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

A high-resolution near-infrared extraterrestrial solar spectrum derived from ground-based Fourier transform spectrometer measurements

NASA Astrophysics Data System (ADS)

Menang, Kaah P.; Coleman, Marc D.; Gardiner, Tom D.; Ptashnik, Igor V.; Shine, Keith P.

2013-06-01

A detailed spectrally resolved extraterrestrial solar spectrum (ESS) is important for line-by-line radiative transfer modeling in the near-IR. Very few observationally based high-resolution ESS are available in this spectral region. Consequently, the theoretically calculated ESS by Kurucz has been widely adopted. We present the CAVIAR (Continuum Absorption at Visible and Infrared Wavelengths and its Atmospheric Relevance) ESS, which is derived using the Langley technique applied to calibrated observations using a ground-based high-resolution Fourier transform spectrometer (FTS) in atmospheric windows from 2000 to 10,000 cm-1 (1-5 µm). There is good agreement between the strengths and positions of solar lines between the CAVIAR and the satellite-based Atmospheric Chemistry Experiment-FTS ESS, in the spectral region where they overlap, and good agreement with other ground-based FTS measurements in two near-IR windows. However, there are significant differences in the structure between the CAVIAR ESS and spectra from semiempirical models. In addition, we found a difference of up to 8% in the absolute (and hence the wavelength-integrated) irradiance between the CAVIAR ESS and that of Thuillier et al., which was based on measurements from the Atmospheric Laboratory for Applications and Science satellite and other sources. In many spectral regions, this difference is significant, because the coverage factor k = 2 (or 95% confidence limit) uncertainties in the two sets of observations do not overlap. Because the total solar irradiance is relatively well constrained, if the CAVIAR ESS is correct, then this would indicate an integrated "loss" of solar irradiance of about 30 W m-2 in the near-IR that would have to be compensated by an increase at other wavelengths.

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

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

Airborne measurements in the infrared using FTIR-based imaging hyperspectral sensors

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Lagueux, P.; Farley, V.; Marcotte, F.; Chamberland, M.

2009-09-01

Hyperspectral ground mapping is being used in an ever-increasing extent for numerous applications in the military, geology and environmental fields. The different regions of the electromagnetic spectrum help produce information of differing nature. The visible, near-infrared and short-wave infrared radiation (400 nm to 2.5 μm) has been mostly used to analyze reflected solar light, while the mid-wave (3 to 5 μm) and long-wave (8 to 12 μm or thermal) infrared senses the self-emission of molecules directly, enabling the acquisition of data during night time. Push-broom dispersive sensors have been typically used for airborne hyperspectral mapping. However, extending the spectral range towards the mid-wave and long-wave infrared brings performance limitations due to the self emission of the sensor itself. The Fourier-transform spectrometer technology has been extensively used in the infrared spectral range due to its high transmittance as well as throughput and multiplex advantages, thereby reducing the sensor self-emission problem. Telops has developed the Hyper-Cam, a rugged and compact infrared hyperspectral imager. The Hyper-Cam is based on the Fourier-transform technology yielding high spectral resolution and enabling high accuracy radiometric calibration. It provides passive signature measurement capability, with up to 320x256 pixels at spectral resolutions of up to 0.25 cm-1. The Hyper-Cam has been used on the ground in several field campaigns, including the demonstration of standoff chemical agent detection. More recently, the Hyper-Cam has been integrated into an airplane to provide airborne measurement capabilities. A special pointing module was designed to compensate for airplane attitude and forward motion. To our knowledge, the Hyper-Cam is the first commercial airborne hyperspectral imaging sensor based on Fourier-transform infrared technology. The first airborne measurements and some preliminary performance criteria for the Hyper-Cam are presented in this paper.

Airborne measurements in the infrared using FTIR-based imaging hyperspectral sensors

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Farley, V.; Lagueux, P.; Marcotte, F.; Chamberland, M.

2009-05-01

Hyperspectral ground mapping is being used in an ever-increasing extent for numerous applications in the military, geology and environmental fields. The different regions of the electromagnetic spectrum help produce information of differing nature. The visible, near-infrared and short-wave infrared radiation (400 nm to 2.5 μm) has been mostly used to analyze reflected solar light, while the mid-wave (3 to 5 μm) and long-wave (8 to 12 μm or thermal) infrared senses the self-emission of molecules directly, enabling the acquisition of data during night time. Push-broom dispersive sensors have been typically used for airborne hyperspectral mapping. However, extending the spectral range towards the mid-wave and long-wave infrared brings performance limitations due to the self emission of the sensor itself. The Fourier-transform spectrometer technology has been extensively used in the infrared spectral range due to its high transmittance as well as throughput and multiplex advantages, thereby reducing the sensor self-emission problem. Telops has developed the Hyper-Cam, a rugged and compact infrared hyperspectral imager. The Hyper-Cam is based on the Fourier-transform technology yielding high spectral resolution and enabling high accuracy radiometric calibration. It provides passive signature measurement capability, with up to 320x256 pixels at spectral resolutions of up to 0.25 cm-1. The Hyper-Cam has been used on the ground in several field campaigns, including the demonstration of standoff chemical agent detection. More recently, the Hyper-Cam has been integrated into an airplane to provide airborne measurement capabilities. A special pointing module was designed to compensate for airplane attitude and forward motion. To our knowledge, the Hyper-Cam is the first commercial airborne hyperspectral imaging sensor based on Fourier-transform infrared technology. The first airborne measurements and some preliminary performance criteria for the Hyper-Cam are presented in this paper.

Retrieval Analysis of the CO2 1.6 μm Band in Solar Absorption Spectra Measured by a Ground-Based High-Resolution Fourier Transform Spectrometer at Tsukuba

NASA Astrophysics Data System (ADS)

Ohyama, H.; Morino, I.; Nagahama, T.; Suto, H.; Oguma, H.; Machida, T.; Sugimoto, N.; Nakane, H.; Nakagawa, K.

2006-12-01

The global measurements of greenhouse gases from space are being planned, such as GOSAT (Greenhouse gases Observing SATellite) and OCO (Orbiting Carbon Observatory). Satellite remote sensing needs validations with other measurement techniques, for example, in-situ or sampling measurement by aircraft or ground station, or remote sensing measurement by ground-based Fourier Transform Spectrometer (FTS). The ground-based FTS measurement can provide the column amounts of atmospheric composition by a retrieval analysis with relatively high precision. In 2001, we started a project to observe the atmospheric compositions in solar absorption spectra by a ground- based high-resolution FTS (Bruker IFS 120 HR) located at Tsukuba, Japan. Three years ago, optical components of the FTS were replaced for measuring greenhouse gases such as carbon dioxide (CO2) and methane (CH4) in the near-infrared region: a CaF2 beam splitter, an InSb detector, and a 1.4-2.4 μm optical filter. The measurements were carried out once a day for ~100 days per year. We also made simultaneous FTS and aircraft in-situ measurements on August 10, 2004 and March 30, 2005. The retrieval analysis was performed for the measured spectra in the CO2 1.6 μm band. We used SEASCRAPE PLUS (Sequential Evaluation Algorithm for Simultaneous and Concurrent Retrieval of Atmospheric Parameter Estimates PLUS, Remote Sensing Analysis Systems, Inc.) as a retrieval analysis program. The column amounts were compared with those derived from in-situ measurements complemented by model data; differences are less than 1%. We have derived the diurnal variations of CO2 on the same days as in-situ measurements, and they showed tendencies similar to the tower measurements at the Meteorological Research Institute in Tsukuba.

Measurements of reactive trace gases and variable O3 formation rates in some South Carolina biomass burning plumes [Discussions

Treesearch

S. K. Akagi; R. J. Yokelson; I. R. Burling; S. Meinardi; I. Simpson; D. R. Blake; G. R. McMeeking; A. Sullivan; T. Lee; S. Kreidenweis; S. Urbanski; J. Reardon; D. W. T. Griffith; T. J. Johnson; D. R. Weise

2012-01-01

In October–November 2011 we measured trace gas emission factors from seven prescribed fires in South Carolina (SC), US, using two Fourier transform infrared spectrometer (FTIR) systems and whole air sampling (WAS) into canisters followed by gas-chromatographic analysis. A total of 97 trace gas species were quantified from both airborne and ground-based sampling...

Far Infrared Spectrometry of the Cosmic Background Radiation

DOE R&D Accomplishments Database

Mather, J. C.

1974-01-01

I describe two experiments to measure the cosmic background radiation near 1 mm wavelength. The first was a ground-based search for spectral lines, made with a Fabry-Perot interferometer and an InSb detector. The second is a measurement of the spectrum from 3 to 18 cm{sup -1}, made with a balloon-borne Fourier transform spectrometer. It is a polarizing Michelson interferometer, cooled in liquid helium, and operated with a germanium bolometer. I give the theory of operation, construction details, and experimental results. The first experiment was successfully completed but the second suffered equipment malfunction on its first flight. I describe the theory of Fourier transformations and give a new understanding of convolutional phase correction computations. I discuss for infrared bolometer calibration procedures, and tabulate test results on nine detectors. I describe methods of improving bolometer sensitivity with immersion optics and with conductive film blackening.

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.

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.

Quantitative evaluation of multiple adulterants in roasted coffee by Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS) and chemometrics.

PubMed

Reis, Nádia; Franca, Adriana S; Oliveira, Leandro S

2013-10-15

The current study presents an application of Diffuse Reflectance Infrared Fourier Transform Spectroscopy for detection and quantification of fraudulent addition of commonly employed adulterants (spent coffee grounds, coffee husks, roasted corn and roasted barley) to roasted and ground coffee. Roasted coffee samples were intentionally blended with the adulterants (pure and mixed), with total adulteration levels ranging from 1% to 66% w/w. Partial Least Squares Regression (PLS) was used to relate the processed spectra to the mass fraction of adulterants and the model obtained provided reliable predictions of adulterations at levels as low as 1% w/w. A robust methodology was implemented that included the detection of outliers. High correlation coefficients (0.99 for calibration; 0.98 for validation) coupled with low degrees of error (1.23% for calibration; 2.67% for validation) confirmed that DRIFTS can be a valuable analytical tool for detection and quantification of adulteration in ground, roasted coffee. Copyright © 2013 Elsevier B.V. All rights reserved.

The total carbon column observing network.

PubMed

Wunch, Debra; Toon, Geoffrey C; Blavier, Jean-François L; Washenfelder, Rebecca A; Notholt, Justus; Connor, Brian J; Griffith, David W T; Sherlock, Vanessa; Wennberg, Paul O

2011-05-28

A global network of ground-based Fourier transform spectrometers has been founded to remotely measure column abundances of CO(2), CO, CH(4), N(2)O and other molecules that absorb in the near-infrared. These measurements are directly comparable with the near-infrared total column measurements from space-based instruments. With stringent requirements on the instrumentation, acquisition procedures, data processing and calibration, the Total Carbon Column Observing Network (TCCON) achieves an accuracy and precision in total column measurements that is unprecedented for remote-sensing observations (better than 0.25% for CO(2)). This has enabled carbon-cycle science investigations using the TCCON dataset, and allows the TCCON to provide a link between satellite measurements and the extensive ground-based in situ network. © 2011 The Royal Society

Evaluation of photostability of solid-state nicardipine hydrochloride polymorphs by using Fourier-transformed reflection-absorption infrared spectroscopy - effect of grinding on the photostability of crystal form.

PubMed

Teraoka, Reiko; Otsuka, Makoto; Matsuda, Yoshihisa

2004-11-22

Photostability and physicochemical properties of nicardipine hydrochloride polymorphs (alpha- and beta-form) were studied by using Fourier-transformed reflection-absorption infrared spectroscopy (FT-IR-RAS) of the tablets, X-ray powder diffraction analysis, differential scanning calorimetry (DSC), and color difference measurement. It was clear from the results of FT-IR-RAS spectra after irradiation that nicardipine hydrochloride in the solid state decomposed to its pyridine derivative when exposed to light. The photostability of the ground samples of two forms was also measured in the same manner. The two crystalline forms of the drug changed to nearly amorphous form after 150 min grinding in a mixer mill. X-ray powder diffraction patterns of those ground samples showed almost halo patterns. The nicardipine hydrochloride content on the surface of the tablet was determined based on the absorbance at 1700 cm(-1) attributable to the C=O stretch vibration in FT-IR-RAS spectra before and after irradiation by fluorescent lamp (3500 lx). The photodegradation followed apparently the first-order kinetics for any sample. The apparent photodegradation rate constant of beta-form was greater than that of alpha-form. The ground samples decomposed rapidly under the same light irradiation as compared with the intact crystalline forms. The photodegradation rate constant decreased with increase of the heat of fusion. copyright 2004 Elsevier B.V.

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.

SIELETERS: A Static Fourier Transform Infrared Imaging Spectrometer for Airborne Hyperspectral Measurements

DTIC Science & Technology

2009-10-01

cryostat and cooled at a temperature under 77K by a Stirling cryocooler , as represented on the following Figure 5 : Cryostat...Figure 5. Detector cryostat and cryocooler The read-out frequency of the detectors is adapted to the ground speed of the plane above...Cold shield Detector plane Cryocoole r Cryocoole r compresso r Fixed frame Roll frame Pitch frame Yaw frame SIELETERS: a Static Fourier

[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.

Analytical Method Used to Calculate Pile Foundations with the Widening Up on a Horizontal Static Impact

NASA Astrophysics Data System (ADS)

Kupchikova, N. V.; Kurbatskiy, E. N.

2017-11-01

This paper presents a methodology for the analytical research solutions for the work pile foundations with surface broadening and inclined side faces in the ground array, based on the properties of Fourier transform of finite functions. The comparative analysis of the calculation results using the suggested method for prismatic piles, piles with surface broadening prismatic with precast piles and end walls with precast wedges on the surface is described.

Interpretation of aeromagnetic data over Abeokuta and its environs, Southwest Nigeria, using spectral analysis (Fourier transform technique)

NASA Astrophysics Data System (ADS)

Olurin, Oluwaseun T.; Ganiyu, Saheed A.; Hammed, Olaide S.; Aluko, Taiwo J.

2016-10-01

This study presents the results of spectral analysis of magnetic data over Abeokuta area, Southwestern Nigeria, using fast Fourier transform (FFT) in Microsoft Excel. The study deals with the quantitative interpretation of airborne magnetic data (Sheet No. 260), which was conducted by the Nigerian Geological Survey Agency in 2009. In order to minimise aliasing error, the aeromagnetic data was gridded at spacing of 1 km. Spectral analysis technique was used to estimate the magnetic basement depth distributed at two levels. The result of the interpretation shows that the magnetic sources are mainly distributed at two levels. The shallow sources (minimum depth) range in depth from 0.103 to 0.278 km below ground level and are inferred to be due to intrusions within the region. The deeper sources (maximum depth) range in depth from 2.739 to 3.325 km below ground and are attributed to the underlying basement.

Fourier transform microwave spectroscopy of the SiCl+ ion

NASA Astrophysics Data System (ADS)

Tanaka, Keiichi; Harada, Kensuke; Cabezas, Carlos; Endo, Yasuki

2018-03-01

Fourier transform microwave spectra for the J = 1 ← 0 and 2 ← 1 rotational transitions of the SiCl+ ion were observed for two isotopologues (35 Cl and 37 Cl) in the ground and the first excited vibrational states of the ground 1Σ+ electronic state. Thanks to the high resolution of the FTMW spectrometer, hyperfine structures due to the quadrupole moment of the chlorine nucleus and the nuclear spin-rotation interaction were fully resolved. The observed FTMW spectra were combined with previously reported MMW and diode laser spectra in an analysis to determine the mass-independent Dunham coefficients Uk,l as well as a mass scaling parameter Δ01Cl = - 0.856 (30) . The equilibrium bond length of SiCl+ determined is re = 1.9439729 (10) Å and the nuclear quadrupole coupling constant of Si35 Cl+ is eQqe = - 11.8788 (23) MHz.

High-resolution Fourier transform infrared synchrotron spectroscopy of the NO2 in-plane rock band of nitromethane

NASA Astrophysics Data System (ADS)

Dawadi, Mahesh B.; Twagirayezu, Sylvestre; Perry, David S.; Billinghurst, Brant E.

2015-09-01

The high-resolution rotationally resolved Fourier-transform infrared spectrum of the NO2 in-plane rock band (440-510 cm-1) of nitromethane (CH3NO2) has been recorded using the Far-Infrared Beamline at the Canadian Light Source, with a resolution of 0.00096 cm-1. About 1773 transitions reaching the upper state levels m‧ = 0; Ka‧ ⩽ 7;J‧ ⩽ 50 have been assigned using an automated ground-state combination difference program together with the traditional Loomis-Wood approach. These data from the lowest torsional state, m‧ = 0, were fit using the six-fold torsion-rotation program developed by Ilyushin et al. (2010). The analysis reveals that the rotational energy level structure in the upper vibrational state is similar to that of the ground vibrational state, but the sign and magnitude of high-order constants are significantly changed suggesting the presence of multiple perturbations.

Mesures spectroscopiques de constituants et de polluants atmosphériques par techniques in situ et à distance, au sol ou embarquéesSpectroscopic measurements of atmospheric constituents and pollutants by in situ and remote techniques from the ground and in flight

NASA Astrophysics Data System (ADS)

Camy-Peyret, Claude; Payan, Sébastien; Jeseck, Pascal; Té, Yao

2001-09-01

Infrared spectroscopy is a powerful tool for precise measurements of atmospheric trace species concentrations through the use of characteristic spectral signatures of the different molecular species and their associated vibration-rotation bands in the mid- or near-infrared. Different methods based on quantitative spectroscopy permit tropospheric or stratospheric measurements: in situ long path absorption, atmospheric absorption/emission by Fourier transform spectroscopy with high spectral resolution instruments on the ground, airborne, balloon-borne or satellite-borne.

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

Signal processing applications of massively parallel charge domain computing devices

NASA Technical Reports Server (NTRS)

Fijany, Amir (Inventor); Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor)

1999-01-01

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array.

Use of the fractional Fourier transform in {pi}/2 converters of laser modes

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

Malyutin, A A

2004-02-28

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

A new Fourier transform based CBIR scheme for mammographic mass classification: a preliminary invariance assessment

NASA Astrophysics Data System (ADS)

Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin

2015-03-01

The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.

[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.

[Optical-fiber Fourier transform spectrometer].

PubMed

Liu, Yong; Li, Bao-sheng; Liu, Yan; Zhai, Yu-feng; Wang, An

2006-10-01

A novel Fourier transform spectrum analyzer based on a single mode fiber Mach-Zehnder interferometer is reported. An optical fiber Fourier transform spectrometer, with bulk optics components replaced by fiber optical components and with the moving mirror replaced by a piezoelectric element fiber stretcher was constructed. The output spectrum of a LD below threshold was measured. Experiment result agrees with that by using grating spectrum analyzer, showing the feasibility of the optic fiber Fourier transform spectrometer for practical spectrum measurement. Spectrum resolution -7 cm(-1) was obtained in our experiment. The resolution can be further improved by increasing the maximum optical path difference.

Frequency and time domain three-dimensional inversion of electromagnetic data for a grounded-wire source

NASA Astrophysics Data System (ADS)

Sasaki, Yutaka; Yi, Myeong-Jong; Choi, Jihyang; Son, Jeong-Sul

2015-01-01

We present frequency- and time-domain three-dimensional (3-D) inversion approaches that can be applied to transient electromagnetic (TEM) data from a grounded-wire source using a PC. In the direct time-domain approach, the forward solution and sensitivity were obtained in the frequency domain using a finite-difference technique, and the frequency response was then Fourier-transformed using a digital filter technique. In the frequency-domain approach, TEM data were Fourier-transformed using a smooth-spectrum inversion method, and the recovered frequency response was then inverted. The synthetic examples show that for the time derivative of magnetic field, frequency-domain inversion of TEM data performs almost as well as time-domain inversion, with a significant reduction in computational time. In our synthetic studies, we also compared the resolution capabilities of the ground and airborne TEM and controlled-source audio-frequency magnetotelluric (CSAMT) data resulting from a common grounded wire. An airborne TEM survey at 200-m elevation achieved a resolution for buried conductors almost comparable to that of the ground TEM method. It is also shown that the inversion of CSAMT data was able to detect a 3-D resistivity structure better than the TEM inversion, suggesting an advantage of electric-field measurements over magnetic-field-only measurements.

The morphing of geographical features by Fourier transformation.

PubMed

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

A Space Object Detection Algorithm using Fourier Domain Likelihood Ratio Test

NASA Astrophysics Data System (ADS)

Becker, D.; Cain, S.

Space object detection is of great importance in the highly dependent yet competitive and congested space domain. Detection algorithms employed play a crucial role in fulfilling the detection component in the situational awareness mission to detect, track, characterize and catalog unknown space objects. Many current space detection algorithms use a matched filter or a spatial correlator to make a detection decision at a single pixel point of a spatial image based on the assumption that the data follows a Gaussian distribution. This paper explores the potential for detection performance advantages when operating in the Fourier domain of long exposure images of small and/or dim space objects from ground based telescopes. A binary hypothesis test is developed based on the joint probability distribution function of the image under the hypothesis that an object is present and under the hypothesis that the image only contains background noise. The detection algorithm tests each pixel point of the Fourier transformed images to make the determination if an object is present based on the criteria threshold found in the likelihood ratio test. Using simulated data, the performance of the Fourier domain detection algorithm is compared to the current algorithm used in space situational awareness applications to evaluate its value.

Fourier transform-wavefront reconstruction for the pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Quirós-Pacheco, Fernando; Correia, Carlos; Esposito, Simone

The application of Fourier-transform reconstruction techniques to the pyramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with ≈40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method.

Dynamic response of a poroelastic half-space to accelerating or decelerating trains

NASA Astrophysics Data System (ADS)

Cao, Zhigang; Boström, Anders

2013-05-01

The dynamic response of a fully saturated poroelastic half-space due to accelerating or decelerating trains is investigated by a semi-analytical method. The ground is modeled as a saturated poroelastic half-space and Biot's theory is applied to characterize the soil medium, taking the coupling effects between the soil skeleton and the pore fluid into account. A detailed track system is considered incorporating rails, sleepers and embankment, which are modeled as Euler-Bernoulli beams, an anisotropic Kirchhoff plate, and an elastic layer, respectively. The acceleration or deceleration of the train is simulated by properly choosing the time history of the train speed using Fourier transforms combined with Fresnel integrals in the transformed domain. The time domain results are obtained by the fast Fourier transform (FFT). It is found that the deceleration of moving trains can cause a significant increase to the ground vibrations as well as the excess pore water pressure responses at the train speed 200 km/h. Furthermore, the single-phase elastic soil model would underestimate the vertical displacement responses caused by both the accelerating and decelerating trains at the speed 200 km/h.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

PubMed

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

High-resolution Fourier transform synchrotron spectroscopy of the C-S stretching band of methyl mercaptan, CH332SH

NASA Astrophysics Data System (ADS)

Lees, R. M.; Xu, Li-Hong; Billinghurst, B. E.

2016-01-01

The C-S stretching fundamental band of 12CH332SH, the principal isotopologue of methyl mercaptan, has been investigated by Fourier transform infrared spectroscopy on the Far-Infrared beamline at the Canadian Light Source synchrotron. The band is centered around 710 cm-1 and shows well-resolved a-type parallel structure. Most of the A and E spectral sub-bands have been assigned up to K = 12 for the vt = 0 torsional state and K = 9 for the vt = 1 state, along with a smaller variety of sub-bands for vt = 2. C-S stretching energy term values have been determined employing known ground-state energies, and have been fitted to series expansions in powers of J(J + 1) to determine the substate origins. The origins have in turn been fitted to a Fourier model to characterize the oscillatory torsional energy structure of the C-S stretching state. The amplitude of oscillation of the vt = 0 torsional curves is significantly larger for the C-S stretch state compared to the ground state. A strategy devised to relate this amplitude to an effective torsional barrier height indicates a decrease of about 7% in the effective V3 for the C-S stretch. The vibrational frequency determined for the stretching fundamental from the Fourier fit is 710.3 cm-1. The C-S stretching manifold is crossed by excited vt = 4 torsional levels of the ground state, and strong torsion-vibrational resonant coupling is observed via perturbations in the spectrum together with forbidden sub-bands induced by mixing and intensity borrowing.

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Gong, Li-Hua; He, Xiang-Tao; Tan, Ru-Chao; Zhou, Zhi-Hong

2018-01-01

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.

Experimental image alignment system

NASA Technical Reports Server (NTRS)

Moyer, A. L.; Kowel, S. T.; Kornreich, P. G.

1980-01-01

A microcomputer-based instrument for image alignment with respect to a reference image is described which uses the DEFT sensor (Direct Electronic Fourier Transform) for image sensing and preprocessing. The instrument alignment algorithm which uses the two-dimensional Fourier transform as input is also described. It generates signals used to steer the stage carrying the test image into the correct orientation. This algorithm has computational advantages over algorithms which use image intensity data as input and is suitable for a microcomputer-based instrument since the two-dimensional Fourier transform is provided by the DEFT sensor.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

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

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

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

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

PubMed

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

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.

The morphing of geographical features by Fourier transformation

PubMed Central

Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features’ continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable. PMID:29351344

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.; ...

2017-01-13

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

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

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

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.

