectral filtering, and Fourier analysis is examined. Techniques for making programmable transversal filters are briefly outlined.

Time-Frequency Representations for Speech Signals.

DTIC Science & Technology

1987-06-01

and subsequent processing can take these weights into account . This is, in principle , safer, but pratically it is much harder to think about processing...and frequency along the other. But how should this idea be made precise (the well-known uncertainty principle of fourier analysis is one of the thorny...produce similar results. q2.3. Non-stationarity 19 it is the unique shape that meets the uncertainty principle with equality. 2.2. The quasi-stationary

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.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Proteoglycan concentrations in healthy and diseased articular cartilage by Fourier transform infrared imaging and principal component regression

NASA Astrophysics Data System (ADS)

Yin, Jianhua; Xia, Yang

2014-12-01

Fourier transform infrared imaging (FTIRI) combining with principal component regression (PCR) analysis were used to determine the reduction of proteoglycan (PG) in articular cartilage after the transection of the anterior cruciate ligament (ACL). A number of canine knee cartilage sections were harvested from the meniscus-covered and meniscus-uncovered medial tibial locations from the control joints, the ACL joints at three time points after the surgery, and their contralateral joints. The PG loss in the ACL cartilage was related positively to the durations after the surgery. The PG loss in the contralateral knees was less than that of the ACL knees. The PG loss in the meniscus-covered cartilage was less than that of the meniscus-uncovered tissue in both ACL and contralateral knees. The quantitative mapping of PG loss could monitor the disease progression and repair processes in arthritis.

Fourier-transform infrared spectroscopy for rapid screening and live-cell monitoring: application to nanotoxicology.

PubMed

Sundaram, S K; Sacksteder, Colette A; Weber, Thomas J; Riley, Brian J; Addleman, R Shane; Harrer, Bruce J; Peterman, John W

2013-01-01

A significant challenge to realize the full potential of nanotechnology for therapeutic and diagnostic applications is to understand and evaluate how live cells interact with an external stimulus, such as a nanosized particle, and the toxicity and broad risk associated with these stimuli. It is difficult to capture the complexity and dynamics of these interactions by following omics-based approaches exclusively, which can be expensive and time-consuming. Attenuated total reflectance-Fourier transform infrared spectroscopy is well suited to provide noninvasive live-cell monitoring of cellular responses to potentially toxic nanosized particles or other stimuli. This alternative approach provides the ability to carry out rapid toxicity screenings and nondisruptive monitoring of live-cell cultures. We review the technical basis of the approach, the instrument configuration and interface with the biological media, the various effects that impact the data, subsequent data analysis and toxicity, and present some preliminary results on live-cell monitoring.

SIG: a general-purpose signal processing program

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

Lager, D.; Azevedo, S.

1986-02-01

SIG is a general-purpose signal processing, analysis, and display program. Its main purpose is to perform manipulations on time- and frequency-domain signals. It also accommodates other representations for data such as transfer function polynomials. Signal processing operations include digital filtering, auto/cross spectral density, transfer function/impulse response, convolution, Fourier transform, and inverse Fourier transform. Graphical operations provide display of signals and spectra, including plotting, cursor zoom, families of curves, and multiple viewport plots. SIG provides two user interfaces with a menu mode for occasional users and a command mode for more experienced users. Capability exits for multiple commands per line, commandmore » files with arguments, commenting lines, defining commands, automatic execution for each item in a repeat sequence, etc. SIG is presently available for VAX(VMS), VAX (BERKELEY 4.2 UNIX), SUN (BERKELEY 4.2 UNIX), DEC-20 (TOPS-20), LSI-11/23 (TSX), and DEC PRO 350 (TSX). 4 refs., 2 figs.« less

The Effect of Three-Dimensional Freestream Disturbances on the Supersonic Flow Past a Wedge

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Lasseigne, D. Glenn; Hussaini, M. Y.

1997-01-01

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al, through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e. time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock.

How long does it take to boil an egg? A simple approach to the energy transfer equation

NASA Astrophysics Data System (ADS)

Roura, P.; Fort, J.; Saurina, J.

2000-01-01

The heating of simple geometric objects immersed in an isothermal bath is analysed qualitatively through Fourier's law. The approximate temperature evolution is compared with the exact solution obtained by solving the transport differential equation, the discrepancies being smaller than 20%. Our method succeeds in giving the solution as a function of the Fourier modulus so that the scale laws hold. It is shown that the time needed to homogenize temperature variations that extend over mean distances xm is approximately xm2/icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/>, where icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/> is the thermal diffusivity. This general relationship also applies to atomic diffusion. Within the approach presented there is no need to write down any differential equation. As an example, the analysis is applied to the process of boiling an egg.

Electromagnetic pulse propagation in dispersive planar dielectrics.

PubMed

Moten, K; Durney, C H; Stockham, T G

1989-01-01

The responses of a plane-wave pulse train irradiating a lossy dispersive dielectric half-space are investigated. The incident pulse train is expressed as a Fourier series with summing done by the inverse fast Fourier transform. The Fourier series technique is adopted to avoid the many difficulties often encountered in finding the inverse Fourier transform when transform analyses are used. Calculations are made for propagation in pure water, and typical waveforms inside the dielectric half-space are presented. Higher harmonics are strongly attenuated, resulting in a single continuous sinusoidal waveform at the frequency of the fundamental depth in the material. The time-averaged specific absorption rate (SAR) for pulse-train propagation is shown to be the sum of the time-averaged SARs of the individual harmonic components of the pulse train. For the same average power, calculated SARs reveal that pulse trains generally penetrate deeper than carrier-frequency continuous waves but not deeper than continuous waves at frequencies approaching the fundamental of the pulse train. The effects of rise time on the propagating pulse train in the dielectrics are shown and explained. Since most practical pulsed systems are very limited in bandwidth, no pronounced differences between their response and continuous wave (CW) response would be expected. Typical results for pulse-train propagation in arrays of dispersive planar dielectric slabs are presented. Expressing the pulse train as a Fourier series provides a practical way of interpreting the dispersion characteristics from the spectral point of view.

Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion.

PubMed

Dai, Yitang; Li, Jilong; Zhang, Ziping; Yin, Feifei; Li, Wangzhe; Xu, Kun

2017-07-10

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 10 4 -km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

Real-Time Fourier Transformed Holographic Associative Memory With Photorefractive Material

NASA Astrophysics Data System (ADS)

Changsuk, Oh; Hankyu, Park

1989-02-01

We describe a volume holographic associative memory using photorefractive material and conventional planar mirror. Multiple hologram is generated with two angular multiplexed writing beams and Fourier transformed object beam in BaTiO3 crystal at 0.6328 μm. Complete image can be recalled successfully by partial input of original stored image. It is proved that our system is useful for optical implementation of real-time associative memory and location addressable memory.

Analysis of biomedical time signals for characterization of cutaneous diabetic micro-angiopathy

NASA Astrophysics Data System (ADS)

Kraitl, Jens; Ewald, Hartmut

2007-02-01

Photo-plethysmography (PPG) is frequently used in research on microcirculation of blood. It is a non-invasive procedure and takes minimal time to be carried out. Usually PPG time series are analyzed by conventional linear methods, mainly Fourier analysis. These methods may not be optimal for the investigation of nonlinear effects of the hearth circulation system like vasomotion, autoregulation, thermoregulation, breathing, heartbeat and vessels. The wavelet analysis of the PPG time series is a specific, sensitive nonlinear method for the in vivo identification of hearth circulation patterns and human health status. This nonlinear analysis of PPG signals provides additional information which cannot be detected using conventional approaches. The wavelet analysis has been used to study healthy subjects and to characterize the health status of patients with a functional cutaneous microangiopathy which was associated with diabetic neuropathy. The non-invasive in vivo method is based on the radiation of monochromatic light through an area of skin on the finger. A Photometrical Measurement Device (PMD) has been developed. The PMD is suitable for non-invasive continuous online monitoring of one or more biologic constituent values and blood circulation patterns.

Automated spectral and timing analysis of AGNs

NASA Astrophysics Data System (ADS)

Munz, F.; Karas, V.; Guainazzi, M.

2006-12-01

% We have developed an autonomous script that helps the user to automate the XMM-Newton data analysis for the purposes of extensive statistical investigations. We test this approach by examining X-ray spectra of bright AGNs pre-selected from the public database. The event lists extracted in this process were studied further by constructing their energy-resolved Fourier power-spectrum density. This analysis combines energy distributions, light-curves, and their power-spectra and it proves useful to assess the variability patterns present is the data. As another example, an automated search was based on the XSPEC package to reveal the emission features in 2-8 keV range.

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

PubMed

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Fourier collocation time domain method for numerically solving Maxwell's equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1991-01-01

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

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.

Calculation of power spectrums from digital time series with missing data points

NASA Technical Reports Server (NTRS)

Murray, C. W., Jr.

1980-01-01

Two algorithms are developed for calculating power spectrums from the autocorrelation function when there are missing data points in the time series. Both methods use an average sampling interval to compute lagged products. One method, the correlation function power spectrum, takes the discrete Fourier transform of the lagged products directly to obtain the spectrum, while the other, the modified Blackman-Tukey power spectrum, takes the Fourier transform of the mean lagged products. Both techniques require fewer calculations than other procedures since only 50% to 80% of the maximum lags need be calculated. The algorithms are compared with the Fourier transform power spectrum and two least squares procedures (all for an arbitrary data spacing). Examples are given showing recovery of frequency components from simulated periodic data where portions of the time series are missing and random noise has been added to both the time points and to values of the function. In addition the methods are compared using real data. All procedures performed equally well in detecting periodicities in the data.

Autofocus algorithm using one-dimensional Fourier transform and Pearson correlation

NASA Astrophysics Data System (ADS)

Bueno Mario, A.; Alvarez-Borrego, Josue; Acho, L.