VUV Fourier-Transform absorption study of the npπ1 Πu-, v, N ←X1 Σg+, v″ = 0,N″ transitions in D2

NASA Astrophysics Data System (ADS)

Glass-Maujean, M.; Jungen, Ch.; Dickenson, G. D.; Ubachs, W.; de Oliveira, N.; Joyeux, D.; Nahon, L.

2015-09-01

The DESIRS beamline of the SOLEIL synchrotron facility, equipped with a vacuum ultraviolet Fourier-Transform spectrometer has been used to measure Q (N″) (N -N″ = 0) absorption transitions of the D2 molecule. Some 212 Q-lines were assigned and their transition frequencies determined up to excitation energies of 137 000 cm-1 above the ground state, thereby extending the earlier work by various authors, and considerably improving the spectral accuracy (<0.1 cm-1). The assignments have been aided by first principles multichannel quantum defect theory (MQDT) calculations which also provide predictions of the autoionization widths of the upper levels.

Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

PubMed

Yan, Xin-Zhong

2011-07-01

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

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

Spectroscopy of selected metal-containing diatomic molecules

NASA Astrophysics Data System (ADS)

Gordon, Iouli E.

Fourier transform infrared emission spectra of MnH and MnD were observed in the ground X7Sigma+ electronic state. The vibration-rotation bands from v = 1 → 0 to v = 3 → 2 for MnH, and from v = 1 → 0 to v = 4 → 3 for MnD were recorded at an instrumental resolution of 0.0085 cm-1. Spectroscopic constants were determined for each vibrational level and equilibrium constants were found from a Dunham-type fit. The equilibrium vibrational constant oe for MnH was found to be 1546.84518(65) cm-1, the equilibrium rotational constant Be was found to be 5.6856789(103) cm-1 and the equilibrium bond distance re was determined to be 1.7308601(47) A. New high resolution emission spectra of CoH and CoD molecules have been recorded in the 640 nm to 3.5 mum region using a Fourier transform spectrometer. Many bands were observed for the A'3phi- X3phi electronic transition of CoH and CoD. In addition, a new [13.3]4 electronic state was found by observing the [13.3]4-X3phi3 and [13.3]4- X3phi4 transitions in the spectrum of CoD. Analysis of the transitions with DeltaO = 0, +/-1 provided more accurate values of spin-orbit splittings between O = 4 and O = 3 components. The ground state for both molecules was fitted both to band and Dunham-type constants. The estimated band constants of the perturbed upper states were also obtained. The emission spectrum of gas-phase YbO has been investigated using a Fourier transform spectrometer. A total of 8 red-degraded bands in the range 9 800--11 300 cm-1 were recorded at a resolution of 0.04 cm-1. Because of the multiple isotopomers present in the spectra, only 3 bands were rotationally analyzed. Perturbations were identified in two of these bands and all 3 transitions were found to terminate at the X1Sigma+ ground electronic state. The electronic configurations that give rise to the observed states are discussed and molecular parameters for all of the analyzed bands are reported. Electronic spectra of the previously unobserved EuH and EuD molecules were studied by means of Fourier transform spectroscopy and laser-induced fluorescence. The extreme complexity of these transitions made rotational assignments of EuH bands impossible. However, the spin-spin interaction constant, lambda, and Fermi contact parameter, bF, in the ground X9Sigma- electronic state were estimated for the 151EuH and 153EuH isotopologues. Electronic spectra of SmH, SmCl, TmH and ErF molecules were recorded for the first time using Fourier transform spectrometer. The poor signal to noise ratio of the observed bands coupled with their complexity prevented a rotational analysis. The electronic states that may be involved in the observed transitions are discussed.

Spectroscopy of selected metal-containing diatomic molecules

NASA Astrophysics Data System (ADS)

Gordon, Iouli

Fourier transform infrared emission spectra of MnH and MnD were observed in the ground X7[sigma]+ electronic state. The vibration-rotation bands from v = 1 to 0 to v = 3 to 2 for MnH, and from v = 1 to 0 to v = 4 to 3 for MnD were recorded at an instrumental resolution of 0. 0085 cm-1. Spectroscopic constants were determined for each vibrational level and equilibrium constants were found from a Dunham-type fit. The equilibrium vibrational constant [omega]e for MnH was found to be 1546. 84518(65) cm-1, the equilibrium rotational constant Be was found to be 5. 6856789(103) cm-1 and the equilibrium bond distance re was determined to be 1. 7308601(47) ?. New high resolution emission spectra of CoH and CoD molecules have been recorded in the 640 nm to 3. 5 _m region using a Fourier transform spectrometer. Many bands were observed for the A'3?-X3? electronic transition of CoH and CoD. In addition, a new [13. 3]4 electronic state was found by observing the [13. 3]4- X3?3 and [13. 3]4-X3?4 transitions in the spectrum of CoD. Analysis of the transitions with [delta][omega] = 0, ?1 provided more accurate values of spin-orbit splittings between [omega] = 4 and [omega] = 3 components. The ground state for both molecules was fitted both to band and Dunham-type constants. The estimated band constants of the perturbed upper states were also obtained. The emission spectrum of gas-phase YbO has been investigated using a Fourier transform spectrometer. A total of 8 red-degraded bands in the range 9 800 ? 11 300 cm-1 were recorded at a resolution of 0. 04 cm-1. Because of the multiple isotopomers present in the spectra, only 3 bands were rotationally analyzed. Perturbations were identified in two of these bands and all 3 transitions were found to terminate at the X1[sigma]+ ground electronic state. The electronic configurations that give rise to the observed states are discussed and molecular parameters for all of the analyzed bands are reported. Electronic spectra of the previously unobserved EuH and EuD molecules were studied by means of Fourier transform spectroscopy and laser-induced fluorescence. The extreme complexity of these transitions made rotational assignments of EuH bands impossible. However, the spin-spin interaction constant, [lambda], and Fermi contact parameter, bF, in the ground X9[sigma]- electronic state were estimated for the 151EuH and 153EuH isotopologues. Electronic spectra of SmH, SmCl, TmH and ErF molecules were recorded for the first time using Fourier transform spectrometer. The poor signal to noise ratio of the observed bands coupled with their complexity prevented a rotational analysis. The electronic states that may be involved in the observed transitions are discussed.

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

PubMed

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

Technical Note: New ground-based FTIR measurements at Ile de La Réunion: observations, error analysis, and comparisons with independent data

NASA Astrophysics Data System (ADS)

Senten, C.; de Mazière, M.; Dils, B.; Hermans, C.; Kruglanski, M.; Neefs, E.; Scolas, F.; Vandaele, A. C.; Vanhaelewyn, G.; Vigouroux, C.; Carleer, M.; Coheur, P. F.; Fally, S.; Barret, B.; Baray, J. L.; Delmas, R.; Leveau, J.; Metzger, J. M.; Mahieu, E.; Boone, C.; Walker, K. A.; Bernath, P. F.; Strong, K.

2008-01-01

Ground-based high spectral resolution Fourier-transform infrared (FTIR) solar absorption spectroscopy is a powerful remote sensing technique to obtain information on the total column abundances and on the vertical distribution of various constituents in the atmosphere. This work presents results from two short-term FTIR measurement campaigns in 2002 and 2004, held at the (sub)tropical site Ile de La Réunion (21°S, 55°E). These campaigns represent the first FTIR observations carried out at this site. The results include total column amounts from the surface up to 100 km of ozone (O3), methane (CH4), nitrous oxide (N2O), carbon monoxide (CO), ethane (C2H6), hydrogen chloride (HCl), hydrogen fluoride (HF) and nitric acid (HNO3), as well as some vertical profile information for the first four mentioned trace gases. The data are characterised in terms of the vertical information content and associated error budget. In the 2004 time series, the seasonal increase of the CO concentration was observed by the end of October, along with a sudden rise that has been attributed to biomass burning events in southern Africa and Madagascar. This attribution was based on trajectory modeling. In the same period, other biomass burning gases such as C2H6 also show an enhancement in their total column amounts which is highly correlated with the increase of the CO total columns. The observed total column values for CO are consistent with correlative data from MOPITT (Measurements Of Pollution In The Troposphere). Comparisons between our ground-based FTIR observations and space-borne observations from ACE-FTS (Atmospheric Chemistry Experiment - Fourier Transform Spectrometer) and HALOE (Halogen Occultation Experiment) confirm the feasibility of the FTIR measurements at Ile de La Réunion.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

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

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.

Ground roll attenuation using polarization analysis in the t-f-k domain

NASA Astrophysics Data System (ADS)

Wang, C.; Wang, Y.

2017-07-01

S waves travel slower than P waves and have a lower dominant frequency. Therefore, applying common techniques such as time-frequency filtering and f-k filtering to separate S waves from ground roll is difficult because ground roll is also characterized by slow velocity and low frequency. In this study, we present a method for attenuating ground roll using a polarization filtering method based on the t-f-k transform. We describe the particle motion of the waves by complex vector signals. Each pair of frequency components, whose frequencies have the same absolute value but different signs, of the complex signal indicate an elliptical or linear motion. The polarization parameters of the elliptical or linear motion are explicitly related to the two Fourier coefficients. We then extend these concepts to the t-f-k domain and propose a polarization filtering method for ground roll attenuation based on the t-f-k transform. The proposed approach can define automatically the time-varying reject zones on the f-k panel at different times as a function of the reciprocal ellipticity. Four attributes, time, frequency, apparent velocity and polarization are used to identify and extract the ground roll simultaneously. Thus, the ground roll and body waves can be separated as long as they are dissimilar in one of these attributes. We compare our method with commonly used filtering techniques by applying the methods to synthetic and real seismic data. The results indicate that our method can attenuate ground roll while preserving body waves more effectively than the other methods.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography.

PubMed

Xu, Daguang; Huang, Yong; Kang, Jin U

2014-06-16

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Ground-based FTIR retrievals of SF6 on Reunion Island

NASA Astrophysics Data System (ADS)

Zhou, Minqiang; Langerock, Bavo; Vigouroux, Corinne; Wang, Pucai; Hermans, Christian; Stiller, Gabriele; Walker, Kaley A.; Dutton, Geoff; Mahieu, Emmanuel; De Mazière, Martine

2018-02-01

SF6 total columns were successfully retrieved from FTIR (Fourier transform infrared) measurements (Saint Denis and Maïdo) on Reunion Island (21° S, 55° E) between 2004 and 2016 using the SFIT4 algorithm: the retrieval strategy and the error budget were presented. The FTIR SF6 retrieval has independent information in only one individual layer, covering the whole of the troposphere and the lower stratosphere. The trend in SF6 was analysed based on the FTIR-retrieved dry-air column-averaged mole fractions (XSF6) on Reunion Island, the in situ measurements at America Samoa (SMO) and the collocated satellite measurements (Michelson Interferometer for Passive Atmospheric Sounding, MIPAS, and Atmospheric Chemistry Experiment Fourier Transform Spectrometer, ACE-FTS) in the southern tropics. The SF6 annual growth rate from FTIR retrievals is 0.265 ± 0.013 pptv year-1 for 2004-2016, which is slightly weaker than that from the SMO in situ measurements (0.285 ± 0.002 pptv year-1) for the same time period. The SF6 trend in the troposphere from MIPAS and ACE-FTS observations is also close to the ones from the FTIR retrievals and the SMO in situ measurements.

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

PubMed

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

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

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

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

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

Maynooth Optical Aeronomical Facility

NASA Technical Reports Server (NTRS)

Mulligan, Francis J.; Niciejewski, Rick J.

1994-01-01

Ground-based measurements of upper atmospheric parameters, such as temperature and wind velocity, can be made by observing airglow emissions that have a well-defined altitude profile and that are known to be representative of the emitting region. We describe the optical observatory at Maynooth (53.23 deg N, 6.4 deg W) at which two instruments, a Fabry-Perot interferometer and a Fourier transform spectrometer, are used to record atmospheric airglow emissions in Ireland at visible and near-infrared wavelengths, respectively. Descriptions of the instruments, data acquisition, and analysis procedures are provided, together with some sample results.

Multi-year comparisons of ground-based and space-borne Fourier transform spectrometers in the high Arctic between 2006 and 2013

NASA Astrophysics Data System (ADS)

Griffin, Debora; Walker, Kaley A.; Conway, Stephanie; Kolonjari, Felicia; Strong, Kimberly; Batchelor, Rebecca; Boone, Chris D.; Dan, Lin; Drummond, James R.; Fogal, Pierre F.; Fu, Dejian; Lindenmaier, Rodica; Manney, Gloria L.; Weaver, Dan

2017-09-01

This paper presents 8 years (2006-2013) of measurements obtained from Fourier transform spectrometers (FTSs) in the high Arctic at the Polar Environment Atmospheric Research Laboratory (PEARL; 80.05° N, 86.42° W). These measurements were taken as part of the Canadian Arctic ACE (Atmospheric Chemistry Experiment) validation campaigns that have been carried out since 2004 during the polar sunrise period (from mid-February to mid-April). Each spring, two ground-based FTSs were used to measure total and partial columns of HF, O3, and trace gases that impact O3 depletion, namely, HCl and HNO3. Additionally, some tropospheric greenhouse gases and pollutant species were measured, namely CH4, N2O, CO, and C2H6. During the same time period, the satellite-based ACE-FTS made measurements near Eureka and provided profiles of the same trace gases. Comparisons have been carried out between the measurements from the Portable Atmospheric Research Interferometric Spectrometer for the InfraRed (PARIS-IR) and the co-located high-resolution Bruker 125HR FTS, as well as with the latest version of the ACE-FTS retrievals (v3.5). The total column comparison between the two co-located ground-based FTSs, PARIS-IR and Bruker 125HR, found very good agreement for most of these species (except HF), with differences well below the estimated uncertainties ( ≤ 6  %) and with high correlations (R ≥ 0. 8). Partial columns have been used for the ground-based to space-borne comparison, with coincident measurements selected based on time, distance, and scaled potential vorticity (sPV). The comparisons of the ground-based measurements with ACE-FTS show good agreement in the partial columns for most species within 6  % (except for C2H6 and PARIS-IR HF), which is consistent with the total retrieval uncertainty of the ground-based instruments. The correlation coefficients (R) of the partial column comparisons for all eight species range from approximately 0.75 to 0.95. The comparisons show no notable increases of the mean differences over these 8 years, indicating the consistency of these datasets and suggesting that the space-borne ACE-FTS measurements have been stable over this period. In addition, changes in the amounts of these trace gases during springtime between 2006 and 2013 are presented and discussed. Increased O3 (0. 9  %  yr-1), HCl (1. 7  %  yr-1), HF (3. 8  %  yr-1), CH4 (0.5  % yr-1), and C2H6 (2. 3 % yr-1, 2009-2013) have been found with the PARIS-IR dataset, the longer of the two ground-based records.

Discrete Fourier Transform in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Fourier Deconvolution Methods for Resolution Enhancement in Continuous-Wave EPR Spectroscopy.

PubMed

Reed, George H; Poyner, Russell R

2015-01-01

An overview of resolution enhancement of conventional, field-swept, continuous-wave electron paramagnetic resonance spectra using Fourier transform-based deconvolution methods is presented. Basic steps that are involved in resolution enhancement of calculated spectra using an implementation based on complex discrete Fourier transform algorithms are illustrated. Advantages and limitations of the method are discussed. An application to an experimentally obtained spectrum is provided to illustrate the power of the method for resolving overlapped transitions. © 2015 Elsevier Inc. All rights reserved.

Fourier transform infrared emission spectra of MnH and MnD

NASA Astrophysics Data System (ADS)

Gordon, Iouli E.; Appadoo, Dominique R. T.; Shayesteh, Alireza; Walker, Kaley A.; Bernath, Peter F.

2005-01-01

Fourier transform infrared emission spectra of MnH and MnD were observed in the ground X7Σ + electronic state. The vibration-rotation bands from v = 1 → 0 to v = 3 → 2 for MnH and from v = 1 → 0 to v = 4 → 3 for MnD were recorded at an instrumental resolution of 0.0085 cm -1. Spectroscopic constants were determined for each vibrational level and equilibrium constants were found from a Dunham-type fit. The equilibrium vibrational constant ( ωe) for MnH was found to be 1546.84518(65) cm -1, the equilibrium rotational constant ( Be) is 5.6856789(103) cm -1 and the eqilibrium bond distance ( re) was determined to be 1.7308601(47) Å.

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

ERIC Educational Resources Information Center

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

Adsorption properties of biomass-based activated carbon prepared with spent coffee grounds and pomelo skin by phosphoric acid activation

NASA Astrophysics Data System (ADS)

Ma, Xiaodong; Ouyang, Feng

2013-03-01

Activated carbon prepared from spent coffee grounds and pomelo skin by phosphoric acid activation had been employed as the adsorbent for ethylene and n-butane at room temperature. Prepared activated carbon was characterized by means of nitrogen adsorption-desorption, X-ray powder diffraction, scanning electron microscope and Fourier transform infrared spectroscope. It was confirmed that pore structure played an important role during the adsorption testes. Adsorption isotherms of ethylene and n-butane fitted well with Langmuir equation. The prepared samples owned better adsorption capacity for n-butane than commercial activated carbon. Isosteric heats of adsorptions at different coverage were calculated through Clausius-Clapeyron equation. Micropore filling effect was explained in a thermodynamic way.

Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability

NASA Technical Reports Server (NTRS)

Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.

2007-01-01

The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.

Accurate measurements of solar spectral irradiance between 4000-10000 cm-1

NASA Astrophysics Data System (ADS)

Elsey, J.; Coleman, M. D.; Gardiner, T.; Shine, K. P.

2017-12-01

The near-infrared solar spectral irradiance (SSI) is an important input into simulations of weather and climate; the distribution of energy throughout this region of the spectrum influences atmospheric heating rates and the global hydrological cycle through absorption and scattering by water vapour. Current measurements by a mixture of ground-based and space-based instruments show differences of around 10% in the 4000-7000 cm-1 region, with no resolution to this controversy in sight. This work presents observations of SSI taken using a ground-based Fourier Transform spectrometer between 4000-10000 cm-1 at a field site in Camborne, UK, with particular focus on a rigorously defined uncertainty budget. While there is good agreement between this work and the commonly-used ATLAS3 spectrum between 7000-10000 cm-1, the SSI is systematically lower by 10% than ATLAS3 between 4000-7000 cm-1, with no overlap within the k = 2 measurement uncertainties.

Molecular Isotopic Distribution Analysis (MIDAs) with Adjustable Mass Accuracy

NASA Astrophysics Data System (ADS)

Alves, Gelio; Ogurtsov, Aleksey Y.; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

Molecular Isotopic Distribution Analysis (MIDAs) with adjustable mass accuracy.

PubMed

Alves, Gelio; Ogurtsov, Aleksey Y; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

Wavelet based detection of manatee vocalizations

NASA Astrophysics Data System (ADS)

Gur, Berke M.; Niezrecki, Christopher

2005-04-01

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of watercraft collisions in Florida's coastal waterways. Several boater warning systems, based upon manatee vocalizations, have been proposed to reduce the number of collisions. Three detection methods based on the Fourier transform (threshold, harmonic content and autocorrelation methods) were previously suggested and tested. In the last decade, the wavelet transform has emerged as an alternative to the Fourier transform and has been successfully applied in various fields of science and engineering including the acoustic detection of dolphin vocalizations. As of yet, no prior research has been conducted in analyzing manatee vocalizations using the wavelet transform. Within this study, the wavelet transform is used as an alternative to the Fourier transform in detecting manatee vocalizations. The wavelet coefficients are analyzed and tested against a specified criterion to determine the existence of a manatee call. The performance of the method presented is tested on the same data previously used in the prior studies, and the results are compared. Preliminary results indicate that using the wavelet transform as a signal processing technique to detect manatee vocalizations shows great promise.

Investigation of Tropospheric Pollutants and Stratospheric Ozone Using Infrared Fourier Transform Spectrometers from the Ground, Space and Balloons

NASA Astrophysics Data System (ADS)

Griffin, Debora

This thesis focusses on transport and composition of boreal fire plumes, evolution of trace gases in the Arctic, multi-year comparisons of ground-based and satellite-borne instruments, and depletion of Arctic ozone. Two similar Fourier Transform Spectrometer (FTS) instruments were utilized: (1) the ground-based and balloon-borne Portable Atmospheric Research Interferometric Spectrometer for the InfraRed (PARIS-IR) and (2) the space-borne Atmospheric Chemistry Experiment (ACE) FTS. Additional datasets, from other satellite and ground-based instruments, as well as Chemical Transport Models (CTMs) complemented the analysis. Transport and composition of boreal fire plumes were analysed with PARIS-IR measurements taken in Halifax, Nova Scotia. This study analysed the retrievals of different FTSs and investigated transport and composition of a smoke plume utilizing various models. The CO retrievals of three different FTSs (PARIS-IR, DA8, and IASI) were consistent and detected a smoke plume between 19 and 21 July 2011. These measurements were similar to the concentrations computed by GEOS-Chem ( 3% for CO and 8% for C2H6). Multi-year comparisons (2006-2013) of ground-based and satellite-borne FTSs near Eureka, Nunavut were carried out utilizing measurements from PARIS-IR, the Bruker 125HR and ACEFTS. The mean and interannual differences between the datasets were investigated for eight species (ozone, HCl, HNO3, HF, CH4, N2O, CO, and C2H6) and good agreement between these instruments was found. Furthermore, the evolution of the eight gases was investigated and increasing ozone, HCl, HF, CH4 and C2H6 were found. Springtime Arctic ozone depletion was studied, where six different methods to estimate ozone depletion were evaluated using the ACE-FTS dataset. It was shown that CH4, N2O, HF, and CCl2F2 are suitable tracers to estimate the ozone loss. The loss estimates (mixing ratio and partial column) are consistent for all six methods. Finally, PARIS-IR was prepared for a balloon-borne measurement campaign and a new suntracker for these measurements was designed and tested. The balloon was launched in September 2015. The suntracker performed with a +/-0.04° accuracy. From the balloon-borne sunset spectra, an ozone profile was retrieved and is consistent with measurements from a nearby ozonesonde within approximately 10 %.

Bright Points and Subflares in UV Lines and in X-Rays

NASA Technical Reports Server (NTRS)

Rovira, M.; Schmieder, B.; Demoulin, P.; Simnett, G. M.; Hagyard, M. J.; Reichmann, E.; Tandberg-Hanssen, E.

1998-01-01

We have analysed an active region which was observed in Halpha (MSDP), UV lines (SMM/UVSP), and in X rays (SMM/HXIS). In this active region there were only a few subflares and many small bright points visible in UV and in X rays. Using an extrapolation based on the Fourier transform we have computed magnetic field lines connecting different photospheric magnetic polarities from ground-based magnetograms. Along the magnetic inversion lines we find 2 different zones: 1. a high shear region (less than 70 degrees) where subflares occur 2. a low shear region along the magnetic inversion line where UV bright points are observed.

Gravity data inversion to determine 3D topographycal density contrast of Banten area, Indonesia based on fast Fourier transform

NASA Astrophysics Data System (ADS)

Windhari, Ayuty; Handayani, Gunawan

2015-04-01

The 3D inversion gravity anomaly to estimate topographical density using a matlab source code from gridded data provided by Parker Oldenburg algorithm based on fast Fourier transform was computed. We extend and improved the source code of 3DINVERT.M invented by Gomez Ortiz and Agarwal (2005) using the relationship between Fourier transform of the gravity anomaly and the sum of the Fourier transform from the topography density. We gave density contrast between the two media to apply the inversion. FFT routine was implemented to construct amplitude spectrum to the given mean depth. The results were presented as new graphics of inverted topography density, the gravity anomaly due to the inverted topography and the difference between the input gravity data and the computed ones. It terminates when the RMS error is lower than pre-assigned value used as convergence criterion or until maximum of iterations is reached. As an example, we used the matlab program on gravity data of Banten region, Indonesia.

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 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.

Empirical transfer functions for stations in the Central California seismological network

USGS Publications Warehouse

Bakun, W.H.; Dratler, Jay

1976-01-01

A sequence of calibration signals composed of a station identification code, a transient from the release of the seismometer mass at rest from a known displacement from the equilibrium position, and a transient from a known step in voltage to the amplifier input are generated by the automatic daily calibration system (ADCS) now operational in the U.S. Geological Survey central California seismographic network. Documentation of a sequence of interactive programs to compute, from the calibration data, the complex transfer functions for the seismographic system (ground motion through digitizer) the electronics (amplifier through digitizer), and the seismometer alone are presented. The analysis utilizes the Fourier transform technique originally suggested by Espinosa et al (1962). Section I is a general description of seismographic calibration. Section II contrasts the 'Fourier transform' and the 'least-squares' techniques for analyzing transient calibration signals. Theoretical consideration for the Fourier transform technique used here are described in Section III. Section IV is a detailed description of the sequence of calibration signals generated by the ADCS. Section V is a brief 'cookbook description' of the calibration programs; Section VI contains a detailed sample program execution. Section VII suggests the uses of the resultant empirical transfer functions. Supplemental interactive programs by which smooth response functions, suitable for reducing seismic data to ground motion, are also documented in Section VII. Appendices A and B contain complete listings of the Fortran source Codes while Appendix C is an update containing preliminary results obtained from an analysis of some of the calibration signals from stations in the seismographic network near Oroville, California.

Rovibrational intensities and electric dipole moment function of the X2 Pi hydroxyl radical

NASA Technical Reports Server (NTRS)

Chackerian, C., Jr.; Goorvitch, D.; Benidar, A.; Farrenq, R.; Guelachvili, G.; Martin, P. M.; Abrams, M. C.; Davis, S. P.

1992-01-01

Recent work aimed at determining the absolute rovibrational transition intensities for the ground electronic state of the hydroxyl radical is reviewed. Two new sets of Fourier transform emission spectra of OH are described which were recorded at the University of Paris and at the Kitt Peak National Solar Observatory.

Innovative design method of automobile profile based on Fourier descriptor

NASA Astrophysics Data System (ADS)

Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei

2017-10-01

Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

PubMed

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

2007-09-01

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

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...

Dynamic analysis of slab track on multi-layered transversely isotropic saturated soils subjected to train loads

NASA Astrophysics Data System (ADS)

Zhan, Yongxiang; Yao, Hailin; Lu, Zheng; Yu, Dongming

2014-12-01

The dynamic responses of a slab track on transversely isotropic saturated soils subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate the rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground systems are solved using the double Fourier transform, and the dynamic responses in the time domain are obtained by the inverse Fourier transform. The results show that a train load with high velocity will generate a larger response in transversely isotropic saturated soil than the lower velocity load, and special attention should be paid on the pore pressure in the vicinity of the ground surface. The anisotropic parameters of a surface soil layer will have greater influence on the displacement and excess pore water pressure than those of the subsoil layer. The traditional design method taking ground soil as homogeneous isotropic soil is unsafe for the case of RE < 1 and RG < 1, so a transversely isotropic foundation model is of great significance to the design for high train velocities.

Fourier transform synchrotron spectroscopy of torsional and CO-stretching bands of CH 3 17 OH

NASA Astrophysics Data System (ADS)

Moruzzi, G.; Murphy, R. J.; Vos, J.; Lees, R. M.; Predoi-Cross, A.; Billinghurst, B. E.

2011-07-01

The Fourier transform spectrum of the CH 317OH isotopologue of methanol has been recorded in the 65-1200 cm -1 spectral region at a resolution of 0.00096 cm -1 using synchrotron source radiation at the Canadian Light Source. Here we present an extension to higher torsional states of our investigation of the torsion-rotation transitions within the small-amplitude vibrational ground state, now including assignments of more than 16 500 lines involving quantum numbers in the ranges v t ⩽ 3, J ⩽ 30 and | K| ⩽ 12, as well as a study of the strong CO-stretching band centered at 1020 cm -1. Energy term values have been determined for assigned ground and CO-stretching levels by use of the Ritz program, and have been fitted to series expansions in powers of J( J + 1) to determine substate origins and effective B values. Several Fermi anharmonic and Coriolis level-crossing resonances coupling the CO stretch with high torsional ground-state levels have been identified and characterized. The study is motivated by astrophysical applications, with a principal aim being the compilation of an extensive set of energy term values to permit prediction of astronomically observable sub-millimetre transitions to within an uncertainty of a few MHz.

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

NASA Astrophysics Data System (ADS)

Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.

Estimating ionospheric currents by inversion from ground-based geomagnetic data and calculating geoelectric fields for studies of geomagnetically induced currents

NASA Astrophysics Data System (ADS)

de Villiers, J. S.; Pirjola, R. J.; Cilliers, P. J.

2016-09-01

This research focuses on the inversion of geomagnetic variation field measurements to obtain the source currents in the ionosphere and magnetosphere, and to determine the geoelectric fields at the Earth's surface. During geomagnetic storms, the geoelectric fields create geomagnetically induced currents (GIC) in power networks. These GIC may disturb the operation of power systems, cause damage to power transformers, and even result in power blackouts. In this model, line currents running east-west along given latitudes are postulated to exist at a certain height above the Earth's surface. This physical arrangement results in the fields on the ground being composed of a zero magnetic east component and a nonzero electric east component. The line current parameters are estimated by inverting Fourier integrals (over wavenumber) of elementary geomagnetic fields using the Levenberg-Marquardt technique. The output parameters of the model are the ionospheric current strength and the geoelectric east component at the Earth's surface. A conductivity profile of the Earth is adapted from a shallow layered-Earth model for one observatory, together with a deep-layer model derived from satellite observations. This profile is used to obtain the ground surface impedance and therefore the reflection coefficient in the integrals. The inputs for the model are a spectrum of the geomagnetic data for 31 May 2013. The output parameters of the model are spectrums of the ionospheric current strength and of the surface geoelectric field. The inverse Fourier transforms of these spectra provide the time variations on the same day. The geoelectric field data can be used as a proxy for GIC in the prediction of GIC for power utilities. The current strength data can assist in the interpretation of upstream solar wind behaviour.

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

Fourier transform infrared spectroscopy for Kona coffee authentication.

PubMed

Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X

2009-06-01

Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations.

Determination of the altitude of the nitric acid layer from very high resolution ground-based IR solar spectra

NASA Technical Reports Server (NTRS)

Blatherwick, R. D.; Murcray, F. J.; Murcray, D. G.; Locker, M. H.

1991-01-01

A ground-based solar spectrum at a spectral resolution of about 0.002/cm is used to determine the altitude of the HNO3 layer. The 870/cm spectral region, which is essentially free from absorptions from other species, is employed. The data were obtained with the University of Denver 2.5-m maximum path difference Fourier Transform interferometer spectrometer system. A set of 13 HNO3 vertical profiles were used in the analysis. The best fit obtained for the 'starting' profile (which is centered at 24 km), and the best fit for the profile centered at 26 km are shown. For displacements of greater than 2 km, the discrepancy between the synthetic and observed spectra becomes readily discernible by inspection of the spectra. It is shown that the 'best fit' rms residuals are quite sensitive to the assumed altitude of the HNO3 layer.

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

ERIC Educational Resources Information Center

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

MRS3D: 3D Spherical Wavelet Transform on the Sphere

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2011-12-01

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

Production and physicochemical properties of carboxymethyl cellulose films enriched with spent coffee grounds polysaccharides.

PubMed

Ballesteros, Lina F; Cerqueira, Miguel A; Teixeira, José A; Mussatto, Solange I

2018-01-01

Extracts rich in polysaccharides were obtained by alkali pretreatment (PA) or autohydrolysis (PB) of spent coffee grounds, and incorporated into a carboxymethyl cellulose (CMC)-based film aiming at the development of bio-based films with new functionalities. Different concentrations of PA or PB (up to 0.20% w/v) were added to the CMC-based film and the physicochemical properties of the final films were determined. Scanning electron microscopy, Fourier-transform infrared spectroscopy, X-ray diffraction, thermogravimetric analysis, as well as determinations of optical and mechanical properties, moisture content, solubility in water, water vapor permeability, contact angle and sorption isotherms were performed. The addition of PA or PB resulted in important changes in the properties of the CMC-based film, mainly in color and opacity. The polysaccharides incorporation significantly improved the light barrier of the film and provided an enhancement or at least a preservation in the physicochemical properties. Copyright © 2017 Elsevier B.V. All rights reserved.

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

DTIC Science & Technology

2014-10-16

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

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.

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.

Formulation of the rotational transformation of wave fields and their application to digital holography.

PubMed

Matsushima, Kyoji

2008-07-01

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematically satisfies the Helmholtz equation. Moreover, to verify the formulation and its usefulness in wave optics, it is also demonstrated that the transformation makes it possible to reconstruct an image on arbitrarily tilted planes from a wave field captured experimentally by using digital holography.

Object Classification Based on Analysis of Spectral Characteristics of Seismic Signal Envelopes

NASA Astrophysics Data System (ADS)

Morozov, Yu. V.; Spektor, A. A.

2017-11-01

A method for classifying moving objects having a seismic effect on the ground surface is proposed which is based on statistical analysis of the envelopes of received signals. The values of the components of the amplitude spectrum of the envelopes obtained applying Hilbert and Fourier transforms are used as classification criteria. Examples illustrating the statistical properties of spectra and the operation of the seismic classifier are given for an ensemble of objects of four classes (person, group of people, large animal, vehicle). It is shown that the computational procedures for processing seismic signals are quite simple and can therefore be used in real-time systems with modest requirements for computational resources.

Investigations of the functional states of dendritic cells under different conditioned microenvironments by Fourier transformed infrared spectroscopy.

PubMed

Dong, Rong; Long, Jinhua; Xu, Xiaoli; Zhang, Chunlin; Wen, Zongyao; Li, Long; Yao, Weijuan; Zeng, Zhu

2014-01-10

Dendritic cells are potent and specialized antigen presenting cells, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. The dendritic cell-based vaccination against cancer has been clinically achieved promising successes. But there are still many challenges in its clinical application, especially for how to identify the functional states. The CD14+ monocytes were isolated from human peripheral blood after plastic adherence and purified to approximately 98% with cocktail immunomagnetic beads. The immature dendritic cells and mature dendritic cells were induced by traditional protocols. The resulting dendritic cells were cocultured with normal cells and cancer cells. The functional state of dendritic cells including immature dendritic cells (imDCs) and mature dendritic cells (mDCs) under different conditioned microenvironments were investigated by Fourier transformed infrared spectroscopy (FTIR) and molecular biological methods. The results of Fourier transformed infrared spectroscopy showed that the gene transcription activity and energy states of dendritic cells were specifically suppressed by tumor cells (P < 0.05 or 0.01). The expression levels of NF-kappa B (NF-κB) in dendritic cells were also specifically inhibited by tumor-derived factors (P < 0.05 or 0.01). Moreover, the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were closely correlated with the expression levels of NF-κB (R2:0.69 and R2:0.81, respectively). Our results confirmed that the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were positively correlated with the expression levels of NF-κB, suggesting that Fourier transformed infrared spectroscopy technology could be clinically applied to identify the functional states of dendritic cell when performing dendritic cell-based vaccination. It's significant for the simplification and standardization of dendritic cell-based vaccination clinical preparation protocols.

Removal of the Gibbs phenomenon and its application to fast-Fourier-transform-based mode solvers.

PubMed

Wangüemert-Pérez, J G; Godoy-Rubio, R; Ortega-Moñux, A; Molina-Fernández, I

2007-12-01

A simple strategy for accurately recovering discontinuous functions from their Fourier series coefficients is presented. The aim of the proposed approach, named spectrum splitting (SS), is to remove the Gibbs phenomenon by making use of signal-filtering-based concepts and some properties of the Fourier series. While the technique can be used in a vast range of situations, it is particularly suitable for being incorporated into fast-Fourier-transform-based electromagnetic mode solvers (FFT-MSs), which are known to suffer from very poor convergence rates when applied to situations where the field distributions are highly discontinuous (e.g., silicon-on-insulator photonic wires). The resultant method, SS-FFT-MS, is exhaustively tested under the assumption of a simplified one-dimensional model, clearly showing a dramatic improvement of the convergence rates with respect to the original FFT-based methods.

Validation of ACE-FTS measurements of CFC-11, CFC-12, and HCFC-22 using ground-based FTIR spectrometers

NASA Astrophysics Data System (ADS)

Kolonjari, F.; Walker, K. A.; Mahieu, E.; Batchelor, R. L.; Bernath, P. F.; Boone, C.; Conway, S. A.; Dan, L.; Griffin, D.; Harrett, A.; Kasai, Y.; Kagawa, A.; Lindenmaier, R.; Strong, K.; Whaley, C.

2013-12-01

Satellite datasets can be an effective global monitoring tool for long-lived compounds in the atmosphere. The Atmospheric Chemistry Experiment (ACE) is a mission on-board the Canadian satellite SCISAT-1. The primary instrument on SCISAT-1 is a high-resolution infrared Fourier transform spectrometer (ACE-FTS) which is capable of measuring a range of gases including key chlorofluorocarbon (CFC) and hydrochlorofluorocarbon (HCFC) species. These families of species are of interest because of their significant contribution to anthropogenic ozone depletion and to global warming. To assess the quality of data derived from satellite measurements, validation using other data sources is essential. Ground-based Fourier transform infrared (FTIR) spectrometers are particularly useful for this purpose. In this study, five FTIR spectrometers located at four sites around the world are used to validate the CFC-11 (CCl3F), CFC-12 (CCl2F2), and HCFC-22 (CHClF2) retrieved profiles from ACE-FTS measurements. These species are related because HCFC-22 was the primary replacement for CFC-11 and CFC-12 in refrigerant and propellant applications. The FTIR spectrometers used in this study record solar absorption spectra at Eureka (Canada), Jungfraujoch (Switzerland), Poker Flat (USA), and Toronto (Canada). The retrieval of CFC-11, CFC-12, and HCFC-22 are not standard products for many of these instruments, and as such, a harmonization of retrieval parameters between the sites has been conducted. The retrievals of these species from the FTIR spectra are sensitive from the surface to approximately 20 km, while the ACE-FTS profiles extend from approximately 6 to 30 km. For each site, partial column comparisons between coincident measurements of the three species and a validation of the observed trends will be discussed.

Simultaneous retrieval of atmospheric CO2 and light path modification from space-based spectroscopic observations of greenhouse gases: methodology and application to GOSAT measurements over TCCON sites.

PubMed

Oshchepkov, Sergey; Bril, Andrey; Yokota, Tatsuya; Yoshida, Yukio; Blumenstock, Thomas; Deutscher, Nicholas M; Dohe, Susanne; Macatangay, Ronald; Morino, Isamu; Notholt, Justus; Rettinger, Markus; Petri, Christof; Schneider, Matthias; Sussman, Ralf; Uchino, Osamu; Velazco, Voltaire; Wunch, Debra; Belikov, Dmitry

2013-02-20

This paper presents an improved photon path length probability density function method that permits simultaneous retrievals of column-average greenhouse gas mole fractions and light path modifications through the atmosphere when processing high-resolution radiance spectra acquired from space. We primarily describe the methodology and retrieval setup and then apply them to the processing of spectra measured by the Greenhouse gases Observing SATellite (GOSAT). We have demonstrated substantial improvements of the data processing with simultaneous carbon dioxide and light path retrievals and reasonable agreement of the satellite-based retrievals against ground-based Fourier transform spectrometer measurements provided by the Total Carbon Column Observing Network (TCCON).

Infrared Fourier spectrometer for laboratory use and for astronomical studies from aircraft and ground-based telescopes

NASA Technical Reports Server (NTRS)

Larson, H. P.; Fink, U.

1975-01-01

A portable, versatile, IR Fourier spectrometer is described that provides 0.5 per cm spectral resolution in the 0.87-5.6-micron region. This spectrometer is employed in a varied program of astronomical observations from ground-based telescopes and from the NASA 91.5-cm airborne IR telescope. A number of spectral results are presented to illustrate the performance of this spectrometer in astronomical applications.

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.

Unsupervised malaria parasite detection based on phase spectrum.

PubMed

Fang, Yuming; Xiong, Wei; Lin, Weisi; Chen, Zhenzhong

2011-01-01

In this paper, we propose a novel method for malaria parasite detection based on phase spectrum. The method first obtains the amplitude spectrum and phase spectrum for blood smear images through Quaternion Fourier Transform (QFT). Then it gets the reconstructed image based on Inverse Quaternion Fourier transform (IQFT) on a constant amplitude spectrum and the original phase spectrum. The malaria parasite areas can be detected easily from the reconstructed blood smear images. Extensive experiments have demonstrated the effectiveness of this novel method.

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.

Time domain analysis of thin-wire antennas over lossy ground using the reflection-coefficient approximation

NASA Astrophysics Data System (ADS)

FernáNdez Pantoja, M.; Yarovoy, A. G.; Rubio Bretones, A.; GonzáLez GarcíA, S.

2009-12-01

This paper presents a procedure to extend the methods of moments in time domain for the transient analysis of thin-wire antennas to include those cases where the antennas are located over a lossy half-space. This extended technique is based on the reflection coefficient (RC) approach, which approximates the fields incident on the ground interface as plane waves and calculates the time domain RC using the inverse Fourier transform of Fresnel equations. The implementation presented in this paper uses general expressions for the RC which extend its range of applicability to lossy grounds, and is proven to be accurate and fast for antennas located not too near to the ground. The resulting general purpose procedure, able to treat arbitrarily oriented thin-wire antennas, is appropriate for all kind of half-spaces, including lossy cases, and it has turned out to be as computationally fast solving the problem of an arbitrary ground as dealing with a perfect electric conductor ground plane. Results show a numerical validation of the method for different half-spaces, paying special attention to the influence of the antenna to ground distance in the accuracy of the results.

Estimation of phase derivatives using discrete chirp-Fourier-transform-based method.

PubMed

Gorthi, Sai Siva; Rastogi, Pramod

2009-08-15

Estimation of phase derivatives is an important task in many interferometric measurements in optical metrology. This Letter introduces a method based on discrete chirp-Fourier transform for accurate and direct estimation of phase derivatives, even in the presence of noise. The method is introduced in the context of the analysis of reconstructed interference fields in digital holographic interferometry. We present simulation and experimental results demonstrating the utility of the proposed method.

Computing the Power-Density Spectrum for an Engineering Model

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1982-01-01

Computer program for calculating of power-density spectrum (PDS) from data base generated by Advanced Continuous Simulation Language (ACSL) uses algorithm that employs fast Fourier transform (FFT) to calculate PDS of variable. Accomplished by first estimating autocovariance function of variable and then taking FFT of smoothed autocovariance function to obtain PDS. Fast-Fourier-transform technique conserves computer resources.

Propagation Characteristics Of Weakly Guiding Optical Fibers

NASA Technical Reports Server (NTRS)

Manshadi, Farzin

1992-01-01

Report discusses electromagnetic propagation characteristics of weakly guiding optical-fiber structures having complicated shapes with cross-sectional dimensions of order of wavelength. Coupling, power-dividing, and transition dielectric-waveguide structures analyzed. Basic data computed by scalar-wave, fast-Fourier-transform (SW-FFT) technique, based on numerical solution of scalar version of wave equation by forward-marching fast-Fourier-transform method.

Fourier transform magnitudes are unique pattern recognition templates.

PubMed

Gardenier, P H; McCallum, B C; Bates, R H

1986-01-01

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.

Digital watermarking algorithm research of color images based on quaternion Fourier transform

NASA Astrophysics Data System (ADS)

An, Mali; Wang, Weijiang; Zhao, Zhen

2013-10-01

A watermarking algorithm of color images based on the quaternion Fourier Transform (QFFT) and improved quantization index algorithm (QIM) is proposed in this paper. The original image is transformed by QFFT, the watermark image is processed by compression and quantization coding, and then the processed watermark image is embedded into the components of the transformed original image. It achieves embedding and blind extraction of the watermark image. The experimental results show that the watermarking algorithm based on the improved QIM algorithm with distortion compensation achieves a good tradeoff between invisibility and robustness, and better robustness for the attacks of Gaussian noises, salt and pepper noises, JPEG compression, cropping, filtering and image enhancement than the traditional QIM algorithm.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

PubMed

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

In situ CF3 Detection in Low Pressure Inductive Discharges by Fourier Transform Infrared Spectroscopy

NASA Technical Reports Server (NTRS)

Kim, J. S.; Cappelli, M. A.; Sharma, S. P.; Arnold, J. O. (Technical Monitor)

1998-01-01

The detection of CF(x) (x=1-3) radicals in low pressure discharges using source gases such as CF4 and CHF3 is of importance to the understanding of their chemical structure and relevance in plasma based etching processes. These radicals are known to contribute to the formation of fluorocarbon polymer films, which affect the selectivity and anisotropy of etching. In this study, we present preliminary results of the quantitative measurement of trifluoromethyl radicals, CF3, in low pressure discharges. The discharge studied here is an inductively (transformer) coupled plasma (ICP) source in the GEC reference cell, operating on pure CF4 at pressures ranging from 10 - 100 mTorr, This plasma source generates higher electron number densities at lower operating pressures than obtainable with the parallel-plate capacitively coupled version of the GEC reference cell. Also, this expanded operating regime is more relevant to new generations of industrial plasma reactors being used by the microelectronics industry. Fourier transform infrared (FTIR) spectroscopy is employed to observe the absorption band of CF3 radicals in the electronic ground state X2Al in the region of 1233-1270/cm. The spectrometer is equipped with a high sensitivity HgCdTe (MCT) detector and has a fixed resolution of 0.125/cm. The CF3 concentrations are measured for a range of operating pressures and discharge power levels.

Methods for performing fast discrete curvelet transforms of data

DOEpatents

Candes, Emmanuel; Donoho, David; Demanet, Laurent

2010-11-23

Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while another is based on the wrapping of specially selected Fourier samples. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Both implementations are fast in the sense that they run in about O(n.sup.2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n.sup.3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Theory of Wavelet-Based Coarse-Graining Hierarchies for Molecular Dynamics

DTIC Science & Technology

2017-04-01

resolution. ............................................... 15 Fig. 6 Fourier transform of the y-component of 1,000 atoms in crystalline PE (100,800 atoms...of magnitude of optimal representation. . 16 Fig. 7 Top row: Fourier transform of the y-component of a 100,800 atom crystalline PE sampled at 1 fs. 3... transform of the z-component of alanine dipeptide in vacuum excluding zero frequency to allow detail at other frequencies. MD at 500 K and 1 atm. Left

Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

Discrimination between landmine and mine-like targets using wavelets and spectral analysis

NASA Astrophysics Data System (ADS)

Mohana, Mahmoud A.; Abbas, Abbas M.; Gomaa, Mohamed L.; Ebrahim, Shereen M.

2013-06-01

Landmine is an explosive apparatus hidden in or on the ground, which blows up when a person or vehicle passes over it. Egypt is one of the countries suffering due to the unexploded ordnance (UXO). Around 2 million UXO are present in the Egyptian soil especially at Al-Alameen province, north of the western desert. Detection of buried landmines is a problem of military and humanitarian importance. Ground penetrating radar (GPR) is a powerful and non-destructive geophysical approach with a wide range of advantages in the field of landmine inspection. In the present paper, we apply different simulation models with Vivaldi antenna and mine-like targets by using the CST Microwave studio program. The field work is carried out by using a GPR device of model SIR 2000 from GSSI (Geophysical Survey Systems Incorporation) connected to 900 MHz antenna where the targets were buried in sand soil. Depending on the fact that the receiving powers (reflected, refracted and scattered) from the different materials are different, we study the spectral power densities for the received power from the different targets. The techniques used in this study are: direct fast Fourier transform, short time Fourier transform (spectrogram), wavelets transform and denoising techniques. Our results ought to be considered as finger prints for different scanned targets during this work. So we can discriminate between landmines and mine-like targets.

Prediction and measurements of vibrations from a railway track lying on a peaty ground

NASA Astrophysics Data System (ADS)

Picoux, B.; Rotinat, R.; Regoin, J. P.; Le Houédec, D.

2003-10-01

This paper introduces a two-dimensional model for the response of the ground surface due to vibrations generated by a railway traffic. A semi-analytical wave propagation model is introduced which is subjected to a set of harmonic moving loads and based on a calculation method of the dynamic stiffness matrix of the ground. In order to model a complete railway system, the effect of a simple track model is taken into account including rails, sleepers and ballast especially designed for the study of low vibration frequencies. The priority has been given to a simple formulation based on the principle of spatial Fourier transforms compatible with good numerical efficiency and yet providing quick solutions. In addition, in situ measurements for a soft soil near a railway track were carried out and will be used to validate the numerical implementation. The numerical and experimental results constitute a significant body of useful data to, on the one hand, characterize the response of the environment of tracks and, on the other hand, appreciate the importance of the speed and weight on the behaviour of the structure.

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)

Simulation of Ground Winds Time Series for the NASA Crew Launch Vehicle (CLV)

NASA Technical Reports Server (NTRS)

Adelfang, Stanley I.

2008-01-01

Simulation of wind time series based on power spectrum density (PSD) and spectral coherence models for ground wind turbulence is described. The wind models, originally developed for the Shuttle program, are based on wind measurements at the NASA 150-m meteorological tower at Cape Canaveral, FL. The current application is for the design and/or protection of the CLV from wind effects during on-pad exposure during periods from as long as days prior to launch, to seconds or minutes just prior to launch and seconds after launch. The evaluation of vehicle response to wind will influence the design and operation of constraint systems for support of the on-pad vehicle. Longitudinal and lateral wind component time series are simulated at critical vehicle locations. The PSD model for wind turbulence is a function of mean wind speed, elevation and temporal frequency. Integration of the PSD equation over a selected frequency range yields the variance of the time series to be simulated. The square root of the PSD defines a low-pass filter that is applied to adjust the components of the Fast Fourier Transform (FFT) of Gaussian white noise. The first simulated time series near the top of the launch vehicle is the inverse transform of the adjusted FFT. Simulation of the wind component time series at the nearest adjacent location (and all other succeeding next nearest locations) is based on a model for the coherence between winds at two locations as a function of frequency and separation distance, where the adjacent locations are separated vertically and/or horizontally. The coherence function is used to calculate a coherence weighted FFT of the wind at the next nearest location, given the FFT of the simulated time series at the previous location and the essentially incoherent FFT of the wind at the selected location derived a priori from the PSD model. The simulated time series at each adjacent location is the inverse Fourier transform of the coherence weighted FFT. For a selected design case, the equations, the process and the simulated time series at multiple vehicle stations are presented.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

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.

Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

2018-05-01

In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

Laser and Fourier transform spectroscopy of 7Li88Sr

NASA Astrophysics Data System (ADS)

Schwanke, Erik; Knöckel, Horst; Stein, Alexander; Pashov, Asen; Ospelkaus, Silke; Tiemann, Eberhard

2017-12-01

LiSr was produced in a heat-pipe oven and its thermal emission spectrum around 9300 cm-1 was recorded by a high resolution Fourier transform spectrometer. In addition, selected lines of the spectrum of deeply bound vibrational levels of the {1}2{{{Σ }}}+ and {2}2{{{Σ }}}+ states were studied using laser excitation to facilitate the assignment of the lines. The ground state could be described for {v}{\\prime\\prime }=0 to 2, {N}{\\prime\\prime } up to 105 and the {2}2{{{Σ }}}+ state for {v}{\\prime }=0 up to {N}{\\prime }=68. For both states, Dunham coefficients, spin-rotation parameters and potential energy curves were evaluated. A coupling of the {2}2{{{Σ }}}+ state to the {1}2{{\\Pi }} state was observed, allowing a local description with Dunham coefficients of the {1}2{{\\Pi }} state and an approximate evaluation of the coupling strength.

High-resolution Fourier transform infrared spectroscopy and analysis of the ν12 fundamental band of ethylene- d4

NASA Astrophysics Data System (ADS)

Tan, T. L.; Goh, K. L.; Ong, P. P.; Teo, H. H.

1999-12-01

The Fourier transform infrared (IR) spectrum of the ν12 fundamental band of ethylene- d4 (C 2D 4) has been measured with an unapodized resolution of 0.004 cm -1 in the frequency range of 1030-1130 cm -1. A total of 1340 assigned transitions have been analyzed and fitted using a Watson's A-reduced Hamiltonian in the Ir representation to derive rovibrational constants for the upper state ( v12=1) up to five quartic terms with a standard deviation of 0.00042 cm -1. They represent the most accurate constants for the band thus far. The ground state rovibrational constants were also further improved by a fit of combination-differences from the IR measurements. The relatively unperturbed band was found to be basically A-type with a band centre at 1076.98492±0.00003 cm -1.

Microwave Fourier transform spectroscopy of rotational and rovibrational transitions in the {ν 2}/{ν 4} dyad of silane- 28Si

NASA Astrophysics Data System (ADS)

Oldani, M.; Bauder, A.; Pierre, G.

1986-06-01

Rotational and rovibrational transitions of silane- 28Si in the {ν 2}/{ν 4} dyad have been observed directly with a pulsed microwave Fourier transform spectrometer operating in the 8- to 18-GHz frequency range. Seventeen transitions of the types ν4 ← ν4, ν2 ← ν2, ν2 ← ν4, and ν4 ← ν2 have been observed and assigned. The transitions are generally weaker than those of the vibrational ground state and weaker than the corresponding transitions of methane- d4. The observed microwave transitions have been analyzed in combination with previous high-resolution infrared measurements (G. Pierre, A. Valentin, and L. Henry, Canad. J. Phys. (1986), in press) in a least-squares fit of the vibration-rotation constants t s,s'Ω(K,n Γ) of the {ν 2}/{ν 4}- dyad Hamiltonian.

Super-Resolution for Color Imagery

DTIC Science & Technology

2017-09-01

separately; however, it requires performing the super-resolution computation 3 times. We transform images in the default red, green, blue (RGB) color space...chrominance components based on ARL’s alias-free image upsampling using Fourier-based windowing methods. A reverse transformation is performed on... Transformation from sRGB to CIELAB............................................... 3 Fig. 2 YCbCr mathematical coordinate transformation

Hypercomplex Fourier transforms of color images.

PubMed

Ell, Todd A; Sangwine, Stephen J

2007-01-01

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

NASA Astrophysics Data System (ADS)

Oganesov, Armen; Vahala, George; Vahala, Linda; Soe, Min

2018-04-01

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.

Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.

PubMed

Mendlovic, D; Ozaktas, H M; Lohmann, A W

1994-09-10

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.

Analog 65/130 nm CMOS 5 GHz Sub-Arrays with ROACH-2 FPGA Beamformers for Hybrid Aperture-Array Receivers

DTIC Science & Technology

2017-03-20

sub-array, which is based on all-pass filters (APFs) is realized using 130 nm CMOS technology. Approximate- discrete Fourier transform (a-DFT...fixed beams are directed at known directions [9]. The proposed approximate- discrete Fourier transform (a-DFT) based multi-beamformer [9] yields L...to digital conversion daughter board. occurs in the discrete time domain (in ROACH-2 FPGA platform) following signal digitization (see Figs. 1(d) and

Secret sharing based on quantum Fourier transform

NASA Astrophysics Data System (ADS)

Yang, Wei; Huang, Liusheng; Shi, Runhua; He, Libao

2013-07-01

Secret sharing plays a fundamental role in both secure multi-party computation and modern cryptography. We present a new quantum secret sharing scheme based on quantum Fourier transform. This scheme enjoys the property that each share of a secret is disguised with true randomness, rather than classical pseudorandomness. Moreover, under the only assumption that a top priority for all participants (secret sharers and recovers) is to obtain the right result, our scheme is able to achieve provable security against a computationally unbounded attacker.

Fizeau Fourier transform imaging spectroscopy: missing data reconstruction.

PubMed

Thurman, Samuel T; Fienup, James R

2008-04-28

Fizeau Fourier transform imaging spectroscopy yields both spatial and spectral information about an object. Spectral information, however, is not obtained for a finite area of low spatial frequencies. A nonlinear reconstruction algorithm based on a gray-world approximation is presented. Reconstruction results from simulated data agree well with ideal Michelson interferometer-based spectral imagery. This result implies that segmented-aperture telescopes and multiple telescope arrays designed for conventional imaging can be used to gather useful spectral data through Fizeau FTIS without the need for additional hardware.

SCIAMACHY and FTS CO2 Retrievals Using the OCO Retrieval Algorithm

NASA Technical Reports Server (NTRS)

Boesch, Hartmut; Buchwitz, M.; Sen, Bhaswar; Toon, Geoffrey C.; Washenfelder, Rebecca A.; Wennberg, Paul O.

2005-01-01

The Orbiting Carbon Observatory (OCO) mission will make the first global, space-based measurements of atmospheric C02 with the precision and coverage needed to characterize C02 sources and sinks on regional scales. OCO will make spectrally and spatially highly resolved measurements of reflected sunlight in the 02A -band and two near-infrared C02 bands. To test the OCO retrieval algorithm, SCIAMACHY and ground-based Fourier Transform Spectrometer (FTS) measurements at Park Falls, Wisconsin have been analyzed. Good agreement between SCIAMACHY and FTS C02 columns has been found with SCIAMACHY showing a much larger scatter than FTS measurements. Both SCIAMACHY and FTS overestimate the surface pressure by a few percent which significantly impacts retrieved C02 columns.

Rigid body mode identification of the PAH-2 helicopter using the eigensystem realization algorithm

NASA Technical Reports Server (NTRS)

Schenk, Axel; Pappa, Richard S.

1992-01-01

The rigid body modes of the PAH-2 'Tiger' helicopter were identified using the Eigensystem Realization Algorithm (ERA). This work complements ground vibration tests performed using DLR's traditional phase resonance technique and the ISSPA (Identification of Structural System Parameters) method. Rigid body modal parameters are important for ground resonance prediction. Time-domain data for ERA were obtained by inverse Fourier transformation of frequency response functions measured with stepped-sine excitation. Mode purity (based on the Phase Resonance Criterion) was generally equal to or greater than corresponding results obtained in the ground vibration tests. All identified natural frequencies and mode shapes correlate well with corresponding ground vibration test results. The modal identification approach discussed in this report has become increasingly attractive in recent years due to the steadily declining cost and increased performance of scientific computers. As illustrated in this application, modern time-domain methods can be successfully applied to data acquired using DLR's existing test equipment. Some suggestions are made for future applications of time domain modal identification in this manner.

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.

PASSIVELY ESTIMATING INDEX OF REFRACTION FOR SPECULAR REFLECTORS USING POLARIMETRIC HYPERSPECTRAL IMAGING

DTIC Science & Technology

2016-12-22

23 6 Band-averaged radiance image with checkerboard is shown in the upper left. The 2-D Fourier transform of the image is...red is 1) that is multiplied by the Fourier transform of the original image. The inverse Fourier transform is then taken to get the final image with...Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 IFTS Imaging Fourier Transform Spectrometer

Transfer Functions Via Laplace- And Fourier-Borel Transforms

NASA Technical Reports Server (NTRS)

Can, Sumer; Unal, Aynur

1991-01-01

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

NASA Astrophysics Data System (ADS)

Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

2017-10-01

Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

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.

Surf zone characterization from Unmanned Aerial Vehicle imagery

NASA Astrophysics Data System (ADS)

Holman, Rob A.; Holland, K. Todd; Lalejini, Dave M.; Spansel, Steven D.

2011-11-01

We investigate the issues and methods for estimating nearshore bathymetry based on wave celerity measurements obtained using time series imagery from small unmanned aircraft systems (SUAS). In contrast to time series imagery from fixed cameras or from larger aircraft, SUAS data are usually short, gappy in time, and unsteady in aim in high frequency ways that are not reflected by the filtered navigation metadata. These issues were first investigated using fixed camera proxy data that have been intentionally degraded to mimic these problems. It has been found that records as short as 50 s or less can yield good bathymetry results. Gaps in records associated with inadvertent look-away during unsteady flight would normally prevent use of the required standard Fast Fourier Transform methods. However, we found that a full Fourier Transform could be implemented on the remaining valid record segments and was effective if at least 50% of total record length remained intact. Errors in image geo-navigation were stabilized based on fixed ground fiducials within a required land portion of the image. The elements of a future method that could remove this requirement were then outlined. Two test SUAS data runs were analyzed and compared to survey ground truth data. A 54-s data run at Eglin Air Force Base on the Gulf of Mexico yielded a good bathymetry product that compared well with survey data (standard deviation of 0.51 m in depths ranging from 0 to 4 m). A shorter (30.5 s) record from Silver Strand Beach (near Coronado) on the US west coast provided a good approximation of the surveyed bathymetry but was excessively deep offshore and had larger errors (1.19 m for true depths ranging from 0 to 6 m), consistent with the short record length. Seventy-three percent of the bathymetry estimates lay within 1 m of the truth for most of the nearshore.

Copy-move forgery detection utilizing Fourier-Mellin transform log-polar features

NASA Astrophysics Data System (ADS)

Dixit, Rahul; Naskar, Ruchira

2018-03-01

In this work, we address the problem of region duplication or copy-move forgery detection in digital images, along with detection of geometric transforms (rotation and rescale) and postprocessing-based attacks (noise, blur, and brightness adjustment). Detection of region duplication, following conventional techniques, becomes more challenging when an intelligent adversary brings about such additional transforms on the duplicated regions. In this work, we utilize Fourier-Mellin transform with log-polar mapping and a color-based segmentation technique using K-means clustering, which help us to achieve invariance to all the above forms of attacks in copy-move forgery detection of digital images. Our experimental results prove the efficiency of the proposed method and its superiority to the current state of the art.

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.

An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

PubMed Central

Füsti-Molnár, László; Merz, Kenneth M.

2008-01-01

An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring. PMID:18624561

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.

Ground-based measurements of the 1.3 to 0.3 millimeter spectrum of Jupiter and Saturn, and their detailed calibration.

PubMed

Pardo, Juan R; Serabyn, Eugene; Wiedner, Martina C; Moreno, Raphäel; Orton, Glenn

2017-07-01

One of the legacies of the now retired Caltech Submillimeter Observatory (CSO) is presented in this paper. We measured for the first time the emission of the giant planets Jupiter and Saturn across the 0.3 to 1.3 mm wavelength range using a Fourier Transform Spectrometer mounted on the 10.4-meter dish of the CSO at Mauna Kea, Hawaii, 4100 meters above sea level. A careful calibration, including the evaluation of the antenna performance over such a wide wavelength range and the removal of the Earth's atmosphere effects, has allowed the detection of broad absorption lines on those planets' atmospheres. The calibrated data allowed us to verify the predictions of standard models for both planets in this spectral region, and to confirm the absolute radiometry in the case of Jupiter. Besides their physical interest, the results are also important as both planets are calibration references in the current era of operating ground-based and space-borne submillimeter instruments.

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

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

ERIC Educational Resources Information Center

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

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

Surveying the IR corona during the 2017 solar eclipse

NASA Astrophysics Data System (ADS)

Bryans, P.; Hannigan, J. W.; Sewell, S. D.; Judge, P. G.

2017-12-01

The spectral emission of the infrared solar corona is the most promising direct diagnostic of the coronal magnetic field, and yet remains poorly measured. During the 2017 total solar eclipse, we will perform the first spectral survey of the IR corona using the NCAR Airborne Interferometer. This Fourier Transform Infrared Spectrometer is configured to observe the coronal spectrum from 1.5 to 5.5 microns at R 10,000 from a ground-based site. The location is atop Casper Mountain, Wyoming (42.73ºN, 106.32ºW, 2400 masl), 8 km from the center-line of totality. In this presentation, we will outline the need for such measurements, describe the instrument design and adaptation for the eclipse measurement, observation scheme, and present preliminary results. We will also discuss implications for observing infrared coronal lines from the ground, for example with the upcoming DKIST facility.

Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar

2007-09-01

We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.

The angular difference function and its application to image registration.

PubMed

Keller, Yosi; Shkolnisky, Yoel; Averbuch, Amir

2005-06-01

The estimation of large motions without prior knowledge is an important problem in image registration. In this paper, we present the angular difference function (ADF) and demonstrate its applicability to rotation estimation. The ADF of two functions is defined as the integral of their spectral difference along the radial direction. It is efficiently computed using the pseudopolar Fourier transform, which computes the discrete Fourier transform of an image on a near spherical grid. Unlike other Fourier-based registration schemes, the suggested approach does not require any interpolation. Thus, it is more accurate and significantly faster.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

Methodological effects in Fourier transform infrared (FTIR) spectroscopy: Implications for structural analyses of biomacromolecular samples

NASA Astrophysics Data System (ADS)

Kamnev, Alexander A.; Tugarova, Anna V.; Dyatlova, Yulia A.; Tarantilis, Petros A.; Grigoryeva, Olga P.; Fainleib, Alexander M.; De Luca, Stefania

2018-03-01

A set of experimental data obtained by Fourier transform infrared (FTIR) spectroscopy (involving the use of samples ground and pressed with KBr, i.e. in a polar halide matrix) and by matrix-free transmission FTIR or diffuse reflectance infrared Fourier transform (DRIFT) spectroscopic methodologies (involving measurements of thin films or pure powdered samples, respectively) were compared for several different biomacromolecular substances. The samples under study included poly-3-hydroxybutyrate (PHB) isolated from cell biomass of the rhizobacterium Azospirillum brasilense; dry PHB-containing A. brasilense biomass; pectin (natural carboxylated heteropolysaccharide of plant origin; obtained from apple peel) as well as its chemically modified derivatives obtained by partial esterification of its galacturonide-chain hydroxyl moieties with palmitic, oleic and linoleic acids. Significant shifts of some FTIR vibrational bands related to polar functional groups of all the biomacromolecules under study, induced by the halide matrix used for preparing the samples for spectroscopic measurements, were shown and discussed. A polar halide matrix used for preparing samples for FTIR measurements was shown to be likely to affect band positions not only per se, by affecting band energies or via ion exchange (e.g., with carboxylate moieties), but also by inducing crystallisation of metastable amorphous biopolymers (e.g., PHB of microbial origin). The results obtained have important implications for correct structural analyses of polar, H-bonded and/or amphiphilic biomacromolecular systems using different methodologies of FTIR spectroscopy.

Coherent time-stretch transformation for real-time capture of wideband signals.

PubMed

Buckley, Brandon W; Madni, Asad M; Jalali, Bahram

2013-09-09

Time stretch transformation of wideband waveforms boosts the performance of analog-to-digital converters and digital signal processors by slowing down analog electrical signals before digitization. The transform is based on dispersive Fourier transformation implemented in the optical domain. A coherent receiver would be ideal for capturing the time-stretched optical signal. Coherent receivers offer improved sensitivity, allow for digital cancellation of dispersion-induced impairments and optical nonlinearities, and enable decoding of phase-modulated optical data formats. Because time-stretch uses a chirped broadband (>1 THz) optical carrier, a new coherent detection technique is required. In this paper, we introduce and demonstrate coherent time stretch transformation; a technique that combines dispersive Fourier transform with optically broadband coherent detection.

Intelligent Automatic Classification of True and Counterfeit Notes Based on Spectrum Analysis

NASA Astrophysics Data System (ADS)

Matsunaga, Shohei; Omatu, Sigeru; Kosaka, Toshohisa

The purpose of this paper is to classify bank notes into “true” or “counterfeit” ones faster and more precisely compared with a conventional method. We note that thin lines are represented by direct lines in the images of true notes while they are represented in the counterfeit notes by dotted lines. This is due to properties of dot printers or scanner levels. To use the properties, we propose two method to classify a note into true or counterfeited one by checking whether there exist thin lines or dotted lines of the note. First, we use Fourier transform of the note to find quantity of features for classification and we classify a note into true or counterfeit one by using the features by Fourier transform. Then we propose a classification method by using wavelet transform in place of Fourier transform. Finally, some classification results are illustrated to show the effectiveness of the proposed methods.

Recent progress in synchrotron-based frequency-domain Fourier-transform THz-EPR.

PubMed

Nehrkorn, Joscha; Holldack, Karsten; Bittl, Robert; Schnegg, Alexander

2017-07-01

We describe frequency-domain Fourier-transform THz-EPR as a method to assign spin-coupling parameters of high-spin (S>1/2) systems with very large zero-field splittings. The instrumental foundations of synchrotron-based FD-FT THz-EPR are presented, alongside with a discussion of frequency-domain EPR simulation routines. The capabilities of this approach is demonstrated for selected mono- and multinuclear HS systems. Finally, we discuss remaining challenges and give an outlook on the future prospects of the technique. Copyright © 2017 Elsevier Inc. All rights reserved.

Occurrence of weak, sub-micron, tropospheric aerosol events at high Arctic latitudes

NASA Astrophysics Data System (ADS)

O'Neill, N. T.; Pancrati, O.; Baibakov, K.; Eloranta, E.; Batchelor, R. L.; Freemantle, J.; McArthur, L. J. B.; Strong, K.; Lindenmaier, R.

2008-07-01

Numerous fine mode (sub-micron) aerosol optical events were observed during the summer of 2007 at the High Arctic atmospheric observatory (PEARL) located at Eureka, Nunavut, Canada. Half of these events could be traced to forest fires in southern and eastern Russia and the Northwest Territories of Canada. The most notable findings were that (a) a combination of ground-based measurements (passive sunphotometry, high spectral resolution lidar) could be employed to determine that weak (near sub-visual) fine mode events had occurred, and (b) this data combined with remote sensing imagery products (MODIS, OMI-AI, FLAMBE fire sources), Fourier transform spectroscopy and back trajectories could be employed to identify the smoke events.

Instrumental sensing of stationary source emissions. [sulphur dioxide remote sensing for coal-burning power plants

NASA Technical Reports Server (NTRS)

Herget, W. F.; Conner, W. D.

1977-01-01

A variety of programs have been conducted within EPA to evaluate the capability of various ground-based remote-sensing techniques for measuring the SO2 concentration, velocity, and opacity of effluents from coal-burning power plants. The results of the remote measurements were compared with the results of instack measurements made using EPA reference methods. Attention is given to infrared gas-filter correlation radiometry for SO2 concentration, Fourier-transform infrared spectroscopy for SO2 concentration, ultraviolet matched-filter correlation spectroscopy for SO2 concentration, infrared and ultraviolet television for velocity and SO2 concentration, infrared laser-Doppler velocimetry for plume velocity, and visible laser radar for plume opacity.

Nighttime and daytime variation of atmospheric NO2 from ground-based infrared measurements

NASA Technical Reports Server (NTRS)

Flaud, J.-M.; Camy-Peyret, C.; Brault, J. W.; Rinsland, C. P.; Cariolle, D.

1988-01-01

During the period of Feb. 28 to Mar. 2, 1986, 19 high resolution atmospheric spectra have been recorded during the night using the moon or during the day using the sun as a source with the Fourier transform spectrometer at the McMath Solar telescope on Kitt Peak. The NO2 absorption peak located at 2914.65/cm has been used to derive from the spectra the total vertical column densities of atmospheric NO2. A rather rapid decrease of the NO2 amount during the night has been observed, and its daytime increase from sunrise to sunset has been confirmed. A comparison with the predictions of a photochemical model is given.

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

PubMed

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

2016-09-19

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

Discrimination of organic coffee via Fourier transform infrared-photoacoustic spectroscopy.

PubMed

Gordillo-Delgado, Fernando; Marín, Ernesto; Cortés-Hernández, Diego Mauricio; Mejía-Morales, Claudia; García-Salcedo, Angela Janet

2012-08-30

Procedures for the evaluation of the origin and quality of ground and roasted coffee are constantly needed for the associated industry due to complexity of the related market. Conventional Fourier transform infrared (FTIR) spectroscopy can be used for detecting changes in functional groups of compounds, such as coffee. However, dispersion, reflection and non-homogeneity of the sample matrix can cause problems resulting in low spectral quality. On the other hand, sample preparation frequently takes place in a destructive way. To overcome these difficulties, in this work a photoacoustic cell has been adapted as a detector in a FTIR spectrophotometer to perform a study of roasted and ground coffee from three varieties of Coffea arabica grown by organic and conventional methods. Comparison between spectra of coffee recorded by FTIR-photoacoustic spectrometry (PAS) and by FTIR spectrophotometry showed a better resolution of the former method, which, aided by principal components analysis, allowed the identification of some absorption bands that allow the discrimination between organic and conventional coffee. The results obtained provide information about the spectral behavior of coffee powder which can be useful for establishing discrimination criteria. It has been demonstrated that FTIR-PAS can be a useful experimental tool for the characterization of coffee. Copyright © 2012 Society of Chemical Industry.

Classification and identification of Rhodobryum roseum Limpr. and its adulterants based on fourier-transform infrared spectroscopy (FTIR) and chemometrics.

PubMed

Cao, Zhen; Wang, Zhenjie; Shang, Zhonglin; Zhao, Jiancheng

2017-01-01

Fourier-transform infrared spectroscopy (FTIR) with the attenuated total reflectance technique was used to identify Rhodobryum roseum from its four adulterants. The FTIR spectra of six samples in the range from 4000 cm-1 to 600 cm-1 were obtained. The second-derivative transformation test was used to identify the small and nearby absorption peaks. A cluster analysis was performed to classify the spectra in a dendrogram based on the spectral similarity. Principal component analysis (PCA) was used to classify the species of six moss samples. A cluster analysis with PCA was used to identify different genera. However, some species of the same genus exhibited highly similar chemical components and FTIR spectra. Fourier self-deconvolution and discrete wavelet transform (DWT) were used to enhance the differences among the species with similar chemical components and FTIR spectra. Three scales were selected as the feature-extracting space in the DWT domain. The results show that FTIR spectroscopy with chemometrics is suitable for identifying Rhodobryum roseum and its adulterants.

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.

A differential optical absorption spectroscopy method for retrieval from ground-based Fourier transform spectrometers measurements of the direct solar beam

NASA Astrophysics Data System (ADS)

Huo, Yanfeng; Duan, Minzheng; Tian, Wenshou; Min, Qilong

2015-08-01

A differential optical absorption spectroscopy (DOAS)-like algorithm is developed to retrieve the column-averaged dryair mole fraction of carbon dioxide from ground-based hyper-spectral measurements of the direct solar beam. Different to the spectral fitting method, which minimizes the difference between the observed and simulated spectra, the ratios of multiple channel-pairs—one weak and one strong absorption channel—are used to retrieve from measurements of the shortwave infrared (SWIR) band. Based on sensitivity tests, a super channel-pair is carefully selected to reduce the effects of solar lines, water vapor, air temperature, pressure, instrument noise, and frequency shift on retrieval errors. The new algorithm reduces computational cost and the retrievals are less sensitive to temperature and H2O uncertainty than the spectral fitting method. Multi-day Total Carbon Column Observing Network (TCCON) measurements under clear-sky conditions at two sites (Tsukuba and Bremen) are used to derive xxxx for the algorithm evaluation and validation. The DOAS-like results agree very well with those of the TCCON algorithm after correction of an airmass-dependent bias.

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

A hybrid silicon membrane spatial light modulator for optical information processing

NASA Technical Reports Server (NTRS)

Pape, D. R.; Hornbeck, L. J.

1984-01-01

A new two dimensional, fast, analog, electrically addressable, silicon based membrane spatial light modulator (SLM) was developed for optical information processing applications. Coherent light reflected from the mirror elements is phase modulated producing an optical Fourier transform of an analog signal input to the device. The DMD architecture and operating parameters related to this application are presented. A model is developed that describes the optical Fourier transform properties of the DMD.

Using vertical Fourier transforms to invert potential-field data to magnetization or density models in the presence of topography

USGS Publications Warehouse

Phillips, Jeffrey

2014-01-01

A physical property inversion approach based on the use of 3D (or 2D) Fourier transforms to calculate the potential-field within a 3D (or 2D) volume from a known physical property distribution within the volume is described. Topographic surfaces and observations at arbitrary locations are easily accommodated. The limitations of the approach and applications to real data are considered.

Quaternion-Based Texture Analysis of Multiband Satellite Images: Application to the Estimation of Aboveground Biomass in the East Region of Cameroon.