2004-10-01

A new autofocus algorithm based on one-dimensional Fourier transform and Pearson correlation for Z automatized microscope is proposed. Our goal is to determine in fast response time and accuracy, the best focused plane through an algorithm. We capture in bright and dark field several images set at different Z distances from biological organism sample. The algorithm uses the one-dimensional Fourier transform to obtain the image frequency content of a vectors pattern previously defined comparing the Pearson correlation of these frequency vectors versus the reference image frequency vector, the most out of focus image, we find the best focusing. Experimental results showed the algorithm has fast response time and accuracy in getting the best focus plane from captured images. In conclusions, the algorithm can be implemented in real time systems due fast response time, accuracy and robustness. The algorithm can be used to get focused images in bright and dark field and it can be extended to include fusion techniques to construct multifocus final images beyond of this paper.

Analysis of microstrip patch antennas using finite difference time domain method

NASA Astrophysics Data System (ADS)

Reineix, Alain; Jecko, Bernard

1989-11-01

The study of microstrip patch antennas is directly treated in the time domain, using a modified finite-difference time-domain (FDTD) method. Assuming an appropriate choice of excitation, the frequency dependence of the relevant parameters can readily be found using the Fourier transform of the transient current. The FDTD method allows a rigorous treatment of one or several dielectric interfaces. Different types of excitation can be taken into consideration (coaxial, microstrip lines, etc.). Plotting the spatial distribution of the current density gives information about the resonance modes. The usual frequency-depedent parameters (input impedance, radiation pattern) are given for several examples.

A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

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

Nash, Patrick L.

2008-01-10

Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation {delta}{sub perpendicular} {sup FDA} of 1/r ({partial_derivative})/({partial_derivative}r) r({partial_derivative})/({partial_derivative}r) that possesses an associated exact unitary representation of e{sup i/2{lambda}}{sup {delta}{sub perpendicular}{sup FDA}}. The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown tomore » be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium.« less

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.

Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity.

PubMed

Jubery, Talukder Z; Shook, Johnathon; Parmley, Kyle; Zhang, Jiaoping; Naik, Hsiang S; Higgins, Race; Sarkar, Soumik; Singh, Arti; Singh, Asheesh K; Ganapathysubramanian, Baskar

2016-01-01

Soybean canopy outline is an important trait used to understand light interception ability, canopy closure rates, row spacing response, which in turn affects crop growth and yield, and directly impacts weed species germination and emergence. In this manuscript, we utilize a methodology that constructs geometric measures of the soybean canopy outline from digital images of canopies, allowing visualization of the genetic diversity as well as a rigorous quantification of shape parameters. Our choice of data analysis approach is partially dictated by the need to efficiently store and analyze large datasets, especially in the context of planned high-throughput phenotyping experiments to capture time evolution of canopy outline which will produce very large datasets. Using the Elliptical Fourier Transformation (EFT) and Fourier Descriptors (EFD), canopy outlines of 446 soybean plant introduction (PI) lines from 25 different countries exhibiting a wide variety of maturity, seed weight, and stem termination were investigated in a field experiment planted as a randomized complete block design with up to four replications. Canopy outlines were extracted from digital images, and subsequently chain coded, and expanded into a shape spectrum by obtaining the Fourier coefficients/descriptors. These coefficients successfully reconstruct the canopy outline, and were used to measure traditional morphometric traits. Highest phenotypic diversity was observed for roundness, while solidity showed the lowest diversity across all countries. Some PI lines had extraordinary shape diversity in solidity. For interpretation and visualization of the complexity in shape, Principal Component Analysis (PCA) was performed on the EFD. PI lines were grouped in terms of origins, maturity index, seed weight, and stem termination index. No significant pattern or similarity was observed among the groups; although interestingly when genetic marker data was used for the PCA, patterns similar to canopy outline traits was observed for origins, and maturity indexes. These results indicate the usefulness of EFT method for reconstruction and study of canopy morphometric traits, and provides opportunities for data reduction of large images for ease in future use.

Modification of kaolinite surfaces through mechanochemical activation with quartz: A diffuse reflectance infrared fourier transform and chemometrics study.

PubMed

Carmody, Onuma; Frost, Ray L; Kristóf, János; Kokot, Serge; Kloprogge, J Theo; Makó, Eva

2006-12-01

Studies of kaolinite surfaces are of industrial importance. One useful method for studying the changes in kaolinite surface properties is to apply chemometric analyses to the kaolinite surface infrared spectra. A comparison is made between the mechanochemical activation of Kiralyhegy kaolinites with significant amounts of natural quartz and the mechanochemical activation of Zettlitz kaolinite with added quartz. Diffuse reflectance infrared Fourier transform (DRIFT) spectra were analyzed using principal component analysis (PCA) and multi-criteria decision making (MCDM) methods, the preference ranking organization method for enrichment evaluations (PROMETHEE) and geometrical analysis for interactive assistance (GAIA). The clear discrimination of the Kiralyhegy spectral objects on the two PC scores plots (400-800 and 800-2030 cm(-1)) indicated the dominance of quartz. Importantly, no ordering of any spectral objects appeared to be related to grinding time in the PC plots of these spectral regions. Thus, neither the kaolinite nor the quartz are systematically responsive to grinding time according to the spectral criteria investigated. The third spectral region (2600-3800 cm(-1), OH vibrations), showed apparent systematic ordering of the Kiralyhegy and, to a lesser extent, Zettlitz spectral objects with grinding time. This was attributed to the effect of the natural quartz on the delamination of kaolinite and the accompanying phenomena (i.e., formation of kaolinite spheres and water). The mechanochemical activation of kaolinite and quartz, through dry grinding, results in changes to the surface structure. Different grinding times were adopted to study the rate of destruction of the kaolinite and quartz structures. This relationship (i.e., grinding time) was classified using PROMETHEE and GAIA methodology.