PubMed

Djiongo Kenfack, Cedrigue Boris; Monga, Olivier; Mpong, Serge Moto; Ndoundam, René

2018-03-01

Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model (FOTO). Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images.

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

NASA Astrophysics Data System (ADS)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

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

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.

Fourier removal of stripe artifacts in IRAS images

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1987-01-01

By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.

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.

The derivative-free Fourier shell identity for photoacoustics.

PubMed

Baddour, Natalie

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

NASA Astrophysics Data System (ADS)

Zhang, B.; Sang, Jun; Alam, Mohammad S.

2013-03-01

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.

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.

A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers

NASA Technical Reports Server (NTRS)

Campbell, Joel

2008-01-01

A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.

Transient excitation and data processing techniques employing the fast fourier transform for aeroelastic testing

NASA Technical Reports Server (NTRS)

Jennings, W. P.; Olsen, N. L.; Walter, M. J.

1976-01-01

The development of testing techniques useful in airplane ground resonance testing, wind tunnel aeroelastic model testing, and airplane flight flutter testing is presented. Included is the consideration of impulsive excitation, steady-state sinusoidal excitation, and random and pseudorandom excitation. Reasons for the selection of fast sine sweeps for transient excitation are given. The use of the fast fourier transform dynamic analyzer (HP-5451B) is presented, together with a curve fitting data process in the Laplace domain to experimentally evaluate values of generalized mass, model frequencies, dampings, and mode shapes. The effects of poor signal to noise ratios due to turbulence creating data variance are discussed. Data manipulation techniques used to overcome variance problems are also included. The experience is described that was gained by using these techniques since the early stages of the SST program. Data measured during 747 flight flutter tests, and SST, YC-14, and 727 empennage flutter model tests are included.

Radiometric modeling and calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) ground based measurement experiment

NASA Astrophysics Data System (ADS)

Tian, Jialin; Smith, William L.; Gazarik, Michael J.

2008-12-01

The ultimate remote sensing benefits of the high resolution Infrared radiance spectrometers will be realized with their geostationary satellite implementation in the form of imaging spectrometers. This will enable dynamic features of the atmosphere's thermodynamic fields and pollutant and greenhouse gas constituents to be observed for revolutionary improvements in weather forecasts and more accurate air quality and climate predictions. As an important step toward realizing this application objective, the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) Engineering Demonstration Unit (EDU) was successfully developed under the NASA New Millennium Program, 2000-2006. The GIFTS-EDU instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The GIFTS calibration is achieved using internal blackbody calibration references at ambient (260 K) and hot (286 K) temperatures. In this paper, we introduce a refined calibration technique that utilizes Principle Component (PC) analysis to compensate for instrument distortions and artifacts, therefore, enhancing the absolute calibration accuracy. This method is applied to data collected during the GIFTS Ground Based Measurement (GBM) experiment, together with simultaneous observations by the accurately calibrated AERI (Atmospheric Emitted Radiance Interferometer), both simultaneously zenith viewing the sky through the same external scene mirror at ten-minute intervals throughout a cloudless day at Logan Utah on September 13, 2006. The accurately calibrated GIFTS radiances are produced using the first four PC scores in the GIFTS-AERI regression model. Temperature and moisture profiles retrieved from the PC-calibrated GIFTS radiances are verified against radiosonde measurements collected throughout the GIFTS sky measurement period. Using the GIFTS GBM calibration model, we compute the calibrated radiances from data collected during the moon tracking and viewing experiment events. From which, we derive the lunar surface temperature and emissivity associated with the moon viewing measurements.

Radiometric Modeling and Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)Ground Based Measurement Experiment

NASA Technical Reports Server (NTRS)

Tian, Jialin; Smith, William L.; Gazarik, Michael J.

2008-01-01

The ultimate remote sensing benefits of the high resolution Infrared radiance spectrometers will be realized with their geostationary satellite implementation in the form of imaging spectrometers. This will enable dynamic features of the atmosphere s thermodynamic fields and pollutant and greenhouse gas constituents to be observed for revolutionary improvements in weather forecasts and more accurate air quality and climate predictions. As an important step toward realizing this application objective, the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) Engineering Demonstration Unit (EDU) was successfully developed under the NASA New Millennium Program, 2000-2006. The GIFTS-EDU instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The GIFTS calibration is achieved using internal blackbody calibration references at ambient (260 K) and hot (286 K) temperatures. In this paper, we introduce a refined calibration technique that utilizes Principle Component (PC) analysis to compensate for instrument distortions and artifacts, therefore, enhancing the absolute calibration accuracy. This method is applied to data collected during the GIFTS Ground Based Measurement (GBM) experiment, together with simultaneous observations by the accurately calibrated AERI (Atmospheric Emitted Radiance Interferometer), both simultaneously zenith viewing the sky through the same external scene mirror at ten-minute intervals throughout a cloudless day at Logan Utah on September 13, 2006. The accurately calibrated GIFTS radiances are produced using the first four PC scores in the GIFTS-AERI regression model. Temperature and moisture profiles retrieved from the PC-calibrated GIFTS radiances are verified against radiosonde measurements collected throughout the GIFTS sky measurement period. Using the GIFTS GBM calibration model, we compute the calibrated radiances from data collected during the moon tracking and viewing experiment events. From which, we derive the lunar surface temperature and emissivity associated with the moon viewing measurements.

Validation of MOPITT carbon monoxide using ground-based Fourier transform infrared spectrometer data from NDACC

NASA Astrophysics Data System (ADS)

Buchholz, Rebecca R.; Deeter, Merritt N.; Worden, Helen M.; Gille, John; Edwards, David P.; Hannigan, James W.; Jones, Nicholas B.; Paton-Walsh, Clare; Griffith, David W. T.; Smale, Dan; Robinson, John; Strong, Kimberly; Conway, Stephanie; Sussmann, Ralf; Hase, Frank; Blumenstock, Thomas; Mahieu, Emmanuel; Langerock, Bavo

2017-06-01

The Measurements of Pollution in the Troposphere (MOPITT) satellite instrument provides the longest continuous dataset of carbon monoxide (CO) from space. We perform the first validation of MOPITT version 6 retrievals using total column CO measurements from ground-based remote-sensing Fourier transform infrared spectrometers (FTSs). Validation uses data recorded at 14 stations, that span a wide range of latitudes (80° N to 78° S), in the Network for the Detection of Atmospheric Composition Change (NDACC). MOPITT measurements are spatially co-located with each station, and different vertical sensitivities between instruments are accounted for by using MOPITT averaging kernels (AKs). All three MOPITT retrieval types are analyzed: thermal infrared (TIR-only), joint thermal and near infrared (TIR-NIR), and near infrared (NIR-only). Generally, MOPITT measurements overestimate CO relative to FTS measurements, but the bias is typically less than 10 %. Mean bias is 2.4 % for TIR-only, 5.1 % for TIR-NIR, and 6.5 % for NIR-only. The TIR-NIR and NIR-only products consistently produce a larger bias and lower correlation than the TIR-only. Validation performance of MOPITT for TIR-only and TIR-NIR retrievals over land or water scenes is equivalent. The four MOPITT detector element pixels are validated separately to account for their different uncertainty characteristics. Pixel 1 produces the highest standard deviation and lowest correlation for all three MOPITT products. However, for TIR-only and TIR-NIR, the error-weighted average that includes all four pixels often provides the best correlation, indicating compensating pixel biases and well-captured error characteristics. We find that MOPITT bias does not depend on latitude but rather is influenced by the proximity to rapidly changing atmospheric CO. MOPITT bias drift has been bound geographically to within ±0.5 % yr-1 or lower at almost all locations.

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.

Radar Measurements of Ocean Surface Waves using Proper Orthogonal Decomposition

DTIC Science & Technology

2017-03-30

rely on use of Fourier transforms (FFT) and filtering spectra on the linear dispersion relationship for ocean surface waves. This report discusses...the measured signal (e.g., Young et al., 1985). In addition, the methods often rely on filtering the FFT of radar backscatter or Doppler velocities...to those obtained with conventional FFT and dispersion curve filtering techniques (iv) Compare both results of(iii) to ground truth sensors (i .e

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

PubMed

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

2010-07-05

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

Design of a compact static Fourier transform spectrometer in integrated optics based on a leaky loop structure.

PubMed

Martin, Bruno; Morand, Alain; Benech, Pierre; Leblond, Gregory; Blaize, Sylvain; Lerondel, Gilles; Royer, Pascal; Kern, Pierre; Le Coarer, Etienne

2009-01-15

A compact static Fourier transform spectrometer for integrated optics is proposed. It is based on a plane leaky loop structure combined with a plane waveguide. The interference pattern produced in the loop structure leaks outside of it and is guided in the plane waveguide to the photodetector array. This configuration allows one to control the shape of the field pattern at the end of the plane waveguide. A large fringe pattern with a high interference fringe contrast is obtained. A two-dimensional model based on an aperiodic Fourier modal method is used to modelize the coupling between the bent and the plane waveguides, completed with the Helmholtz-Kirchhoff propagation. This concept gives access to plan and compact spectrometers requiring only a single low-cost realization process step. The simulation has been done to realize a spectrometer in glass integrated optics (Deltalambda=6.1 nm at 1500 nm).

A no-key-exchange secure image sharing scheme based on Shamir's three-pass cryptography protocol and the multiple-parameter fractional Fourier transform.

PubMed

Lang, Jun

2012-01-30

In this paper, we propose a novel secure image sharing scheme based on Shamir's three-pass protocol and the multiple-parameter fractional Fourier transform (MPFRFT), which can safely exchange information with no advance distribution of either secret keys or public keys between users. The image is encrypted directly by the MPFRFT spectrum without the use of phase keys, and information can be shared by transmitting the encrypted image (or message) three times between users. Numerical simulation results are given to verify the performance of the proposed algorithm.

Using the Fast Fourier Transform to Accelerate the Computational Search for RNA Conformational Switches

PubMed Central

Senter, Evan; Sheikh, Saad; Dotu, Ivan; Ponty, Yann; Clote, Peter

2012-01-01

Using complex roots of unity and the Fast Fourier Transform, we design a new thermodynamics-based algorithm, FFTbor, that computes the Boltzmann probability that secondary structures differ by base pairs from an arbitrary initial structure of a given RNA sequence. The algorithm, which runs in quartic time and quadratic space , is used to determine the correlation between kinetic folding speed and the ruggedness of the energy landscape, and to predict the location of riboswitch expression platform candidates. A web server is available at http://bioinformatics.bc.edu/clotelab/FFTbor/. PMID:23284639

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Colorectal Cancer and Colitis Diagnosis Using Fourier Transform Infrared Spectroscopy and an Improved K-Nearest-Neighbour Classifier.

PubMed

Li, Qingbo; Hao, Can; Kang, Xue; Zhang, Jialin; Sun, Xuejun; Wang, Wenbo; Zeng, Haishan

2017-11-27

Combining Fourier transform infrared spectroscopy (FTIR) with endoscopy, it is expected that noninvasive, rapid detection of colorectal cancer can be performed in vivo in the future. In this study, Fourier transform infrared spectra were collected from 88 endoscopic biopsy colorectal tissue samples (41 colitis and 47 cancers). A new method, viz., entropy weight local-hyperplane k-nearest-neighbor (EWHK), which is an improved version of K-local hyperplane distance nearest-neighbor (HKNN), is proposed for tissue classification. In order to avoid limiting high dimensions and small values of the nearest neighbor, the new EWHK method calculates feature weights based on information entropy. The average results of the random classification showed that the EWHK classifier for differentiating cancer from colitis samples produced a sensitivity of 81.38% and a specificity of 92.69%.

Effect of ion clouds micromotion on measured signal in Fourier transform ion cyclotron resonance: Computer simulation.

PubMed

Vladimirov, Gleb; Kostyukevich, Yury; Kharybin, Oleg; Nikolaev, Eugene

2017-08-01

Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.

Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra.

PubMed

Desbiens, Raphaël; Tremblay, Pierre; Genest, Jérôme; Bouchard, Jean-Pierre

2006-01-20

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

Analytical Investigation Of Pigments, Ground Layer And Media Of Cartonnage Fragments From Greek Roman Period

NASA Astrophysics Data System (ADS)

Afifi, Hala. A. M.

Some cartonnage fragments from Hawara, Fayoum Excavation were examined to identify pigments, media and grounds. It belonged to the Greek-Roman period. They were studied by X-ray diffraction (XRD), Energy dispersive X ray analysis (EDS) equipped with Scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR). These techniques were used to identify the composition and morphology of grounds, nature of pigments and media used in cartonnage fragments. The coarse ground layer was composed of calcite and traces of quartz. The fine ground layer used under the pigments directly was composed of calcite only. Carbon black was used as black pigment while lead oxide as red pigment, showing the influence of Roman and Greek pigments on Egyptian art in these later periods. Blue colorant was identified as cuprorivaite and yellow pigment was goethite. Animal glue was used in the four pigments as medium colored.

First low frequency all-sky search for continuous gravitational wave signals

NASA Astrophysics Data System (ADS)

Aasi, J.; Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Amariutei, D. V.; Andersen, M.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Ashton, G.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Bartlett, J.; Barton, M. A.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Behnke, B.; Bejger, M.; Belczynski, C.; Bell, A. S.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Biscans, S.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Bork, R.; Born, M.; Boschi, V.; Bose, Sukanta; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Branco, V.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Calderón Bustillo, J.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Celerier, C.; Cella, G.; Cepeda, C.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, X.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Colombini, M.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Canton, T. Dal; Damjanic, M. D.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Dominguez, E.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Edwards, M.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J. M.; Eikenberry, S. S.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fairhurst, S.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Feldbaum, D.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fisher, R. P.; Flaminio, R.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frede, M.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; Gergely, L. Á.; Germain, V.; Ghosh, A.; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gleason, J. R.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez, J.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Goßler, S.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Groot, P.; Grote, H.; Grover, K.; Grunewald, S.; Guidi, G. M.; Guido, C. J.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammer, D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hoelscher-Obermaier, J.; Hofman, D.; Hollitt, S. E.; Holt, K.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh, M.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Islas, G.; Isler, J. C.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacobson, M. B.; Jang, H.; Jaranowski, P.; Jawahar, S.; Ji, Y.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Haris, K.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Karlen, J. L.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kerrigan, J.; Key, J. S.; Khalili, F. Y.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, K.; Kim, N. G.; Kim, N.; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Klimenko, S.; Kline, J. T.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, A.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, J.; Lee, J. P.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Lewis, J. B.; Li, T. G. F.; Libson, A.; Lin, A. C.; Littenberg, T. B.; Lockerbie, N. A.; Lockett, V.; Lodhia, D.; Logue, J.; Lombardi, A. L.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lubinski, M. J.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; Macarthur, J.; Macdonald, E. P.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Madden-Fong, D. X.; Magaña-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mangini, N. M.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Mastrogiovanni, S.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Mehmet, M.; Meidam, J.; Meinders, M.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moe, B.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Mukherjee, A.; Mukherjee, S.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nagy, M. F.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Okounkova, M.; Oppermann, P.; Oram, R.; O'Reilly, B.; Ortega, W. E.; O'Shaughnessy, R.; Ott, C. D.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Padilla, C. T.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pan, Y.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Papa, M. A.; Paris, H. R.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patrick, Z.; Pedraza, M.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Pickenpack, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poeld, J. H.; Poggiani, R.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qin, J.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Rácz, I.; Radkins, H.; Raffai, P.; Raja, S.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rodger, A. S.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Saleem, M.; Salemi, F.; Sammut, L.; Sanchez, E.; Sandberg, V.; Sanders, J. R.; Santiago-Prieto, I.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Savage, R.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Sevigny, A.; Shaddock, D. A.; Shaffery, P.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Shoemaker, D. H.; Sidery, T. L.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, R.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Steplewski, S.; Stevenson, S. P.; Stone, R.; Strain, K. A.; Straniero, N.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepanczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Tse, M.; Turconi, M.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; Vallisneri, M.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; van den Broeck, C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, M.; Wade, L. E.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; Whitcomb, S. E.; White, D. J.; Whiting, B. F.; Williams, K. J.; Williams, L.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Yablon, J.; Yakushin, I.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zhang, Fan; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

2016-02-01

In this paper we present the results of the first low frequency all-sky search of continuous gravitational wave signals conducted on Virgo VSR2 and VSR4 data. The search covered the full sky, a frequency range between 20 and 128 Hz with a range of spin-down between -1.0 ×10-10 and +1.5 ×10-11 Hz /s , and was based on a hierarchical approach. The starting point was a set of short fast Fourier transforms, of length 8192 s, built from the calibrated strain data. Aggressive data cleaning, in both the time and frequency domains, has been done in order to remove, as much as possible, the effect of disturbances of instrumental origin. On each data set a number of candidates has been selected, using the FrequencyHough transform in an incoherent step. Only coincident candidates among VSR2 and VSR4 have been examined in order to strongly reduce the false alarm probability, and the most significant candidates have been selected. The criteria we have used for candidate selection and for the coincidence step greatly reduce the harmful effect of large instrumental artifacts. Selected candidates have been subject to a follow-up by constructing a new set of longer fast Fourier transforms followed by a further incoherent analysis, still based on the FrequencyHough transform. No evidence for continuous gravitational wave signals was found, and therefore we have set a population-based joint VSR2-VSR4 90% confidence level upper limit on the dimensionless gravitational wave strain in the frequency range between 20 and 128 Hz. This is the first all-sky search for continuous gravitational waves conducted, on data of ground-based interferometric detectors, at frequencies below 50 Hz. We set upper limits in the range between about 1 0-24 and 2 ×10-23 at most frequencies. Our upper limits on signal strain show an improvement of up to a factor of ˜2 with respect to the results of previous all-sky searches at frequencies below 80 Hz.

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

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

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

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

Determination of Fourier Transforms on an Instructional Analog Computer

ERIC Educational Resources Information Center

Anderson, Owen T.; Greenwood, Stephen R.

1974-01-01

An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)

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.

The Effective Hamiltonian for the Ground State of 207Pb19F and New Measurements of the Fine Structure Spectrum Near 1.2 μ m.

NASA Astrophysics Data System (ADS)

Mawhorter, Richard; Murphey, Benjamin; Baum, Alexander; Sears, Trevor J.; Yang, T. Zh.; Rupasinghe, P. M.; McRaven, C. P.; Shafer-Ray, N. E.; Alphei, Lukas D.; Grabow, Jens-Uwe.

2011-06-01

We have measured rotational transitions in the ground, X_1 ^2Π1/2, electronic state of naturally occuring isotopomers of PbF in a supersonic free jet Fourier transform microwave spectrometer. The data for 207Pb19F is particularly interesting because it is a candidate for a future experimental e-EDM measurement. To fit the data for this species to the measurement precision, the nuclear spin-spin dipolar interaction and a second term that can be equivalently viewed as a centrifugal distortion correction to the familiar Frosch and Foley hyperfine coupling terms, or an Ω- dependent correction to the nuclear spin-rotational coupling are required, in addition to the standard terms. To characterize the higher X_2 ^2Π3/2 component of the ground state of PbF, we are attempting a direct measurement of transitions between the two components in a slit jet-cooled sample using a frequency comb-referenced extended cavity diode laser. This spectrum was originally detected in a hot source by Fourier transform near-infrared spectroscopy, but low-J transitions were unresolved at that time. Acknowledgments: Work at Brookhaven National Laboratory was carried out under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. Work by N. E. Shafer-Ray was performed with support from the National Science Foundatation award NSF-0855431. J.-U. Grabow ackonwledges funding from the Deutsche Forschungsgemeinschaft and the Land Niedersachsen. K. Ziebarth, K. Setzer, O. Shestakov and E. Fink J. Molec. Spectrosc. 191, 108 1998.

Note: Modification of an FTIR spectrometer for optoelectronic characterizations.

PubMed

Puspitosari, N; Longeaud, C

2017-08-01

We propose a very simple system to be adapted to a Fourier Transform Infra-Red (FTIR) spectrometer with which three different types of characterizations can be done: the Fourier transform photocurrent spectroscopy, the recording of reflection-transmission spectra of thin film semiconductors, and the acquisition of spectral responses of solar cells. In addition to gather three techniques into a single apparatus, this FTIR-based system also significantly reduces the recording time and largely improves the resolution of the measured spectra compared to standard equipments.

Bell’s measure and implementing quantum Fourier transform with orbital angular momentum of classical light

PubMed Central

Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong

2015-01-01

We perform Bell’s measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell’s inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally. PMID:26369424

Note: Modification of an FTIR spectrometer for optoelectronic characterizations

NASA Astrophysics Data System (ADS)

Puspitosari, N.; Longeaud, C.

2017-08-01

We propose a very simple system to be adapted to a Fourier Transform Infra-Red (FTIR) spectrometer with which three different types of characterizations can be done: the Fourier transform photocurrent spectroscopy, the recording of reflection-transmission spectra of thin film semiconductors, and the acquisition of spectral responses of solar cells. In addition to gather three techniques into a single apparatus, this FTIR-based system also significantly reduces the recording time and largely improves the resolution of the measured spectra compared to standard equipments.

[Spatial domain display for interference image dataset].

PubMed

Wang, Cai-Ling; Li, Yu-Shan; Liu, Xue-Bin; Hu, Bing-Liang; Jing, Juan-Juan; Wen, Jia

2011-11-01

The requirements of imaging interferometer visualization is imminent for the user of image interpretation and information extraction. However, the conventional researches on visualization only focus on the spectral image dataset in spectral domain. Hence, the quick show of interference spectral image dataset display is one of the nodes in interference image processing. The conventional visualization of interference dataset chooses classical spectral image dataset display method after Fourier transformation. In the present paper, the problem of quick view of interferometer imager in image domain is addressed and the algorithm is proposed which simplifies the matter. The Fourier transformation is an obstacle since its computation time is very large and the complexion would be even deteriorated with the size of dataset increasing. The algorithm proposed, named interference weighted envelopes, makes the dataset divorced from transformation. The authors choose three interference weighted envelopes respectively based on the Fourier transformation, features of interference data and human visual system. After comparing the proposed with the conventional methods, the results show the huge difference in display time.

NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS

PubMed Central

BAJAJ, CHANDRAJIT; BAUER, BENEDIKT; BETTADAPURA, RADHAKRISHNA; VOLLRATH, ANTJE

2013-01-01

The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ3 that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant. PMID:24379643

Fast Implicit Methods For Elliptic Moving Interface Problems

DTIC Science & Technology

2015-12-11

analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms...evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which...a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D

The scale of the Fourier transform: a point of view of the fractional Fourier transform

NASA Astrophysics Data System (ADS)

Jimenez, C. J.; Vilardy, J. M.; Salinas, S.; Mattos, L.; Torres, C. O.

2017-01-01

In this paper using the Fourier transform of order fractional, the ray transfer matrix for the symmetrical optical systems type ABCD and the formulae by Collins for the diffraction, we obtain explicitly the expression for scaled Fourier transform conventional; this result is the great importance in optical signal processing because it offers the possibility of scaling the size of output the Fourier distribution of the system, only by manipulating the distance of the diffraction object toward the thin lens, this research also emphasizes on practical limits when a finite spherical converging lens aperture is used. Digital simulation was carried out using the numerical platform of Matlab 7.1.

Multichannel Compressive Sensing MRI Using Noiselet Encoding

PubMed Central

Pawar, Kamlesh; Egan, Gary; Zhang, Jingxin

2015-01-01

The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding. PMID:25965548

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.

Near-common-path interferometer for imaging Fourier-transform spectroscopy in wide-field microscopy

PubMed Central

Wadduwage, Dushan N.; Singh, Vijay Raj; Choi, Heejin; Yaqoob, Zahid; Heemskerk, Hans; Matsudaira, Paul; So, Peter T. C.

2017-01-01

Imaging Fourier-transform spectroscopy (IFTS) is a powerful method for biological hyperspectral analysis based on various imaging modalities, such as fluorescence or Raman. Since the measurements are taken in the Fourier space of the spectrum, it can also take advantage of compressed sensing strategies. IFTS has been readily implemented in high-throughput, high-content microscope systems based on wide-field imaging modalities. However, there are limitations in existing wide-field IFTS designs. Non-common-path approaches are less phase-stable. Alternatively, designs based on the common-path Sagnac interferometer are stable, but incompatible with high-throughput imaging. They require exhaustive sequential scanning over large interferometric path delays, making compressive strategic data acquisition impossible. In this paper, we present a novel phase-stable, near-common-path interferometer enabling high-throughput hyperspectral imaging based on strategic data acquisition. Our results suggest that this approach can improve throughput over those of many other wide-field spectral techniques by more than an order of magnitude without compromising phase stability. PMID:29392168

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.

Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

D'Astous, Y.; Blanchard, M.

1982-05-01

In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

Correspondence Search Mitigation Using Feature Space Anti-Aliasing

DTIC Science & Technology

2007-01-01

trackers are widely used in astro -inertial nav- igation systems for long-range aircraft, space navigation, and ICBM guidance. When ground images are to be...frequency domain representation of the point spread function, H( fx , fy), is called the optical transfer function. Applying the Fourier transform to the...frequency domain representation of the image: I( fx , fy, t) = O( fx , fy, t)H( fx , fy) (4) In most conditions, the projected scene can be treated as a

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

NASA Technical Reports Server (NTRS)

Heisler, R.

1978-01-01

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

Fourier transform millimeter-wave spectroscopy of the ethyl radical in the electronic ground state.