Nonnegative Matrix Factorization for Efficient Hyperspectral Image Projection

NASA Technical Reports Server (NTRS)

Iacchetta, Alexander S.; Fienup, James R.; Leisawitz, David T.; Bolcar, Matthew R.

2015-01-01

Hyperspectral imaging for remote sensing has prompted development of hyperspectral image projectors that can be used to characterize hyperspectral imaging cameras and techniques in the lab. One such emerging astronomical hyperspectral imaging technique is wide-field double-Fourier interferometry. NASA's current, state-of-the-art, Wide-field Imaging Interferometry Testbed (WIIT) uses a Calibrated Hyperspectral Image Projector (CHIP) to generate test scenes and provide a more complete understanding of wide-field double-Fourier interferometry. Given enough time, the CHIP is capable of projecting scenes with astronomically realistic spatial and spectral complexity. However, this would require a very lengthy data collection process. For accurate but time-efficient projection of complicated hyperspectral images with the CHIP, the field must be decomposed both spectrally and spatially in a way that provides a favorable trade-off between accurately projecting the hyperspectral image and the time required for data collection. We apply nonnegative matrix factorization (NMF) to decompose hyperspectral astronomical datacubes into eigenspectra and eigenimages that allow time-efficient projection with the CHIP. Included is a brief analysis of NMF parameters that affect accuracy, including the number of eigenspectra and eigenimages used to approximate the hyperspectral image to be projected. For the chosen field, the normalized mean squared synthesis error is under 0.01 with just 8 eigenspectra. NMF of hyperspectral astronomical fields better utilizes the CHIP's capabilities, providing time-efficient and accurate representations of astronomical scenes to be imaged with the WIIT.

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.

Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms

PubMed Central

Landry, Nicholas W.; Knezevic, Marko

2015-01-01

Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) for delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. PMID:28793566

A new method to cluster genomes based on cumulative Fourier power spectrum.

PubMed

Dong, Rui; Zhu, Ziyue; Yin, Changchuan; He, Rong L; Yau, Stephen S-T

2018-06-20

Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum). Copyright © 2018. Published by Elsevier B.V.

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

Digital signal processing algorithms for automatic voice recognition

NASA Technical Reports Server (NTRS)

Botros, Nazeih M.

1987-01-01

The current digital signal analysis algorithms are investigated that are implemented in automatic voice recognition algorithms. Automatic voice recognition means, the capability of a computer to recognize and interact with verbal commands. The digital signal is focused on, rather than the linguistic, analysis of speech signal. Several digital signal processing algorithms are available for voice recognition. Some of these algorithms are: Linear Predictive Coding (LPC), Short-time Fourier Analysis, and Cepstrum Analysis. Among these algorithms, the LPC is the most widely used. This algorithm has short execution time and do not require large memory storage. However, it has several limitations due to the assumptions used to develop it. The other 2 algorithms are frequency domain algorithms with not many assumptions, but they are not widely implemented or investigated. However, with the recent advances in the digital technology, namely signal processors, these 2 frequency domain algorithms may be investigated in order to implement them in voice recognition. This research is concerned with real time, microprocessor based recognition algorithms.

Array magnetics modal analysis for the DIII-D tokamak based on localized time-series modelling

DOE PAGES

Olofsson, K. Erik J.; Hanson, Jeremy M.; Shiraki, Daisuke; ...

2014-07-14

Here, time-series analysis of magnetics data in tokamaks is typically done using block-based fast Fourier transform methods. This work presents the development and deployment of a new set of algorithms for magnetic probe array analysis. The method is based on an estimation technique known as stochastic subspace identification (SSI). Compared with the standard coherence approach or the direct singular value decomposition approach, the new technique exhibits several beneficial properties. For example, the SSI method does not require that frequencies are orthogonal with respect to the timeframe used in the analysis. Frequencies are obtained directly as parameters of localized time-series models.more » The parameters are extracted by solving small-scale eigenvalue problems. Applications include maximum-likelihood regularized eigenmode pattern estimation, detection of neoclassical tearing modes, including locked mode precursors, and automatic clustering of modes, and magnetics-pattern characterization of sawtooth pre- and postcursors, edge harmonic oscillations and fishbones.« less

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.

Digital signal processing for velocity measurements in dynamical material's behaviour studies.

PubMed

Devlaminck, Julien; Luc, Jérôme; Chanal, Pierre-Yves

2014-03-01

In this work, we describe different configurations of optical fiber interferometers (types Michelson and Mach-Zehnder) used to measure velocities during dynamical material's behaviour studies. We detail the algorithms of processing developed and optimized to improve the performance of these interferometers especially in terms of time and frequency resolutions. Three methods of analysis of interferometric signals were studied. For Michelson interferometers, the time-frequency analysis of signals by Short-Time Fourier Transform (STFT) is compared to a time-frequency analysis by Continuous Wavelet Transform (CWT). The results have shown that the CWT was more suitable than the STFT for signals with low signal-to-noise, and low velocity and high acceleration areas. For Mach-Zehnder interferometers, the measurement is carried out by analyzing the phase shift between three interferometric signals (Triature processing). These three methods of digital signal processing were evaluated, their measurement uncertainties estimated, and their restrictions or operational limitations specified from experimental results performed on a pulsed power machine.

A fast iterative convolution weighting approach for gridding-based direct Fourier three-dimensional reconstruction with correction for the contrast transfer function.

PubMed

Abrishami, V; Bilbao-Castro, J R; Vargas, J; Marabini, R; Carazo, J M; Sorzano, C O S

2015-10-01

We describe a fast and accurate method for the reconstruction of macromolecular complexes from a set of projections. Direct Fourier inversion (in which the Fourier Slice Theorem plays a central role) is a solution for dealing with this inverse problem. Unfortunately, the set of projections provides a non-equidistantly sampled version of the macromolecule Fourier transform in the single particle field (and, therefore, a direct Fourier inversion) may not be an optimal solution. In this paper, we introduce a gridding-based direct Fourier method for the three-dimensional reconstruction approach that uses a weighting technique to compute a uniform sampled Fourier transform. Moreover, the contrast transfer function of the microscope, which is a limiting factor in pursuing a high resolution reconstruction, is corrected by the algorithm. Parallelization of this algorithm, both on threads and on multiple CPU's, makes the process of three-dimensional reconstruction even faster. The experimental results show that our proposed gridding-based direct Fourier reconstruction is slightly more accurate than similar existing methods and presents a lower computational complexity both in terms of time and memory, thereby allowing its use on larger volumes. The algorithm is fully implemented in the open-source Xmipp package and is downloadable from http://xmipp.cnb.csic.es. Copyright © 2015 Elsevier B.V. All rights reserved.

On the Vanishing Dissipation Limit for the Full Navier-Stokes-Fourier System with Non-slip Condition

NASA Astrophysics Data System (ADS)

Wang, Y.-G.; Zhu, S.-Y.

2018-06-01

In this paper, we study the vanishing dissipation limit problem for the full Navier-Stokes-Fourier equations with non-slip boundary condition in a smooth bounded domain Ω \\subseteq R3. By using Kato's idea (Math Sci Res Inst Publ 2:85-98, 1984) of constructing an artificial boundary layer, we obtain a sufficient condition for the convergence of the solution of the full Navier-Stokes-Fourier equations to the solution of the compressible Euler equations in the energy space L2(Ω ) uniformly in time.

Sideband analysis and seismic detection in a large ring laser

NASA Astrophysics Data System (ADS)

Stedman, G. E.; Li, Z.; Bilger, H. R.

1995-08-01

A ring laser unlocked by the Earth's Sagnac effect has attained a frequency resolution of 1 part in 3 \\times 1021 and a rotational resolution of 300 prad. We discuss both theoretically and experimentally the sideband structure of the Earth rotation-induced spectral line induced in the microhertz-hertz region by frequency modulation associated with extra mechanical motion, such as seismic events. The relative sideband height is an absolute measure of the rotational amplitude of that Fourier component. An initial analysis is given of the ring laser record from the Arthur's Pass-Coleridge seismic event of 18 June 1994.

Application of a flight test and data analysis technique to flutter of a drone aircraft

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Abel, I.

1981-01-01

Modal identification results are presented that were obtained from recent flight flutter tests of a drone vehicle with a research wing equipped with an active flutter suppression system (FSS). Frequency and damping of several modes are determined by a time domain modal analysis of the impulse response function obtained by Fourier transformations of data from fast swept sine wave excitation by the FSS control surfaces on the wing. Flutter points are determined for two different altitudes with the FSS off. Data are given for near the flutter boundary with the FSS on.

Automated high-speed Mueller matrix scatterometer.

PubMed

Delplancke, F

1997-08-01

A new scatterometer-polarimeter is described. It measures the angular distribution of intensity and of the complete Mueller matrix of light scattered by rough surfaces and particle suspensions. The measurement time is 1 s/scattering angle in the present configuration but can be reduced to a few milliseconds with modified electronics. The instrument uses polarization modulation and a Fourier analysis of four detected signals to obtain the 16 Mueller matrix elements. This method is particularly well suited to online, real time, industrial process control involving rough surfaces and large particle suspensions (an arithmetic roughness or particle diameter of >1 microm). Some results are given.

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 functional analysis for unsteady aerodynamic modeling

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Chin, Suei

1991-01-01

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

High-Throughput Metabolic Fingerprinting of Legume Silage Fermentations via Fourier Transform Infrared Spectroscopy and Chemometrics

PubMed Central

Johnson, Helen E.; Broadhurst, David; Kell, Douglas B.; Theodorou, Michael K.; Merry, Roger J.; Griffith, Gareth W.