PubMed

Kim, Eunsook; Yamamoto, Satoshi

2004-02-15

The pure rotational spectrum of the ethyl radical (C2H5) has been detected for the first time with the Fourier transform millimeter-wave spectrometer. The ethyl radical is produced by discharging the C2H5I gas diluted in Ar. The 1(01)-0(00) rotational transition of the ethyl radical is observed in the frequency range from 43,680 to 43,780 MHz. The observed spectrum shows a very complicated pattern of the fine and hyperfine structures of a doublet radical with the nuclear spins of five protons. The fine and hyperfine components are assigned with the aid of measurements of the Zeeman splittings. As a result, the 22 lines are ascribed to the transitions in the ground vibronic state (A2"). The rotational constant, the spin-rotation interaction constant, and hyperfine interaction constants are determined by the least-squares fit. The Fermi contact term of the alpha-proton is determined to be -64.1654 MHz in the gas phase, indicating that the structure of the -CH2 is essentially planar. The present rotational spectroscopic study further supports that the methyl group of the ethyl radical can be regarded as a nearly free internal rotor with a low energy barrier. A few unassigned lines still remain, which may be vibrational satellites of the internal rotation mode. Copyright 2004 American Institute of Physics

Representation of Complex Spectra in Auditory Cortex

DTIC Science & Technology

1997-01-01

predict the response to any broadband dynamic sound. Fourier Transform Inverse Transform ∫ [.] exp(±2πjΩx±2πjwt) 2 1 2 / 1 1 a 2 1 2 / 1 1 a...Systems Research University of Maryland Spectro-Temporal Transform Ω wx = log f t w = “ripple velocity” Ω = “ripple frequency” Fourier Transform Inverse ... Transform ∫ [.] exp(±2πjΩx±2πjwt) Real functions in the spectro-temporal domain give rise to complex conjugate symmetric functions in the Fourier

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

PubMed

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

Fast Fourier transform-based solution of 2D and 3D magnetization problems in type-II superconductivity

NASA Astrophysics Data System (ADS)

Prigozhin, Leonid; Sokolovsky, Vladimir

2018-05-01

We consider the fast Fourier transform (FFT) based numerical method for thin film magnetization problems (Vestgården and Johansen 2012 Supercond. Sci. Technol. 25 104001), compare it with the finite element methods, and evaluate its accuracy. Proposed modifications of this method implementation ensure stable convergence of iterations and enhance its efficiency. A new method, also based on the FFT, is developed for 3D bulk magnetization problems. This method is based on a magnetic field formulation, different from the popular h-formulation of eddy current problems typically employed with the edge finite elements. The method is simple, easy to implement, and can be used with a general current–voltage relation; its efficiency is illustrated by numerical simulations.

Phase retrieval of images using Gaussian radial bases.

PubMed

Trahan, Russell; Hyland, David

2013-12-20

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction pattern's frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transform's modulus, without background constraints. A practical example is shown.

Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier.

PubMed

Federico, Alejandro; Kaufmann, Guillermo H

2008-10-01

We evaluate a method based on the two-dimensional directional wavelet transform and the introduction of a spatial carrier to retrieve optical phase distributions in singular scalar light fields. The performance of the proposed phase-retrieval method is compared with an approach based on Fourier transform. The advantages and limitations of the proposed method are discussed.

First Ground-Based Infrared Solar Absorption Measurements of Free Tropospheric Methanol (CH3OH): Multidecade Infrared Time Series from Kitt Peak (31.9 deg N 111.6 deg W): Trend, Seasonal Cycle, and Comparison with Previous Measurements

NASA Technical Reports Server (NTRS)

Rinsland, Curtis P.; Mahieu, Emmanuel; Chiou, Linda; Herbin, Herve

2009-01-01

Atmospheric CH3OH (methanol) free tropospheric (2.09-14-km altitude) time series spanning 22 years has been analyzed on the basis of high-spectral resolution infrared solar absorption spectra of the strong vs band recorded from the U.S. National Solar Observatory on Kitt Peak (latitude 31.9degN, 111.6degW, 2.09-km altitude) with a 1-m Fourier transform spectrometer (FTS). The measurements span October 1981 to December 2003 and are the first long time series of CH3OH measurements obtained from the ground. The results were analyzed with SFIT2 version 3.93 and show a factor of three variations with season, a maximum at the beginning of July, a winter minimum, and no statistically significant long-term trend over the measurement time span.

First Ground-Based Infrared Solar Absorption Measurements of Free Tropospheric Methanol (CH3OH): Multidecade Infrared Time Series from Kitt Peak (31.9 deg N 111.6 deg W): Trend, Seasonal Cycle, and Comparison with Previous Measurements

NASA Technical Reports Server (NTRS)

Rinsland, Curtis P.; Mahieu, Emmanuel; Chiou, Linda; Herbin, Herve

2009-01-01

Atmospheric CH3OH (methanol) free tropospheric (2.09-14-km altitude) time series spanning 22 years has been analyzed on the basis of high-spectral resolution infrared solar absorption spectra of the strong n8 band recorded from the U.S. National Solar Observatory on Kitt Peak (latitude 31.9degN, 111.6degW, 2.09-km altitude) with a 1-m Fourier transform spectrometer (FTS). The measurements span October 1981 to December 2003 and are the first long time series of CH3OH measurements obtained from the ground. The results were analyzed with SFIT2 version 3.93 and show a factor of three variations with season, a maximum at the beginning of July, a winter minimum, and no statistically significant long-term trend over the measurement time span.

Regionally Adaptable Ground Motion Prediction Equation (GMPE) from Empirical Models of Fourier and Duration of Ground Motion

NASA Astrophysics Data System (ADS)

Bora, Sanjay; Scherbaum, Frank; Kuehn, Nicolas; Stafford, Peter; Edwards, Benjamin

2016-04-01

The current practice of deriving empirical ground motion prediction equations (GMPEs) involves using ground motions recorded at multiple sites. However, in applications like site-specific (e.g., critical facility) hazard ground motions obtained from the GMPEs are need to be adjusted/corrected to a particular site/site-condition under investigation. This study presents a complete framework for developing a response spectral GMPE, within which the issue of adjustment of ground motions is addressed in a manner consistent with the linear system framework. The present approach is a two-step process in which the first step consists of deriving two separate empirical models, one for Fourier amplitude spectra (FAS) and the other for a random vibration theory (RVT) optimized duration (Drvto) of ground motion. In the second step the two models are combined within the RVT framework to obtain full response spectral amplitudes. Additionally, the framework also involves a stochastic model based extrapolation of individual Fourier spectra to extend the useable frequency limit of the empirically derived FAS model. The stochastic model parameters were determined by inverting the Fourier spectral data using an approach similar to the one as described in Edwards and Faeh (2013). Comparison of median predicted response spectra from present approach with those from other regional GMPEs indicates that the present approach can also be used as a stand-alone model. The dataset used for the presented analysis is a subset of the recently compiled database RESORCE-2012 across Europe, the Middle East and the Mediterranean region.

Single-Slit Diffraction and the Uncertainty Principle

ERIC Educational Resources Information Center

Rioux, Frank

2005-01-01

A theoretical analysis of single-slit diffraction based on the Fourier transform between coordinate and momentum space is presented. The transform between position and momentum is used to illuminate the intimate relationship between single-slit diffraction and uncertainty principle.

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Pre-Hardware Optimization and Implementation Of Fast Optics Closed Control Loop Algorithms

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Lyon, Richard G.; Herman, Jay R.; Abuhassan, Nader

2004-01-01

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 FFT is particularly useful in two-dimensional (2-D) image processing (FFT2) within optical systems control. However, timing constraints of a fast optics closed control loop would require a supercomputer to run the software implementation of the FFT2 and its inverse, as well as other image processing representative algorithm, such as numerical image folding and fringe feature extraction. A laboratory supercomputer is not always available even for ground operations and is not feasible for a night project. However, the computationally intensive algorithms still warrant alternative implementation using reconfigurable computing technologies (RC) such as Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGA), which provide low cost compact super-computing capabilities. We present a new RC hardware implementation and utilization architecture that significantly reduces the computational complexity of a few basic image-processing algorithm, such as FFT2, image folding and phase diversity for the NASA Solar Viewing Interferometer Prototype (SVIP) using a cluster of DSPs and FPGAs. The DSP cluster utilization architecture also assures avoidance of a single point of failure, while using commercially available hardware. This, combined with the control algorithms pre-hardware optimization, or the first time allows construction of image-based 800 Hertz (Hz) optics closed control loops on-board a spacecraft, based on the SVIP ground instrument. That spacecraft is the proposed Earth Atmosphere Solar Occultation Imager (EASI) to study greenhouse gases CO2, C2H, H2O, O3, O2, N2O from Lagrange-2 point in space. This paper provides an advanced insight into a new type of science capabilities for future space exploration missions based on on-board image processing for control and for robotics missions using vision sensors. It presents a top-level description of technologies required for the design and construction of SVIP and EASI and to advance the spatial-spectral imaging and large-scale space interferometry science and engineering.

A Simple Approach to Fourier Aliasing

ERIC Educational Resources Information Center

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation

NASA Technical Reports Server (NTRS)

Marko, H.

1978-01-01

A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.

Fast frequency domain method to detect skew in a document image

NASA Astrophysics Data System (ADS)

Mehta, Sunita; Walia, Ekta; Dutta, Maitreyee

2015-12-01

In this paper, a new fast frequency domain method based on Discrete Wavelet Transform and Fast Fourier Transform has been implemented for the determination of the skew angle in a document image. Firstly, image size reduction is done by using two-dimensional Discrete Wavelet Transform and then skew angle is computed using Fast Fourier Transform. Skew angle error is almost negligible. The proposed method is experimented using a large number of documents having skew between -90° and +90° and results are compared with Moments with Discrete Wavelet Transform method and other commonly used existing methods. It has been determined that this method works more efficiently than the existing methods. Also, it works with typed, picture documents having different fonts and resolutions. It overcomes the drawback of the recently proposed method of Moments with Discrete Wavelet Transform that does not work with picture documents.

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)

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.

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.

Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform

NASA Astrophysics Data System (ADS)

Li, Yanbin; Zhang, Feng; Li, Yuanchao; Tao, Ran

2015-09-01

A multiple-image cryptosystem is proposed based on the cascaded fractional Fourier transform. During an encryption procedure, each of the original images is directly separated into two phase masks. A portion of the masks is subsequently modulated into an interim mask, which is encrypted into the ciphertext image; the others are used as the encryption keys. Using phase truncation in the fractional Fourier domain, one can use an asymmetric cryptosystem to produce a real-valued noise-like ciphertext, while a legal user can reconstruct all of the original images using a different group of phase masks. The encryption key is an indivisible part of the corresponding original image and is still useful during decryption. The proposed system has high resistance to various potential attacks, including the chosen-plaintext attack. Numerical simulations also demonstrate the security and feasibility of the proposed scheme.

How well do we know the incoming solar infrared radiation?

NASA Astrophysics Data System (ADS)

Elsey, Jonathan; Coleman, Marc; Gardiner, Tom; Shine, Keith

2017-04-01

The solar spectral irradiance (SSI) has been identified as a key climate variable by the Global Climate Observing System (Bojinski et al. 2014, Bull. Amer. Meteor. Soc.). It is of importance in the modelling of atmospheric radiative transfer, and the quantification of the global energy budget. However, in the near-infrared spectral region (between 2000-10000 cm-1) there exists a discrepancy of 7% between spectra measured from the space-based SOLSPEC instrument (Thuillier et al. 2015, Solar Physics) and those from a ground-based Langley technique (Bolseé et al. 2014, Solar Physics). This same difference is also present between different analyses of the SOLSPEC data. This work aims to reconcile some of these differences by presenting an estimate of the near-infrared SSI obtained from ground-based measurements taken using an absolutely calibrated Fourier transform spectrometer. Spectra are obtained both using the Langley technique and by direct comparison with a radiative transfer model, with appropriate handling of both aerosol scattering and molecular continuum absorption. Particular focus is dedicated to the quantification of uncertainty in these spectra, from both the inherent uncertainty in the measurement setup and that from the use of the radiative transfer code and its inputs.

Frequency Management for Electromagnetic Continuous Wave Conductivity Meters

PubMed Central

Mazurek, Przemyslaw; Putynkowski, Grzegorz

2016-01-01

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

Frequency Management for Electromagnetic Continuous Wave Conductivity Meters.

PubMed

Mazurek, Przemyslaw; Putynkowski, Grzegorz

2016-04-07

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

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

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates

PubMed Central

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988

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.

Simultaneous measurement of absolute strain and differential strain based on fiber Bragg grating Fabry-Perot sensor

NASA Astrophysics Data System (ADS)

Wang, Kuiru; Wang, Bo; Yan, Binbin; Sang, Xinzhu; Yuan, Jinhui; Peng, Gang-Ding

2013-10-01

We present a fiber Bragg grating Fabry-Perot (FBG-FP) sensor using the fast Fourier transform (FFT) demodulation for measuring the absolute strain and differential strain simultaneously. The amplitude and phase characteristics of Fourier transform spectrum have been studied. The relation between the amplitude of Fourier spectrum and the differential strain has been presented. We fabricate the fiber grating FP cavity sensor, and carry out the experiment on the measurement of absolute strain and differential strain. Experimental results verify the demodulation method, and show that this sensor has a good accuracy in the scope of measurement. The demodulating method can expand the number of multiplexed sensors combining with wavelength division multiplexing and time division multiplexing.

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.

Computing Fourier integral operators with caustics

NASA Astrophysics Data System (ADS)

Caday, Peter

2016-12-01

Fourier integral operators (FIOs) have widespread applications in imaging, inverse problems, and PDEs. An implementation of a generic algorithm for computing FIOs associated with canonical graphs is presented, based on a recent paper of de Hoop et al. Given the canonical transformation and principal symbol of the operator, a preprocessing step reduces application of an FIO approximately to multiplications, pushforwards and forward and inverse discrete Fourier transforms, which can be computed in O({N}n+(n-1)/2{log}N) time for an n-dimensional FIO. The same preprocessed data also allows computation of the inverse and transpose of the FIO, with identical runtime. Examples demonstrate the algorithm’s output, and easily extendible MATLAB/C++ source code is available from the author.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

A Comparison of Optical versus Hardware Fourier Transforms.

DTIC Science & Technology

1983-10-31

AD- R136 223 A COMPRISON’OF OPTICAL ERSUS HARDWARE FOURIER i/i.TRANSFORMS(U) VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF PHYSICS S P...transform and its inverse filtered Fourier transform obtained with the Digital Image Processing (DIP) hardware system located at the School of Aerospace...transparencies, and provided to us by Dr. Ralph G. Allen, Director of the Laser Effects Branch (Division of Radiation Sciences). The DIP system consisted of: an

Simulation of path delay multiplexing-based Fourier transform spectrometer for fiber Bragg grating interrogation.

PubMed

Chelliah, Pandian; Sahoo, Trilochan; Singh, Sheela; Sujatha, Annie

2015-10-20

A Fourier transform spectrometer (FTS) used for interrogating a fiber Bragg grating (FBG) consists of a scanning-type interferometer. The FTS has a broad wavelength range of operation and good multiplexing capability. However, it has poor wavelength resolution and interrogation speed. We propose a modification to the FTS using path delay multiplexing to improve the same. Using this method, spatial resolution and interrogation time can be improved by n times by using n path delays. In this paper, simulation results for n=2, 5 are shown.

Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors.

PubMed

Lamas-Seco, José J; Castro, Paula M; Dapena, Adriana; Vazquez-Araujo, Francisco J

2015-10-26

Inductive Loop Detectors (ILDs) are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT) of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype.

Atmospheric Pressure Ionization Permanent Magnet Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

PubMed Central

Vilkov, Andrey N.; Gamage, Chaminda M.; Misharin, Alexander S.; Doroshenko, Vladimir M.; Tolmachev, Dmitry A.; Tarasova, Irina A.; Kharybin, Oleg N.; Novoselov, Konstantin P.; Gorshkov, Michael V.

2007-01-01

A new Fourier Transform Ion Cyclotron Resonance mass spectrometer based on a permanent magnet with an atmospheric pressure ionization source was designed and constructed. A mass resolving power (full-width-at-half-maximum) of up to 80,000 in the electron ionization mode and 25,000 in the electrospray mode was obtained. Also, a mass measurement accuracy at low-ppm level has been demonstrated for peptide mixtures in a mass range of up to 1,200 m/z in the isotopically resolved mass spectra. PMID:17587594

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

[Measurements of the concentration of atmospheric CO2 based on OP/FTIR method and infrared reflecting scanning Fourier transform spectrometry].

PubMed

Wei, Ru-Yi; Zhou, Jin-Song; Zhang, Xue-Min; Yu, Tao; Gao, Xiao-Hui; Ren, Xiao-Qiang

2014-11-01

The present paper describes the observations and measurements of the infrared absorption spectra of CO2 on the Earth's surface with OP/FTIR method by employing a mid-infrared reflecting scanning Fourier transform spectrometry, which are the first results produced by the first prototype in China developed by the team of authors. This reflecting scanning Fourier transform spectrometry works in the spectral range 2 100-3 150 cm(-1) with a spectral resolution of 2 cm(-1). Method to measure the atmospheric molecules was described and mathematical proof and quantitative algorithms to retrieve molecular concentration were established. The related models were performed both by a direct method based on the Beer-Lambert Law and by a simulating-fitting method based on HITRAN database and the instrument functions. Concentrations of CO2 were retrieved by the two models. The results of observation and modeling analyses indicate that the concentrations have a distribution of 300-370 ppm, and show tendency that going with the variation of the environment they first decrease slowly and then increase rapidly during the observation period, and reached low points in the afternoon and during the sunset. The concentrations with measuring times retrieved by the direct method and by the simulating-fitting method agree with each other very well, with the correlation of all the data is up to 99.79%, and the relative error is no more than 2.00%. The precision for retrieving is relatively high. The results of this paper demonstrate that, in the field of detecting atmospheric compositions, OP/FTIR method performed by the Infrared reflecting scanning Fourier transform spectrometry is a feasible and effective technical approach, and either the direct method or the simulating-fitting method is capable of retrieving concentrations with high precision.

Atmospheric trace gas analysis using matrix isolation-Fourier Transform Infrared Spectroscopy

NASA Astrophysics Data System (ADS)

Griffith, David W. T.; Schuster, Gerhard

1987-03-01

A novel cryogenic sampling method combining the matrix isolation technique with FTIR spectroscopy has been developed for atmospheric trace gas analysis. It is applicable to a wide range of molecules with detection limits typically in the 10-50 ppt range. The method is described along with some measurements of N2O, CFCl3, CF2Cl2, OCS, CS2, SO2 and PAN from samples collected at ground level and from an aircraft between 9 and 14 km.

Reference software implementation for GIFTS ground data processing

NASA Astrophysics Data System (ADS)

Garcia, R. K.; Howell, H. B.; Knuteson, R. O.; Martin, G. D.; Olson, E. R.; Smuga-Otto, M. J.

2006-08-01

Future satellite weather instruments such as high spectral resolution imaging interferometers pose a challenge to the atmospheric science and software development communities due to the immense data volumes they will generate. An open-source, scalable reference software implementation demonstrating the calibration of radiance products from an imaging interferometer, the Geosynchronous Imaging Fourier Transform Spectrometer1 (GIFTS), is presented. This paper covers essential design principles laid out in summary system diagrams, lessons learned during implementation and preliminary test results from the GIFTS Information Processing System (GIPS) prototype.

Validation and Support of a Quantitative Infrared Instrument Facility and Generation of a Library of Chemical Warfare and Related Materials by Fourier Transform Infrared Spectroscopy

DTIC Science & Technology

2006-11-01

Hampton, VA 23666 November 2006 Approved for public release: distribution is unlimited. 20070907323 ABERDEEN PROVING GROUND, MD 21010-5424 DISCLAIMER...REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour...SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION I AVAILABILITY STATEMENT Approved for public release; distribution is unlimited. 13. SUPPLEMENTARY

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.

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.

A comparison of orthogonal transformations for digital speech processing.

NASA Technical Reports Server (NTRS)

Campanella, S. J.; Robinson, G. S.

1971-01-01

Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.

Image security based on iterative random phase encoding in expanded fractional Fourier transform domains

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Chen, Hang; Blondel, Walter; Shen, Zhenmin; Liu, Shutian

2018-06-01

A novel image encryption method is proposed by using the expanded fractional Fourier transform, which is implemented with a pair of lenses. Here the centers of two lenses are separated at the cross section of axis in optical system. The encryption system is addressed with Fresnel diffraction and phase modulation for the calculation of information transmission. The iterative process with the transform unit is utilized for hiding secret image. The structure parameters of a battery of lenses can be used for additional keys. The performance of encryption method is analyzed theoretically and digitally. The results show that the security of this algorithm is enhanced markedly by the added keys.

Detecting the spatial chirp signals by fractional Fourier lens with transformation materials

NASA Astrophysics Data System (ADS)

Chen, J.; Hu, J.

2018-02-01

Fractional Fourier transform (FrFT) is the general form of the Fourier transform and is an important tool in signal processing. As one typical application of FrFT, detecting the chirp rate (CR, or known as the rate of frequency change) of a chirp signal is important in many optical measurements. The optical FrFT that based on graded index lens fails to detect the high CR chirp because the short wave propagation distance of the impulse in the lens will weaken the paraxial approximation condition. With the help of transformation optics, the improved FrFT lens is proposed to adjust the high CR as well as the impulse location of the given input chirp signal. The designed transformation materials can implement the effect of space compression, making the input chirp signal is equivalent to have lower CR, therefore the system can satisfy the paraxial approximation better. As a result, this lens can improve the detection precision for the high CR. The numerical simulations verified the design. The proposed device may have both theoretical and practical values, and the design demonstrates the ability and flexibility of TO in spatial signal processing.

Improved argument-FFT frequency offset estimation for QPSK coherent optical Systems

NASA Astrophysics Data System (ADS)

Han, Jilong; Li, Wei; Yuan, Zhilin; Li, Haitao; Huang, Liyan; Hu, Qianggao

2016-02-01

A frequency offset estimation (FOE) algorithm based on fast Fourier transform (FFT) of the signal's argument is investigated, which does not require removing the modulated data phase. In this paper, we analyze the flaw of the argument-FFT algorithm and propose a combined FOE algorithm, in which the absolute of frequency offset (FO) is accurately calculated by argument-FFT algorithm with a relatively large number of samples and the sign of FO is determined by FFT-based interpolation discrete Fourier transformation (DFT) algorithm with a relatively small number of samples. Compared with the previous algorithms based on argument-FFT, the proposed one has low complexity and can still effectively work with a relatively less number of samples.

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.

Fourier transform emission spectroscopy of the TiF radical in the 407 nm region

NASA Astrophysics Data System (ADS)

Imajo, Takashi; Kobayashi, Yuki; Nakashima, Yoshihiro; Tanaka, Keiichi; Tanaka, Takehiko

2005-04-01

Ultraviolet emission spectra of the TiF radical in the 407 nm region have been observed at a resolution of 0.04 cm -1 using a Fourier transform spectrometer. A new electronic assignment of 4Γ- X4Φ has been proposed. Rotational analysis has been obtained for the 0-0 and 1-1 vibrational bands of the 4Γ 5/2- X4Φ 3/2, 4Γ 9/2- X4Φ 7/2, and 4Γ 11/2- X4Φ 9/2 subbands and the 0-0 band of 4Γ 7/2- X4Φ 5/2. The lower state rotational and centrifugal distortion constants are consistent with the previous results [J. Mol. Spectrosc. 184 (1997) 186; J. Chem. Phys. 119 (2003) 9496], to the conformation that the lower state of the 407 nm band is the 4Φ ground electronic state. Rough estimates of the vibrational interval Δ G(1/2) and the spin-orbit coupling constant A in the 4Γ state were also obtained.

Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems

NASA Astrophysics Data System (ADS)

Leuschner, Matthias; Fritzen, Felix

2017-11-01

Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.

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

An alternative approach to characterize nonlinear site effects

USGS Publications Warehouse

Zhang, R.R.; Hartzell, S.; Liang, J.; Hu, Y.

2005-01-01

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Optical-Path-Difference Linear Mechanism for the Panchromatic Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

Blavier, Jean-Francois L.; Heverly, Matthew C.; Key, Richard W.; Sander, Stanley P.

2011-01-01

A document discusses a mechanism that uses flex-pivots in a parallelogram arrangement to provide frictionless motion with an unlimited lifetime. A voicecoil actuator drives the parallelogram over the required 5-cm travel. An optical position sensor provides feedback for a servo loop that keeps the velocity within 1 percent of expected value. Residual tip/tilt error is compensated for by a piezo actuator that drives the interferometer mirror. This mechanism builds on previous work that targeted ground-based measurements. The main novelty aspects include cryogenic and vacuum operation, high reliability for spaceflight, compactness of the design, optical layout compatible with the needs of an imaging FTS (i.e. wide overall field-of-view), and mirror optical coatings to cover very broad wavelength range (i.e., 0.26 to 15 m).

Sequential measurement of conjugate variables as an alternative quantum state tomography.

PubMed

Di Lorenzo, Antonio

2013-01-04

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.

Photonic fractional Fourier transformer with a single dispersive device.

PubMed

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-08

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

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.