2004-01-01

Silage quality is typically assessed by the measurement of several individual parameters, including pH, lactic acid, acetic acid, bacterial numbers, and protein content. The objective of this study was to use a holistic metabolic fingerprinting approach, combining a high-throughput microtiter plate-based fermentation system with Fourier transform infrared (FT-IR) spectroscopy, to obtain a snapshot of the sample metabolome (typically low-molecular-weight compounds) at a given time. The aim was to study the dynamics of red clover or grass silage fermentations in response to various inoculants incorporating lactic acid bacteria (LAB). The hyperspectral multivariate datasets generated by FT-IR spectroscopy are difficult to interpret visually, so chemometrics methods were used to deconvolute the data. Two-phase principal component-discriminant function analysis allowed discrimination between herbage types and different LAB inoculants and modeling of fermentation dynamics over time. Further analysis of FT-IR spectra by the use of genetic algorithms to identify the underlying biochemical differences between treatments revealed that the amide I and amide II regions (wavenumbers of 1,550 to 1,750 cm−1) of the spectra were most frequently selected (reflecting changes in proteins and free amino acids) in comparisons between control and inoculant-treated fermentations. This corresponds to the known importance of rapid fermentation for the efficient conservation of forage proteins. PMID:15006782

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.

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.

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.

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.

Plant-based Food and Feed Protein Structure Changes Induced by Gene-transformation heating and bio-ethanol processing: A Synchrotron-based Molecular Structure and Nutrition Research Program

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

P Yu

Unlike traditional 'wet' analytical methods which during processing for analysis often result in destruction or alteration of the intrinsic protein structures, advanced synchrotron radiation-based Fourier transform infrared microspectroscopy has been developed as a rapid and nondestructive and bioanalytical technique. This cutting-edge synchrotron-based bioanalytical technology, taking advantages of synchrotron light brightness (million times brighter than sun), is capable of exploring the molecular chemistry or structure of a biological tissue without destruction inherent structures at ultra-spatial resolutions. In this article, a novel approach is introduced to show the potential of the advanced synchrotron-based analytical technology, which can be used to study plant-basedmore » food or feed protein molecular structure in relation to nutrient utilization and availability. Recent progress was reported on using synchrotron-based bioanalytical technique synchrotron radiation-based Fourier transform infrared microspectroscopy and diffused reflectance infrared Fourier transform spectroscopy to detect the effects of gene-transformation (Application 1), autoclaving (Application 2), and bio-ethanol processing (Application 3) on plant-based food and feed protein structure changes on a molecular basis. The synchrotron-based technology provides a new approach for plant-based protein structure research at ultra-spatial resolutions at cellular and molecular levels.« less

Wavelet analysis of near-resonant series RLC circuit with time-dependent forcing frequency

NASA Astrophysics Data System (ADS)

Caccamo, M. T.; Cannuli, A.; Magazù, S.

2018-07-01

In this work, the results of an analysis of the response of a near-resonant series resistance‑inductance‑capacitance (RLC) electric circuit with time-dependent forcing frequency by means of a wavelet cross-correlation approach are reported. In particular, it is shown how the wavelet approach enables frequency and time analysis of the circuit response to be carried out simultaneously—this procedure not being possible by Fourier transform, since the frequency is not stationary in time. A series RLC circuit simulation is performed by using the Simulation Program with Integrated Circuits Emphasis (SPICE), in which an oscillatory sinusoidal voltage drive signal of constant amplitude is swept through the resonant condition by progressively increasing the frequency over a 20-second time window, linearly, from 0.32 Hz to 6.69 Hz. It is shown that the wavelet cross-correlation procedure quantifies the common power between the input signal (represented by the electromotive force) and the output signal, which in the present case is a current, highlighting not only which frequencies are present but also when they occur, i.e. providing a simultaneous time-frequency analysis. The work is directed toward graduate Physics, Engineering and Mathematics students, with the main intention of introducing wavelet analysis into their data analysis toolkit.

PLANE-INTEGRATED OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROMETRY METHODOLOGY FOR ANAEROBIC SWINE LAGOON EMISSION MEASUREMENTS

EPA Science Inventory

Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...

A Graphical Presentation to Teach the Concept of the Fourier Transform

ERIC Educational Resources Information Center

Besalu, E.

2006-01-01

A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.

Evolutionary Algorithm Based Feature Optimization for Multi-Channel EEG Classification.

PubMed

Wang, Yubo; Veluvolu, Kalyana C

2017-01-01

The most BCI systems that rely on EEG signals employ Fourier based methods for time-frequency decomposition for feature extraction. The band-limited multiple Fourier linear combiner is well-suited for such band-limited signals due to its real-time applicability. Despite the improved performance of these techniques in two channel settings, its application in multiple-channel EEG is not straightforward and challenging. As more channels are available, a spatial filter will be required to eliminate the noise and preserve the required useful information. Moreover, multiple-channel EEG also adds the high dimensionality to the frequency feature space. Feature selection will be required to stabilize the performance of the classifier. In this paper, we develop a new method based on Evolutionary Algorithm (EA) to solve these two problems simultaneously. The real-valued EA encodes both the spatial filter estimates and the feature selection into its solution and optimizes it with respect to the classification error. Three Fourier based designs are tested in this paper. Our results show that the combination of Fourier based method with covariance matrix adaptation evolution strategy (CMA-ES) has the best overall performance.