Method for utilizing properties of the sinc(x) function for phase retrieval on nyquist-under-sampled data

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor); Smith, Jeffrey Scott (Inventor); Aronstein, David L. (Inventor)

2012-01-01

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for simulating propagation of an electromagnetic field, performing phase retrieval, or sampling a band-limited function. A system practicing the method generates transformed data using a discrete Fourier transform which samples a band-limited function f(x) without interpolating or modifying received data associated with the function f(x), wherein an interval between repeated copies in a periodic extension of the function f(x) obtained from the discrete Fourier transform is associated with a sampling ratio Q, defined as a ratio of a sampling frequency to a band-limited frequency, and wherein Q is assigned a value between 1 and 2 such that substantially no aliasing occurs in the transformed data, and retrieves a phase in the received data based on the transformed data, wherein the phase is used as feedback to an optical system.

ANITA Air Monitoring on the International Space Station: Results Compared to Other Measurements

NASA Technical Reports Server (NTRS)

Honne, A.; Schumann-Olsen, H.; Kaspersen, K.; Limero, T.; Macatangay, A.; Mosebach, H.; Kampf, D.; Mudgett, P. D.; James, J. T.; Tan, G.;

General purpose graphic processing unit implementation of adaptive pulse compression algorithms

NASA Astrophysics Data System (ADS)

Cai, Jingxiao; Zhang, Yan

2017-07-01

This study introduces a practical approach to implement real-time signal processing algorithms for general surveillance radar based on NVIDIA graphical processing units (GPUs). The pulse compression algorithms are implemented using compute unified device architecture (CUDA) libraries such as CUDA basic linear algebra subroutines and CUDA fast Fourier transform library, which are adopted from open source libraries and optimized for the NVIDIA GPUs. For more advanced, adaptive processing algorithms such as adaptive pulse compression, customized kernel optimization is needed and investigated. A statistical optimization approach is developed for this purpose without needing much knowledge of the physical configurations of the kernels. It was found that the kernel optimization approach can significantly improve the performance. Benchmark performance is compared with the CPU performance in terms of processing accelerations. The proposed implementation framework can be used in various radar systems including ground-based phased array radar, airborne sense and avoid radar, and aerospace surveillance radar.

Simulation Analysis of Helicopter Ground Resonance Nonlinear Dynamics

NASA Astrophysics Data System (ADS)

Zhu, Yan; Lu, Yu-hui; Ling, Ai-min

2017-07-01

In order to accurately predict the dynamic instability of helicopter ground resonance, a modeling and simulation method of helicopter ground resonance considering nonlinear dynamic characteristics of components (rotor lead-lag damper, landing gear wheel and absorber) is presented. The numerical integral method is used to calculate the transient responses of the body and rotor, simulating some disturbance. To obtain quantitative instabilities, Fast Fourier Transform (FFT) is conducted to estimate the modal frequencies, and the mobile rectangular window method is employed in the predictions of the modal damping in terms of the response time history. Simulation results show that ground resonance simulation test can exactly lead up the blade lead-lag regressing mode frequency, and the modal damping obtained according to attenuation curves are close to the test results. The simulation test results are in accordance with the actual accident situation, and prove the correctness of the simulation method. This analysis method used for ground resonance simulation test can give out the results according with real helicopter engineering tests.

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.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

On the Relationship between Fourier and Response Spectra: Implications for the Adjustment of Empirical Ground-Motion Prediction Equations (GMPEs)

NASA Astrophysics Data System (ADS)

Bora, Sanjay; Scherbaum, Frank; Kuehn, Nicolas; Stafford, Peter

2016-04-01

Often, scaling of response spectral amplitudes, (e.g., spectral acceleration) obtained from empirical ground motion prediction equations (GMPEs), with respect to commonly used seismological parameters such as magnitude, distance and site condition is assumed/referred to be representing a similar scaling of Fourier spectral amplitudes. For instance, the distance scaling of response spectral amplitudes is related with the geometrical spreading of seismic waves. Such comparison of scaling of response spectral amplitudes with that of corresponding Fourier spectral amplitudes is motivated by that, the functional forms of response spectral GMPEs are often derived using the concepts borrowed from Fourier spectral modeling of ground motion. As these GMPEs are subsequently calibrated with empirical observations, this may not appear to pose any major problems in the prediction of ground motion for a particular earthquake scenario. However, the assumption that the Fourier spectral concepts persist for response spectra can lead to undesirable consequences when it comes to the adjustment of response spectral GMPEs to represent conditions not covered in the original empirical data set. In this context, a couple of important questions arise, e.g., what are the distinctions and/or similarities between Fourier and response spectra of ground-motions? And, if they are different, then what is the mechanism responsible for such differences and how do adjustments that are made to FAS manifest in response spectra? We explore the relationship between the Fourier and response spectrum of ground motion by using random vibration theory (RVT). With a simple Brune (1970, 1971) source model, RVT-generated acceleration spectra for a fixed magnitude and distance scenario are used. The RVT analyses reveal that the scaling of low oscillator-frequency response spectral ordinates can be treated as being equivalent to the scaling of the corresponding Fourier spectral ordinates. However, the high oscillator-frequency response spectral ordinates are controlled by a rather wide-band of Fourier spectral ordinates. In fact, the peak ground acceleration (PGA), counter to the popular perception that it is a reflection of the high-frequency characteristics of ground motion, is controlled by the entire Fourier spectrum of ground-motion. Finally, it is demonstrated, how an adjustment made in Fourier spectral amplitudes is different or similar to the same adjustment made in the response spectral amplitudes. For this purpose, two cases: adjustments to the stress parameter (Δσ) (source term) and to attributes reflecting site response (V s-κ0) are considered.

Retrieving cirrus microphysical properties from stellar aureoles

NASA Astrophysics Data System (ADS)

DeVore, J. G.; Kristl, J. A.; Rappaport, S. A.

2013-06-01

The aureoles around stars caused by thin cirrus limit nighttime measurement opportunities for ground-based astronomy, but can provide information on high-altitude ice crystals for climate research. In this paper we attempt to demonstrate quantitatively how this works. Aureole profiles can be followed out to ~0.2° from stars and ~0.5° from Jupiter. Interpretation of diffracted starlight is similar to that for sunlight, but emphasizes larger particles. Stellar diffraction profiles are very distinctive, typically being approximately flat out to a critical angle followed by gradually steepening power-law falloff with slope less steep than -3. Using the relationship between the phase function for diffraction and the average Fourier transform of the projected area of complex ice crystals, we show that defining particle size in terms of average projected area normal to the propagation direction of the starlight leads to a simple, analytic approximation representing large-particle diffraction that is nearly independent of crystal habit. A similar analytic approximation for the diffraction aureole allows it to be separated from the point spread function and the sky background. Multiple scattering is deconvolved using the Hankel transform leading to the diffraction phase function. Application of constrained numerical inversion to the phase function then yields a solution for the particle size distribution in the range between ~50 μm and ~400 μm. Stellar aureole measurements can provide one of the very few, as well as least expensive, methods for retrieving cirrus microphysical properties from ground-based observations.

Linear Transforms for Fourier Data on the Sphere: Application to High Angular Resolution Diffusion MRI of the Brain

PubMed Central

Haldar, Justin P.; Leahy, Richard M.

2013-01-01

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors. PMID:23353603

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

A new strategy for array optimization applied to Brazilian Decimetric Array

NASA Astrophysics Data System (ADS)

Faria, C.; Stephany, S.; Sawant, H. S.

Radio interferometric arrays measure the Fourier transform of the sky brightness distribution in a finite set of points that are determined by the cross-correlation of different pairs of antennas of the array The sky brightness distribution is reconstructed by the inverse Fourier transform of the sampled visibilities The quality of the reconstructed images strongly depends on the array configuration since it determines the sampling function and therefore the points in the Fourier Plane This work proposes a new optimization strategy for the array configuration that is based on the entropy of the distribution of the samples points in the Fourier plane A stochastic optimizer the Ant Colony Optimization employs entropy of the point distribution in the Fourier plane to iteratively refine the candidate solutions The proposed strategy was developed for the Brazilian Decimetric Array BDA a radio interferometric array that is currently being developed for solar observations at the Brazilian Institute for Space Research Configurations results corresponding to the Fourier plane coverage synthesized beam and side lobes levels are shown for an optimized BDA configuration obtained with the proposed strategy and compared to the results for a standard T array configuration that was originally proposed

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.

Improved full analytical polygon-based method using Fourier analysis of the three-dimensional affine transformation.

PubMed

Pan, Yijie; Wang, Yongtian; Liu, Juan; Li, Xin; Jia, Jia

2014-03-01

Previous research [Appl. Opt.52, A290 (2013)] has revealed that Fourier analysis of three-dimensional affine transformation theory can be used to improve the computation speed of the traditional polygon-based method. In this paper, we continue our research and propose an improved full analytical polygon-based method developed upon this theory. Vertex vectors of primitive and arbitrary triangles and the pseudo-inverse matrix were used to obtain an affine transformation matrix representing the spatial relationship between the two triangles. With this relationship and the primitive spectrum, we analytically obtained the spectrum of the arbitrary triangle. This algorithm discards low-level angular dependent computations. In order to add diffusive reflection to each arbitrary surface, we also propose a whole matrix computation approach that takes advantage of the affine transformation matrix and uses matrix multiplication to calculate shifting parameters of similar sub-polygons. The proposed method improves hologram computation speed for the conventional full analytical approach. Optical experimental results are demonstrated which prove that the proposed method can effectively reconstruct three-dimensional scenes.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

PubMed

Scargle, Jeffrey D; Way, M J; Gazis, P R

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA

PubMed Central

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys. PMID:29628519

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

A 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.

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.

Multiparametric approach to unravel the mechanism of Strombolian activity at a multivent system: Mt. Etna case study

NASA Astrophysics Data System (ADS)

Cannata, Andrea; Del Bello, Elisabetta; Kueppers, Ulrich; Privitera, Eugenio; Ricci, Tullio; Scarlato, Piergiorgio; Sciotto, Mariangela; Spina, Laura; Taddeucci, Jacopo; Pena Fernandez, Juan Jose; Sesterhenn, Joern

2016-04-01

On 5th July 2014 an eruptive fissure (hereafter referred to as EF) opened at the base of North-East Crater (NEC) of Mt. Etna. EF produced both Strombolian explosions and lava effusion. Thanks to the multiparametric experiment planned in the framework of MEDSUV project, we had the chance to acquire geophysical and volcanological data, in order to investigate the ongoing volcanic activity at EF. Temporary instruments (2 broadband seismometers, 2 microphones, 3-microphone arrays, a high-speed video camera and a thermal-camera) were deployed near the active vents during 15-16 July 2014 and were integrated with the data recorded by the permanent networks. Several kinds of studies are currently in progress, such as: frequency analysis by Fourier Transform and Short Time Fourier Transform to evaluate the spectral content of both seismic and acoustic signals; partitioning of seismic and acoustic energies, whose time variations could reflect changes in the volcanic dynamics; investigation on the intertimes between explosions to investigate their recurrence behaviour; classification of the waveforms of infrasound events. Furthermore, joint analysis of video signals and seismic-acoustic wavefields outlined relationships between pyroclasts ejection velocity, total erupted mass, peak explosion pressure, and air-ground motion coupling. This multiparametric approach allowed distinguishing and characterizing individually the behavior of the two vents active along the eruptive fissure via their thermal, visible and infrasonic signatures and shed light in the eruptive dynamics.

Fourier transform spectroscopy of the CO-stretching band of O-18 methanol

NASA Astrophysics Data System (ADS)

Lees, R. M.; Murphy, Reba-Jean; Moruzzi, Giovanni; Predoi-Cross, Adriana; Xu, Li-Hong; Appadoo, D. R. T.; Billinghurst, B.; Goulding, R. R. J.; Zhao, Saibei

2009-07-01

The high-resolution Fourier transform spectrum of the ν8 CO-stretching band of CH 318OH between 900 and 1100 cm -1 has been recorded at the Canadian Light Source (CLS) synchrotron facility in Saskatoon, and the majority of the torsion-rotation structure has been analyzed. For the ν t = 0 torsional ground state, subbands have been identified for K values from 0 to 11 for A and E torsional symmetries up to J values typically well over 30. For ν t = 1, A and E subbands have been assigned up to K = 7, and several ν t = 2 subbands have also been identified. Upper-state term values determined from the assigned transitions using the Ritz program have been fitted to J( J + 1) power-series expansions to obtain substate origins and sets of state-specific parameters giving a compact representation of the substate J-dependence. The ν t = 0 subband origins have been fitted to effective molecular constants for the excited CO-stretching state and a torsional barrier of 377.49(32) cm -1 is found, representing a 0.89% increase over the ground-state value. The vibrational energy for the CO-stretch state was found to be 1007.49(7) cm -1. A number of subband-wide and J-localized perturbations have been seen in the spectrum, arising both from anharmonic and Coriolis interactions, and several of the interacting states have been identified.

The Radon cumulative distribution transform and its application to image classification

PubMed Central

Kolouri, Soheil; Park, Se Rim; Rohde, Gustavo K.

2016-01-01

Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier, Wavelet, etc.) are linear transforms, and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here we describe a nonlinear, invertible, low-level image processing transform based on combining the well known Radon transform for image data, and the 1D Cumulative Distribution Transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in transform space. PMID:26685245

Trace Gas Measurements in Nascent, Aged and Cloud-processed Smoke from Africa Savanna Fires by Airborne Fourier Transform Infrared Spectroscopy (AFTIR)

NASA Technical Reports Server (NTRS)

Yokelson, Robert J.; Bertschi, Isaac T.; Christian, Ted J.; Hobbs, Peter V.; Ward, Darold E.; Hao, Wei Min

2003-01-01

We measured stable and reactive trace gases with an airborne Fourier transform infrared spectrometer (AFTIR) on the University of Washington Convair-580 research aircraft in August/September 2000 during the SAFARI 2000 dry season campaign in Southern Africa. The measurements included vertical profiles of C02, CO, H20, and CH4 up to 5.5 km on six occasions above instrumented ground sites and below the TERRA satellite and ER-2 high-flying research aircraft. We also measured the trace gas emissions from 10 African savanna fires. Five of these fires featured extensive ground-based fuel characterization, and two were in the humid savanna ecosystem that accounts for most African biomass burning. The major constituents we detected in nascent CH3OOH, HCHO, CH30H, HCN, NH3, HCOOH, and C2H2. These are the first quantitative measurements of the initial emissions of oxygenated volatile organic compounds (OVOC), NH3, and HCN from African savanna fires. On average, we measured 5.3 g/kg of OVOC and 3.6 g/kg of hydrocarbons (including CH4) in the initial emissions from the fires. Thus, the OVOC will have profound, largely unexplored effects on tropical tropospheric chemistry. The HCN emission factor was only weakly dependent on fire type; the average value (0.53 g/kg) is about 20 times that of a previous recommendation. HCN may be useful as a tracer for savanna fires. Delta O3/Delta CO and Delta CH3COO/Delta CO increased to as much as 9% in <1 h of photochemical processing downwind of fires. Direct measurements showed that cloud processing of smoke greatly reduced CH30H, NH3, CH3COOH, SO2, and NO2 levels, but significantly increased HCHO and NO.

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

Orthogonal fast spherical Bessel transform on uniform grid

NASA Astrophysics Data System (ADS)

Serov, Vladislav V.

2017-07-01

We propose an algorithm for the orthogonal fast discrete spherical Bessel transform on a uniform grid. Our approach is based upon the spherical Bessel transform factorization into the two subsequent orthogonal transforms, namely the fast Fourier transform and the orthogonal transform founded on the derivatives of the discrete Legendre orthogonal polynomials. The method utility is illustrated by its implementation for the problem of a two-atomic molecule in a time-dependent external field simulating the one utilized in the attosecond streaking technique.

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)

Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform

NASA Astrophysics Data System (ADS)

Bekkouche, Toufik; Bouguezel, Saad

2018-03-01

We propose a real-to-real image encryption method. It is a double random amplitude encryption method based on the parametric discrete Fourier transform coupled with chaotic maps to perform the scrambling. The main idea behind this method is the introduction of a complex-to-real conversion by exploiting the inherent symmetry property of the transform in the case of real-valued sequences. This conversion allows the encrypted image to be real-valued instead of being a complex-valued image as in all existing double random phase encryption methods. The advantage is to store or transmit only one image instead of two images (real and imaginary parts). Computer simulation results and comparisons with the existing double random amplitude encryption methods are provided for peak signal-to-noise ratio, correlation coefficient, histogram analysis, and key sensitivity.

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.

Sonic Boom Pressure Signature Uncertainty Calculation and Propagation to Ground Noise

NASA Technical Reports Server (NTRS)

West, Thomas K., IV; Bretl, Katherine N.; Walker, Eric L.; Pinier, Jeremy T.

2015-01-01

The objective of this study was to outline an approach for the quantification of uncertainty in sonic boom measurements and to investigate the effect of various near-field uncertainty representation approaches on ground noise predictions. These approaches included a symmetric versus asymmetric uncertainty band representation and a dispersion technique based on a partial sum Fourier series that allows for the inclusion of random error sources in the uncertainty. The near-field uncertainty was propagated to the ground level, along with additional uncertainty in the propagation modeling. Estimates of perceived loudness were obtained for the various types of uncertainty representation in the near-field. Analyses were performed on three configurations of interest to the sonic boom community: the SEEB-ALR, the 69o DeltaWing, and the LM 1021-01. Results showed that representation of the near-field uncertainty plays a key role in ground noise predictions. Using a Fourier series based dispersion approach can double the amount of uncertainty in the ground noise compared to a pure bias representation. Compared to previous computational fluid dynamics results, uncertainty in ground noise predictions were greater when considering the near-field experimental uncertainty.

Fourier transform and particle swarm optimization based modified LQR algorithm for mitigation of vibrations using magnetorheological dampers

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Kumar, Ashok

2017-11-01

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear-quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure having an MR damper at the ground floor level subjected to three different near-fault historical earthquake time histories, and the outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-storey drift, relative displacement, and acceleration response.

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.

Fourier Phase Domain Steganography: Phase Bin Encoding Via Interpolation

NASA Astrophysics Data System (ADS)

Rivas, Edward

2007-04-01

In recent years there has been an increased interest in audio steganography and watermarking. This is due primarily to two reasons. First, an acute need to improve our national security capabilities in light of terrorist and criminal activity has driven new ideas and experimentation. Secondly, the explosive proliferation of digital media has forced the music industry to rethink how they will protect their intellectual property. Various techniques have been implemented but the phase domain remains a fertile ground for improvement due to the relative robustness to many types of distortion and immunity to the Human Auditory System. A new method for embedding data in the phase domain of the Discrete Fourier Transform of an audio signal is proposed. Focus is given to robustness and low perceptibility, while maintaining a relatively high capacity rate of up to 172 bits/s.

A Primer of Fourier Transform NMR.

ERIC Educational Resources Information Center

Macomber, Roger S.

1985-01-01

Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yi, Cai; Tsui, Kwok-Leung; Lin, Jianhui

2018-02-01

Rolling element bearings are widely used in various industrial machines, such as electric motors, generators, pumps, gearboxes, railway axles, turbines, and helicopter transmissions. Fault diagnosis of rolling element bearings is beneficial to preventing any unexpected accident and reducing economic loss. In the past years, many bearing fault detection methods have been developed. Recently, a new adaptive signal processing method called empirical wavelet transform attracts much attention from readers and engineers and its applications to bearing fault diagnosis have been reported. The main problem of empirical wavelet transform is that Fourier segments required in empirical wavelet transform are strongly dependent on the local maxima of the amplitudes of the Fourier spectrum of a signal, which connotes that Fourier segments are not always reliable and effective if the Fourier spectrum of the signal is complicated and overwhelmed by heavy noises and other strong vibration components. In this paper, sparsity guided empirical wavelet transform is proposed to automatically establish Fourier segments required in empirical wavelet transform for fault diagnosis of rolling element bearings. Industrial bearing fault signals caused by single and multiple railway axle bearing defects are used to verify the effectiveness of the proposed sparsity guided empirical wavelet transform. Results show that the proposed method can automatically discover Fourier segments required in empirical wavelet transform and reveal single and multiple railway axle bearing defects. Besides, some comparisons with three popular signal processing methods including ensemble empirical mode decomposition, the fast kurtogram and the fast spectral correlation are conducted to highlight the superiority of the proposed method.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

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

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less

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.

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

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.

Holographic memory system based on projection recording of computer-generated 1D Fourier holograms.

PubMed

Betin, A Yu; Bobrinev, V I; Donchenko, S S; Odinokov, S B; Evtikhiev, N N; Starikov, R S; Starikov, S N; Zlokazov, E Yu

2014-10-01

Utilization of computer generation of holographic structures significantly simplifies the optical scheme that is used to record the microholograms in a holographic memory record system. Also digital holographic synthesis allows to account the nonlinear errors of the record system to improve the microholograms quality. The multiplexed record of holograms is a widespread technique to increase the data record density. In this article we represent the holographic memory system based on digital synthesis of amplitude one-dimensional (1D) Fourier transform holograms and the multiplexed record of these holograms onto the holographic carrier using optical projection scheme. 1D Fourier transform holograms are very sensitive to orientation of the anamorphic optical element (cylindrical lens) that is required for encoded data object reconstruction. The multiplex record of several holograms with different orientation in an optical projection scheme allowed reconstruction of the data object from each hologram by rotating the cylindrical lens on the corresponding angle. Also, we discuss two optical schemes for the recorded holograms readout: a full-page readout system and line-by-line readout system. We consider the benefits of both systems and present the results of experimental modeling of 1D Fourier holograms nonmultiplex and multiplex record and reconstruction.

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.

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.

A Robust Magnetic Resonance Imager For Ground and Flight Based Measurements of Fluid Physics Phenomena

NASA Technical Reports Server (NTRS)

2002-01-01

Nuclear magnetic resonance (NMR) is a powerful and versatile, noninvasive method for studying fluid transport problems, However, its applications to these types of investigations have been limited. A primary factor that limits the application of NMR has been the lack of a user-friendly, versatile, and inexpensive NMR imaging apparatus that can be used by scientists who are not familiar with sophisticated NMR. To rectify this situation, we developed a user-friendly, NMR imager for projects of relevance to the MRD science community. To that end, we performed preliminary collaborative experiments between NASA, NCMR, and New Mexico Resonance in the high field NMR set up at New Mexico Resonance to track wetting front dynamics in foams under gravity. The experiments were done in a 30 cm, 1.9T Oxford magnet with a TECMAG Libra spectrometer (Tecmag, Inc., Houston, TX). We used two different imaging strategies depending on whether the water in the foam sample was static or moving. Stationary water distributions were imaged with the standard Fourier imaging method, as used in medical MRI, in which data are acquired from all parts of the region of interest at all times and Fourier transformed into a static spatial image.

Conormal distributions in the Shubin calculus of pseudodifferential operators

NASA Astrophysics Data System (ADS)

Cappiello, Marco; Schulz, René; Wahlberg, Patrik

2018-02-01

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

Quantum Color Image Encryption Algorithm Based on A Hyper-Chaotic System and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong

2016-12-01

To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.

F2Dock: Fast Fourier Protein-Protein Docking

PubMed Central

Bajaj, Chandrajit; Chowdhury, Rezaul; Siddavanahalli, Vinay

2009-01-01

The functions of proteins is often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determination and understanding function and structure relationships. In this paper we extend our non-uniform fast Fourier transform docking algorithm to include an adaptive search phase (both translational and rotational) and thereby speed up its execution. We have also implemented a multithreaded version of the adaptive docking algorithm for even faster execution on multicore machines. We call this protein-protein docking code F2Dock (F2 = Fast Fourier). We have calibrated F2Dock based on an extensive experimental study on a list of benchmark complexes and conclude that F2Dock works very well in practice. Though all docking results reported in this paper use shape complementarity and Coulombic potential based scores only, F2Dock is structured to incorporate Lennard-Jones potential and re-ranking docking solutions based on desolvation energy. PMID:21071796

[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.

A study on maize proteins as a potential new tablet excipient.

PubMed

Georget, Dominique M R; Barker, Susan A; Belton, Peter S

2008-06-01

This investigation has examined the use of zein proteins from maize as the major component in oral controlled-release tablets, such formulations often being required to improve patient compliance. Tablets containing ground zein proteins, calcium hydrogen orthophosphate, polyvinyl pyrrolidone, theophylline and magnesium stearate were produced by wet granulation and compression on a single station tablet press and were compared to directly compressed tablets based on zein proteins, calcium hydrogen orthophosphate and theophylline. Non invasive techniques such as Fourier Transform infrared spectroscopy and Fourier Transform Raman spectroscopy were employed to investigate any changes in the secondary structure of zein proteins during tablet production. Random coils, alpha helices and beta sheets predominated and their relative content remained unaffected during grinding, wet granulation and compression, indicating that formulations based on zeins will be robust, i.e. insensitive to minor changes in the production conditions. Drug release from the tablets was studied using a standard pharmacopoeial dissolution test. Dissolution profiles in water, 0.1M HCl (pH=1) and phosphate buffer (pH=6.8) show that only a limited amount of theophylline was released after 4.5h, suggesting that zein proteins could act as a potential vehicle for oral controlled drug release. Analysis of the theophylline release profiles using the Peppas and Sahlin model reveals that diffusion and polymer relaxation occurred in acidic (pH=1) and buffered (pH=6.8) conditions for wet granulated tablets, whereas diffusion was predominant in directly compressed tablets. In conclusion, the present study has shown that zeins can be successfully used as a pharmaceutical excipient, and in particular as a matrix in monolithic controlled release tablets.