Wave propagation model of heat conduction and group speed

NASA Astrophysics Data System (ADS)

Zhang, Long; Zhang, Xiaomin; Peng, Song

2018-03-01

In view of the finite relaxation model of non-Fourier's law, the Cattaneo and Vernotte (CV) model and Fourier's law are presented in this work for comparing wave propagation modes. Independent variable translation is applied to solve the partial differential equation. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed; the speed of propagation is related to the logarithmic heating rate. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. These features show that propagation accelerates when heated and decelerates when cooled. For the model media that follow Fourier's law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite.

A new approach for measuring power spectra and reconstructing time series in active galactic nuclei

NASA Astrophysics Data System (ADS)

Li, Yan-Rong; Wang, Jian-Min

2018-05-01

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parametrizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enables an acceptable time complexity for the approach.

Fractally Fourier decimated homogeneous turbulent shear flow in noninteger dimensions.

PubMed

Fathali, Mani; Khoei, Saber

2017-02-01

Time evolution of the fully resolved incompressible homogeneous turbulent shear flow in noninteger Fourier dimensions is numerically investigated. The Fourier dimension of the flow field is extended from the integer value 3 to the noninteger values by projecting the Navier-Stokes equation on the fractal set of the active Fourier modes with dimensions 2.7≤d≤3.0. The results of this study revealed that the dynamics of both large and small scale structures are nontrivially influenced by changing the Fourier dimension d. While both turbulent production and dissipation are significantly hampered as d decreases, the evolution of their ratio is almost independent of the Fourier dimension. The mechanism of the energy distribution among different spatial directions is also impeded by decreasing d. Due to this deficient energy distribution, turbulent field shows a higher level of the large-scale anisotropy in lower Fourier dimensions. In addition, the persistence of the vortex stretching mechanism and the forward spectral energy transfer, which are three-dimensional turbulence characteristics, are examined at changing d, from the standard case d=3.0 to the strongly decimated flow field for d=2.7. As the Fourier dimension decreases, these forward energy transfer mechanisms are strongly suppressed, which in turn reduces both the small-scale intermittency and the deviation from Gaussianity. Besides the energy exchange intensity, the variations of d considerably modify the relative weights of local to nonlocal triadic interactions. It is found that the contribution of the nonlocal triads to the total turbulent kinetic energy exchange increases as the Fourier dimension increases.

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.

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.

Fourier Ptychographic Microscopy for Rapid, High-Resolution Imaging of Circulating Tumor Cells Enriched by Microfiltration.

PubMed

Williams, Anthony; Chung, Jaebum; Yang, Changhuei; Cote, Richard J

2017-01-01

Examining the hematogenous compartment for evidence of metastasis has increased significantly within the oncology research community in recent years, due to the development of technologies aimed at the enrichment of circulating tumor cells (CTCs), the subpopulation of primary tumor cells that gain access to the circulatory system and are responsible for colonization at distant sites. In contrast to other technologies, filtration-based CTC enrichment, which exploits differences in size between larger tumor cells and surrounding smaller, non-tumor blood cells, has the potential to improve CTC characterization through isolation of tumor cell populations with greater molecular heterogeneity. However, microscopic analysis of uneven filtration surfaces containing CTCs is laborious, time-consuming, and inconsistent, preventing widespread use of filtration-based enrichment technologies. Here, integrated with a microfiltration-based CTC and rare cell enrichment device we have previously described, we present a protocol for Fourier Ptychographic Microscopy (FPM), a method that, unlike many automated imaging platforms, produces high-speed, high-resolution images that can be digitally refocused, allowing users to observe objects of interest present on multiple focal planes within the same image frame. The development of a cost-effective and high-throughput CTC analysis system for filtration-based enrichment technologies could have profound clinical implications for improved CTC detection and analysis.

Wavelets in music analysis and synthesis: timbre analysis and perspectives

NASA Astrophysics Data System (ADS)

Alves Faria, Regis R.; Ruschioni, Ruggero A.; Zuffo, Joao A.

1996-10-01

Music is a vital element in the process of comprehending the world where we live and interact with. Frequency it exerts a subtle but expressive influence over a society's evolution line. Analysis and synthesis of music and musical instruments has always been associated with forefront technologies available at each period of human history, and there is no surprise in witnessing now the use of digital technologies and sophisticated mathematical tools supporting its development. Fourier techniques have been employed for years as a tool to analyze timbres' spectral characteristics, and re-synthesize them from these extracted parameters. Recently many modern implementations, based on spectral modeling techniques, have been leading to the development of new generations of music synthesizers, capable of reproducing natural sounds with high fidelity, and producing novel timbres as well. Wavelets are a promising tool on the development of new generations of music synthesizers, counting on its advantages over the Fourier techniques in representing non-periodic and transient signals, with complex fine textures, as found in music. In this paper we propose and introduce the use of wavelets addressing its perspectives towards musical applications. The central idea is to investigate the capacities of wavelets in analyzing, extracting features and altering fine timbre components in a multiresolution time- scale, so as to produce high quality synthesized musical sounds.

A general statistical test for correlations in a finite-length time series.

PubMed

Hanson, Jeffery A; Yang, Haw

2008-06-07

The statistical properties of the autocorrelation function from a time series composed of independently and identically distributed stochastic variables has been studied. Analytical expressions for the autocorrelation function's variance have been derived. It has been found that two common ways of calculating the autocorrelation, moving-average and Fourier transform, exhibit different uncertainty characteristics. For periodic time series, the Fourier transform method is preferred because it gives smaller uncertainties that are uniform through all time lags. Based on these analytical results, a statistically robust method has been proposed to test the existence of correlations in a time series. The statistical test is verified by computer simulations and an application to single-molecule fluorescence spectroscopy is discussed.

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.

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2013-01-01

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

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

Simultaneous measurement of acoustic and streaming velocities in a standing wave using laser Doppler anemometry.

PubMed

Thompson, Michael W; Atchley, Anthony A

2005-04-01

Laser Doppler anemometry (LDA) with burst spectrum analysis (BSA) is used to study the acoustic streaming generated in a cylindrical standing-wave resonator filled with air. The air column is driven sinusoidally at a frequency of approximately 310 Hz and the resultant acoustic-velocity amplitudes are less than 1.3 m/s at the velocity antinodes. The axial component of fluid velocity is measured along the resonator axis, across the diameter, and as a function of acoustic amplitude. The velocity signals are postprocessed using the Fourier averaging method [Sonnenberger et al., Exp. Fluids 28, 217-224 (2000)]. Equations are derived for determining the uncertainties in the resultant Fourier coefficients. The time-averaged velocity-signal components are seen to be contaminated by significant errors due to the LDA/BSA system. In order to avoid these errors, the Lagrangian streaming velocities are determined using the time-harmonic signal components and the arrival times of the velocity samples. The observed Lagrangian streaming velocities are consistent with Rott's theory [N. Rott, Z. Angew. Math. Phys. 25, 417-421 (1974)], indicating that the dependence of viscosity on temperature is important. The onset of streaming is observed to occur within approximately 5 s after switching on the acoustic field.

Directional dual-tree complex wavelet packet transforms for processing quadrature signals.

PubMed

Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin

2016-03-01

Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals.

[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.

Fourier Transform Infrared Spectroscopy and Multivariate Analysis for Online Monitoring of Dibutyl Phosphate Degradation Product in Tributyl Phosphate/n-Dodecane/Nitric Acid Solvent

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

Tatiana G. Levitskaia; James M. Peterson; Emily L. Campbell

2013-12-01

In liquid–liquid extraction separation processes, accumulation of organic solvent degradation products is detrimental to the process robustness, and frequent solvent analysis is warranted. Our research explores the feasibility of online monitoring of the organic solvents relevant to used nuclear fuel reprocessing. This paper describes the first phase of developing a system for monitoring the tributyl phosphate (TBP)/n-dodecane solvent commonly used to separate used nuclear fuel. In this investigation, the effect of extraction of nitric acid from aqueous solutions of variable concentrations on the quantification of TBP and its major degradation product dibutylphosphoric acid (HDBP) was assessed. Fourier transform infrared (FTIR)more » spectroscopy was used to discriminate between HDBP and TBP in the nitric acid-containing TBP/n-dodecane solvent. Multivariate analysis of the spectral data facilitated the development of regression models for HDBP and TBP quantification in real time, enabling online implementation of the monitoring system. The predictive regression models were validated using TBP/n-dodecane solvent samples subjected to high-dose external ?-irradiation. The predictive models were translated to flow conditions using a hollow fiber FTIR probe installed in a centrifugal contactor extraction apparatus, demonstrating the applicability of the FTIR technique coupled with multivariate analysis for the online monitoring of the organic solvent degradation products.« less

Fourier Transform Infrared Spectroscopy and Multivariate Analysis for Online Monitoring of Dibutyl Phosphate Degradation Product in Tributyl Phosphate /n-Dodecane/Nitric Acid Solvent

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

Levitskaia, Tatiana G.; Peterson, James M.; Campbell, Emily L.

2013-11-05

In liquid-liquid extraction separation processes, accumulation of organic solvent degradation products is detrimental to the process robustness and frequent solvent analysis is warranted. Our research explores feasibility of online monitoring of the organic solvents relevant to used nuclear fuel reprocessing. This paper describes the first phase of developing a system for monitoring the tributyl phosphate (TBP)/n-dodecane solvent commonly used to separate used nuclear fuel. In this investigation, the effect of extraction of nitric acid from aqueous solutions of variable concentrations on the quantification of TBP and its major degradation product dibutyl phosphoric acid (HDBP) was assessed. Fourier Transform Infrared Spectroscopymore » (FTIR) spectroscopy was used to discriminate between HDBP and TBP in the nitric acid-containing TBP/n-dodecane solvent. Multivariate analysis of the spectral data facilitated the development of regression models for HDBP and TBP quantification in real time, enabling online implementation of the monitoring system. The predictive regression models were validated using TBP/n-dodecane solvent samples subjected to the high dose external gamma irradiation. The predictive models were translated to flow conditions using a hollow fiber FTIR probe installed in a centrifugal contactor extraction apparatus demonstrating the applicability of the FTIR technique coupled with multivariate analysis for the online monitoring of the organic solvent degradation products.« less

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.