Efficient differential Fourier-transform spectrometer for precision Sunyaev-Zel'dovich effect measurements

NASA Astrophysics Data System (ADS)

Schillaci, Alessandro; D'Alessandro, Giuseppe; de Bernardis, Paolo; Masi, Silvia; Paiva Novaes, Camila; Gervasi, Massimo; Zannoni, Mario

2014-05-01

Context. Precision measurements of the Sunyaev-Zel'dovich effect in clusters of galaxies require excellent rejection of common-mode signals and wide frequency coverage. Aims: We describe an imaging, efficient, differential Fourier transform spectrometer (FTS), optimized for measurements of faint brightness gradients at millimeter wavelengths. Methods: Our instrument is based on a Martin-Puplett interferometer (MPI) configuration. We combined two MPIs working synchronously to use the whole input power. In our implementation the observed sky field is divided into two halves along the meridian, and each half-field corresponds to one of the two input ports of the MPI. In this way, each detector in the FTS focal planes measures the difference in brightness between two sky pixels, symmetrically located with respect to the meridian. Exploiting the high common-mode rejection of the MPI, we can measure low sky brightness gradients over a high isotropic background. Results: The instrument works in the range ~1-20 cm-1 (30-600 GHz), has a maximum spectral resolution 1 / (2 OPD) = 0.063 cm-1 (1.9 GHz), and an unvignetted throughput of 2.3 cm2sr. It occupies a volume of 0.7 × 0.7 × 0.33 m3 and has a weight of 70 kg. This design can be implemented as a cryogenic unit to be used in space, as well as a room-temperature unit working at the focus of suborbital and ground-based mm-wave telescopes. The first in-flight test of the instrument is with the OLIMPO experiment on a stratospheric balloon; a larger implementation is being prepared for the Sardinia radio telescope.

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.

Improvements to surrogate data methods for nonstationary time series.

PubMed

Lucio, J H; Valdés, R; Rodríguez, L R

2012-05-01

The method of surrogate data has been extensively applied to hypothesis testing of system linearity, when only one realization of the system, a time series, is known. Normally, surrogate data should preserve the linear stochastic structure and the amplitude distribution of the original series. Classical surrogate data methods (such as random permutation, amplitude adjusted Fourier transform, or iterative amplitude adjusted Fourier transform) are successful at preserving one or both of these features in stationary cases. However, they always produce stationary surrogates, hence existing nonstationarity could be interpreted as dynamic nonlinearity. Certain modifications have been proposed that additionally preserve some nonstationarity, at the expense of reproducing a great deal of nonlinearity. However, even those methods generally fail to preserve the trend (i.e., global nonstationarity in the mean) of the original series. This is the case of time series with unit roots in their autoregressive structure. Additionally, those methods, based on Fourier transform, either need first and last values in the original series to match, or they need to select a piece of the original series with matching ends. These conditions are often inapplicable and the resulting surrogates are adversely affected by the well-known artefact problem. In this study, we propose a simple technique that, applied within existing Fourier-transform-based methods, generates surrogate data that jointly preserve the aforementioned characteristics of the original series, including (even strong) trends. Moreover, our technique avoids the negative effects of end mismatch. Several artificial and real, stationary and nonstationary, linear and nonlinear time series are examined, in order to demonstrate the advantages of the methods. Corresponding surrogate data are produced with the classical and with the proposed methods, and the results are compared.

NGA-West2 Empirical Fourier Model for Active Crustal Regions to Generate Regionally Adjustable Response Spectra

NASA Astrophysics Data System (ADS)

Bora, S. S.; Cotton, F.; Scherbaum, F.; Kuehn, N. M.

2016-12-01

Adjustment of median ground motion prediction equations (GMPEs) from data-rich (host) regions to data-poor regions (target) is one of major challenges that remains with the current practice of engineering seismology and seismic hazard analysis. Fourier spectral representation of ground motion provides a solution to address the problem of adjustment that is physically transparent and consistent with the concepts of linear system theory. Also, it provides a direct interface to appreciate the physically expected behavior of seismological parameters on ground motion. In the present study, we derive an empirical Fourier model for computing regionally adjustable response spectral ordinates based on random vibration theory (RVT) from shallow crustal earthquakes in active tectonic regions, following the approach of Bora et al. (2014, 2015). , For this purpose, we use an expanded NGA-West2 database with M 3.2—7.9 earthquakes at distances ranging from 0 to 300 km. A mixed-effects regression technique is employed to further explore various components of variability. The NGA-West2 database expanded over a wide magnitude range provides a better understanding (and constraint) of source scaling of ground motion. The large global volume of the database also allows investigating regional patterns in distance-dependent attenuation (i.e., geometrical spreading and inelastic attenuation) of ground motion as well as in the source parameters (e.g., magnitude and stress drop). Furthermore, event-wise variability and its correlation with stress parameter are investigated. Finally, application of the derived Fourier model in generating adjustable response spectra will be shown.

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.

Sampling and Reconstruction of the Pupil and Electric Field for Phase Retrieval

NASA Technical Reports Server (NTRS)

Dean, Bruce; Smith, Jeffrey; Aronstein, David

2012-01-01

This technology is based on sampling considerations for a band-limited function, which has application to optical estimation generally, and to phase retrieval specifically. The analysis begins with the observation that the Fourier transform of an optical aperture function (pupil) can be implemented with minimal aliasing for Q values down to Q = 1. The sampling ratio, Q, is defined as the ratio of the sampling frequency to the band-limited cut-off frequency. The analytical results are given using a 1-d aperture function, and with the electric field defined by the band-limited sinc(x) function. Perfect reconstruction of the Fourier transform (electric field) is derived using the Whittaker-Shannon sampling theorem for 1

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, C.L.

1996-07-23

An imaging Fourier transform spectrometer is described having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer. 2 figs.

Reconsidering the advantages of the three-dimensional representation of the interferometric transform for imaging with non-coplanar baselines and wide fields of view

NASA Astrophysics Data System (ADS)

Smith, D. M. P.; Young, A.; Davidson, D. B.

2017-07-01

Radio telescopes with baselines that span thousands of kilometres and with fields of view that span tens of degrees have been recently deployed, such as the Low Frequency Array, and are currently being developed, such as the Square Kilometre Array. Additionally, there are proposals for space-based instruments with all-sky imaging capabilities, such as the Orbiting Low Frequency Array. Such telescopes produce observations with three-dimensional visibility distributions and curved image domains. In most work to date, the visibility distribution has been converted to a planar form to compute the brightness map using a two-dimensional Fourier transform. The celestial sphere is faceted in order to counter pixel distortion at wide angles, with each such facet requiring a unique planar form of the visibility distribution. Under the above conditions, the computational and storage complexities of this approach can become excessive. On the other hand, when using the direct Fourier transform approach, which maintains the three-dimensional shapes of the visibility distribution and celestial sphere, the non-coplanar visibility component requires no special attention. Furthermore, as the celestial samples are placed directly on the curved surface of the celestial sphere, pixel distortion at wide angles is avoided. In this paper, a number of examples illustrate that under these conditions (very long baselines and very wide fields of view) the costs of the direct Fourier transform may be comparable to (or even lower than) methods that utilise the two-dimensional fast Fourier transform.

Fast Fourier Transform Co-Processor (FFTC)- Towards Embedded GFLOPs

NASA Astrophysics Data System (ADS)

Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Wite, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland

2012-08-01

Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co- Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment.In frame of the ESA activity “Fast Fourier Transform DSP Co-processor (FFTC)” (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following:Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP.The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance.The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT- based processing tasks.A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses.The presentation will give and overview on the project, including the results of the validation of the FFTC ASIC prototypes.

Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs

NASA Astrophysics Data System (ADS)

Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas

2012-10-01

Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.

Figures of merit for detectors in digital radiography. II. Finite number of secondaries and structured backgrounds.

PubMed

Pineda, Angel R; Barrett, Harrison H

2004-02-01

The current paradigm for evaluating detectors in digital radiography relies on Fourier methods. Fourier methods rely on a shift-invariant and statistically stationary description of the imaging system. The theoretical justification for the use of Fourier methods is based on a uniform background fluence and an infinite detector. In practice, the background fluence is not uniform and detector size is finite. We study the effect of stochastic blurring and structured backgrounds on the correlation between Fourier-based figures of merit and Hotelling detectability. A stochastic model of the blurring leads to behavior similar to what is observed by adding electronic noise to the deterministic blurring model. Background structure does away with the shift invariance. Anatomical variation makes the covariance matrix of the data less amenable to Fourier methods by introducing long-range correlations. It is desirable to have figures of merit that can account for all the sources of variation, some of which are not stationary. For such cases, we show that the commonly used figures of merit based on the discrete Fourier transform can provide an inaccurate estimate of Hotelling detectability.

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain.

PubMed

Haldar, Justin P; Leahy, Richard M

2013-05-01

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors. Copyright © 2013 Elsevier Inc. All rights reserved.

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed...with wipξq “ Gσp|Fpviqpξq|pq řM j“1Gσp|Fpvjqpξq|pq , where F denotes the Fourier transform (ξ are the frequencies) and Gσ is a Gaussian filter of...a combination of SIFT [26] and ORSA [14] algorithms) in order to remove affine transformations (translations, rotations and homothety). The authors

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…

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.

Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

PubMed

Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

2017-08-01

Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

Fast Fourier Transform algorithm design and tradeoffs

NASA Technical Reports Server (NTRS)

Kamin, Ray A., III; Adams, George B., III

1988-01-01

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

AIRS Retrieval Validation During the EAQUATE

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Smith, William L.; Cuomo, Vincenzo; Taylor, Jonathan P.; Barnet, Christopher D.; DiGirolamo, Paolo; Pappalardo, Gelsomina; Larar, Allen M.; Liu, Xu; Newman, Stuart M.

2006-01-01

Atmospheric and surface thermodynamic parameters retrieved with advanced hyperspectral remote sensors of Earth observing satellites are critical for weather prediction and scientific research. The retrieval algorithms and retrieved parameters from satellite sounders must be validated to demonstrate the capability and accuracy of both observation and data processing systems. The European AQUA Thermodynamic Experiment (EAQUATE) was conducted mainly for validation of the Atmospheric InfraRed Sounder (AIRS) on the AQUA satellite, but also for assessment of validation systems of both ground-based and aircraft-based instruments which will be used for other satellite systems such as the Infrared Atmospheric Sounding Interferometer (IASI) on the European MetOp satellite, the Cross-track Infrared Sounder (CrIS) from the NPOESS Preparatory Project and the following NPOESS series of satellites. Detailed inter-comparisons were conducted and presented using different retrieval methodologies: measurements from airborne ultraspectral Fourier transform spectrometers, aircraft in-situ instruments, dedicated dropsondes and radiosondes, and ground based Raman Lidar, as well as from the European Center for Medium range Weather Forecasting (ECMWF) modeled thermal structures. The results of this study not only illustrate the quality of the measurements and retrieval products but also demonstrate the capability of these validation systems which are put in place to validate current and future hyperspectral sounding instruments and their scientific products.

Ground-based infrared spectroscopic measurements of atmospheric hydrogen cyanide

NASA Technical Reports Server (NTRS)

Rinsland, C. P.; Smith, M. A. H.; Rinsland, P. L.; Goldman, A.; Brault, J. W.; Stokes, G. M.

1982-01-01

A number of lines of the nu-3 band of hydrogen cyanide have been detected in solar absorption spectra recorded near sunrise and sunset at Kitt Peak National Observatory (elevation 2095 m) with a 0.01/cm resolution Fourier transform spectrometer. Analysis of two of the strongest and best isolated lines has led to a value of 2.73 x 10 to the 15th molecules/sq cm for the vertical column abundance of HCN above Kitt Peak. The accuracy of this value is estimated as + or - 25%. This result, combined with the stratospheric concentration of HCN derived by Coffey, Mankin, and Cicerone (1981), yields 166 parts per trillion by volume for the average mixing ratio of HCN between 2 and 12 km. This is the first determination of the HCN concentration in the nonurban troposphere.

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2013 CFR

2013-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2014 CFR

2014-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

Time stretch dispersive Fourier transform based single-shot pulse-by-pulse spectrum measurement using a pulse-repetition-frequency-variable gain-switched laser

NASA Astrophysics Data System (ADS)

Furukawa, Hideaki; Makino, Takeshi; Wang, Xiaomin; Kobayashi, Tetsuya; Asghari, Mohammad H.; Trinh, Paul; Jalali, Bahram; Man, Wai Sing; Tsang, Kwong Shing; Wada, Naoya

2018-02-01

The time stretch dispersive Fourier Transform (TS-DFT) technique based on a fiber chromatic dispersion is a powerful tool for pulse-by-pulse single-shot spectrum measurement for highrepetition rate optical pulses. The distributed feedback laser diode (DFB-LD) with the gain switch operation can flexibly change the pulse repetition frequency (PRF). In this paper, we newly introduce a semiconductor gain-switched DFB-LD operating from 1 MHz up to 1 GHz PRF into the TS-DFT based spectrum measurement system to improve the flexibility and the operability. The pulse width can be below 2 ps with a pulse compression technique. We successfully measure the spectrum of each optical pulse at 1 GHz, 100 MHz, and 10 MHz PRF, and demonstrate the flexibility of the measurement system.

Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space

USGS Publications Warehouse

Hsi-Ping, Liu

1990-01-01

Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment. -Author

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

1997-01-01

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

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.

40 CFR Appendix B to Subpart Uuuuu - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2012 CFR

2012-07-01

... Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix B to... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

Adaptive Fourier decomposition based ECG denoising.

PubMed

Wang, Ze; Wan, Feng; Wong, Chi Man; Zhang, Liming

2016-10-01

A novel ECG denoising method is proposed based on the adaptive Fourier decomposition (AFD). The AFD decomposes a signal according to its energy distribution, thereby making this algorithm suitable for separating pure ECG signal and noise with overlapping frequency ranges but different energy distributions. A stop criterion for the iterative decomposition process in the AFD is calculated on the basis of the estimated signal-to-noise ratio (SNR) of the noisy signal. The proposed AFD-based method is validated by the synthetic ECG signal using an ECG model and also real ECG signals from the MIT-BIH Arrhythmia Database both with additive Gaussian white noise. Simulation results of the proposed method show better performance on the denoising and the QRS detection in comparing with major ECG denoising schemes based on the wavelet transform, the Stockwell transform, the empirical mode decomposition, and the ensemble empirical mode decomposition. Copyright © 2016 Elsevier Ltd. All rights reserved.

Radar cross-section reduction based on an iterative fast Fourier transform optimized metasurface

NASA Astrophysics Data System (ADS)

Song, Yi-Chuan; Ding, Jun; Guo, Chen-Jiang; Ren, Yu-Hui; Zhang, Jia-Kai

2016-07-01

A novel polarization insensitive metasurface with over 25 dB monostatic radar cross-section (RCS) reduction is introduced. The proposed metasurface is comprised of carefully arranged unit cells with spatially varied dimension, which enables approximate uniform diffusion of incoming electromagnetic (EM) energy and reduces the threat from bistatic radar system. An iterative fast Fourier transform (FFT) method for conventional antenna array pattern synthesis is innovatively applied to find the best unit cell geometry parameter arrangement. Finally, a metasurface sample is fabricated and tested to validate RCS reduction behavior predicted by full wave simulation software Ansys HFSSTM and marvelous agreement is observed.

An Accurate and Stable FFT-based Method for Pricing Options under Exp-Lévy Processes

NASA Astrophysics Data System (ADS)

Ding, Deng; Chong U, Sio

2010-05-01

An accurate and stable method for pricing European options in exp-Lévy models is presented. The main idea of this new method is combining the quadrature technique and the Carr-Madan Fast Fourier Transform methods. The theoretical analysis shows that the overall complexity of this new method is still O(N log N) with N grid points as the fast Fourier transform methods. Numerical experiments for different exp-Lévy processes also show that the numerical algorithm proposed by this new method has an accuracy and stability for the small strike prices K. That develops and improves the Carr-Madan method.

Analysis of the Advantages and Limitations of Stationary Imaging Fourier Transform Spectrometer. Revised

NASA Technical Reports Server (NTRS)

Beecken, Brian P.; Kleinman, Randall R.

2004-01-01

New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.

Evaluation of radiation loading on finite cylindrical shells using the fast Fourier transform: A comparison with direct numerical integration.

PubMed

Liu, S X; Zou, M S

2018-03-01

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration.

Hyperspectral imaging using the single-pixel Fourier transform technique

NASA Astrophysics Data System (ADS)

Jin, Senlin; Hui, Wangwei; Wang, Yunlong; Huang, Kaicheng; Shi, Qiushuai; Ying, Cuifeng; Liu, Dongqi; Ye, Qing; Zhou, Wenyuan; Tian, Jianguo

2017-03-01

Hyperspectral imaging technology is playing an increasingly important role in the fields of food analysis, medicine and biotechnology. To improve the speed of operation and increase the light throughput in a compact equipment structure, a Fourier transform hyperspectral imaging system based on a single-pixel technique is proposed in this study. Compared with current imaging spectrometry approaches, the proposed system has a wider spectral range (400-1100 nm), a better spectral resolution (1 nm) and requires fewer measurement data (a sample rate of 6.25%). The performance of this system was verified by its application to the non-destructive testing of potatoes.

Miniature, Low-Power, Waveguide Based Infrared Fourier Transform Spectrometer for Spacecraft Remote Sensing

NASA Technical Reports Server (NTRS)

Hewagama, TIlak; Aslam, Shahid; Talabac, Stephen; Allen, John E., Jr.; Annen, John N.; Jennings, Donald E.

2011-01-01

Fourier transform spectrometers have a venerable heritage as flight instruments. However, obtaining an accurate spectrum exacts a penalty in instrument mass and power requirements. Recent advances in a broad class of non-scanning Fourier transform spectrometer (FTS) devices, generally called spatial heterodyne spectrometers, offer distinct advantages as flight optimized systems. We are developing a miniaturized system that employs photonics lightwave circuit principles and functions as an FTS operating in the 7-14 micrometer spectral region. The inteferogram is constructed from an ensemble of Mach-Zehnder interferometers with path length differences calibrated to mimic scan mirror sample positions of a classic Michelson type FTS. One potential long-term application of this technology in low cost planetary missions is the concept of a self-contained sensor system. We are developing a systems architecture concept for wide area in situ and remote monitoring of characteristic properties that are of scientific interest. The system will be based on wavelength- and resolution-independent spectroscopic sensors for studying atmospheric and surface chemistry, physics, and mineralogy. The self-contained sensor network is based on our concept of an Addressable Photonics Cube (APC) which has real-time flexibility and broad science applications. It is envisaged that a spatially distributed autonomous sensor web concept that integrates multiple APCs will be reactive and dynamically driven. The network is designed to respond in an event- or model-driven manner or reconfigured as needed.

High-Resolution Analysis of the ν 6, ν 7, ν 8, and ν 9Bands of H 15N 16O 3Measured by Fourier Transform Spectroscopy

NASA Astrophysics Data System (ADS)

Keller, F.; Perrin, A.; Flaud, J.-M.; Johns, J. W. C.; Lu, Z.; Looi, E. C.

1998-10-01

The analysis of the ν6, ν7, ν8, and ν9bands of H15N16O3located at 646.9641, 578.4719, 743.6166, and 458.2917 cm-1, respectively, has been carried out in the 400-800 cm-1region using high-resolution Fourier transform spectra recorded at Ottawa. Using the ground state energy levels calculated from thev= 0 rotational constants of H15N16O3[A. P. Cox, M. C. Ellis, C. J. Attfield, and A. C. Ferris,J. Mol. Struct.320, 91-106 (1994)], it was possible to assign theA-type ν6and ν7bands and theC-type ν8and ν9bands of H15N16O3up to highJandKarotational quantum numbers. Thev6= 1,v7= 1, v8= 1, andv9= 1 experimental energy levels were then introduced in a least-squares fit calculation and precise upper state Hamiltonian constants (band centers and rotational constants) were determined allowing one to reproduce the infrared data to within the experimental uncertainty.

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.

Multi-Velocity Component LDV

NASA Technical Reports Server (NTRS)

Johnson, Dennis A. (Inventor)

1996-01-01

A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components.

An Evaluation of the Environmental Fate and Behavior of Munitions Materiel (Tetryl and Polar Metabolites of TNT) in Soil and Plant Systems. Environmental Fate and Behavior of Tetryl

DTIC Science & Technology

1992-03-01

attempted to verify product identity and purity by GC with either Fourier transform infrared spectro.icopy (FTIR) or mass spectroscopy (MS) detection...ýl0 5 In-1 z U)-’i0oo -3g’i o -6o0 626o a i60 ito1 2i oo I ’ o [JfnVENUII8ER (cm- FIGURE 3,9. Fourier Transform Infrared Spectroscopy Spectrum of...Fourier Transform Infrared Spectroscopy Spectrum of Tetryl I-I F1U~IGUR Fourier Utransformlfret Spcrop S ectrum of TeasomtinPoutrl 0 , -39 i : : : -. . i

Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

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

Schmittfull, Marcel; Vlah, Zvonimir; McDonald, Patrick

The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a fewmore » orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. In conclusion, the method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.« less

Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

DOE PAGES

Schmittfull, Marcel; Vlah, Zvonimir; McDonald, Patrick

2016-05-01

The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a fewmore » orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. In conclusion, the method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.« less

Flow-through Fourier transform infrared sensor for total hydrocarbons determination in water.

PubMed

Pérez-Palacios, David; Armenta, Sergio; Lendl, Bernhard

2009-09-01

A new flow-through Fourier transform infrared (FT-IR) sensor for oil in water analysis based on solid-phase spectroscopy on octadecyl (C18) silica particles has been developed. The C18 non-polar sorbent is placed inside the sensor and is able to retain hydrocarbons from water samples. The system does not require the use of chlorinated solvents, reducing the environmental impact, and the minimal sample handling stages serve to ensure sample integrity whilst reducing exposure of the analyst to any toxic hydrocarbons present within the samples. Fourier transform infrared (FT-IR) spectra were recorded by co-adding 32 scans at a resolution of 4 cm(-1) and the band located at 1462 cm(-1) due to the CH(2) bending was integrated from 1475 to 1450 cm(-1) using a baseline correction established between 1485 and 1440 cm(-1) using the areas as analytical signal. The technique, which provides a limit of detection (LOD) of 22 mg L(-1) and a precision expressed as relative standard deviation (RSD) lower than 5%, is considerably rapid and allows for a high level of automation.

Fourier Transform Surface Plasmon Resonance of Nanodisks Embedded in Magnetic Nanorods.

PubMed

Jung, Insub; Ih, Seongkeun; Yoo, Haneul; Hong, Seunghun; Park, Sungho

2018-03-14

In this study, we demonstrate the synthesis and application of magnetic plasmonic gyro-nanodisks (GNDs) for Fourier transform surface plasmon resonance based biodetection. Plasmonically active and magnetically responsive gyro-nanodisks were synthesized using electrochemical methods with anodized aluminum templates. Due to the unique properties of GNDs (magnetic responsiveness and surface plasmon bands), periodic extinction signals were generated under an external rotating magnetic field, which is, in turn, converted into frequency domains using Fourier transformation. After the binding of a target on GNDs, an increase in the shear force causes a shift in the frequency domain, which allows us to investigate biodetection for HA1 (the influenza virus). Most importantly, by modulating the number and the location of plasmonic nanodisks (a method for controlling the hydrodynamic forces by rationally designing the nanomaterial architecture), we achieved enhanced biodetection sensitivity. We expect that our results will contribute to improved sensing module performance, as well as a better understanding of dynamic nanoparticle systems, by harnessing the perturbed periodic fluctuation of surface plasmon bands under the modulated magnetic field.

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.

Implementation of a direct-imaging and FX correlator for the BEST-2 array

NASA Astrophysics Data System (ADS)

Foster, G.; Hickish, J.; Magro, A.; Price, D.; Zarb Adami, K.

2014-04-01

A new digital backend has been developed for the Basic Element for SKA Training II (BEST-2) array at Radiotelescopi di Medicina, INAF-IRA, Italy, which allows concurrent operation of an FX correlator, and a direct-imaging correlator and beamformer. This backend serves as a platform for testing some of the spatial Fourier transform concepts which have been proposed for use in computing correlations on regularly gridded arrays. While spatial Fourier transform-based beamformers have been implemented previously, this is, to our knowledge, the first time a direct-imaging correlator has been deployed on a radio astronomy array. Concurrent observations with the FX and direct-imaging correlator allow for direct comparison between the two architectures. Additionally, we show the potential of the direct-imaging correlator for time-domain astronomy, by passing a subset of beams though a pulsar and transient detection pipeline. These results provide a timely verification for spatial Fourier transform-based instruments that are currently in commissioning. These instruments aim to detect highly redshifted hydrogen from the epoch of reionization and/or to perform wide-field surveys for time-domain studies of the radio sky. We experimentally show the direct-imaging correlator architecture to be a viable solution for correlation and beamforming.

Wavelets

NASA Astrophysics Data System (ADS)

Strang, Gilbert

1994-06-01

Several methods are compared that are used to analyze and synthesize a signal. Three ways are mentioned to transform a symphony: into cosine waves (Fourier transform), into pieces of cosines (short-time Fourier transform), and into wavelets (little waves that start and stop). Choosing the best basis, higher dimensions, fast wavelet transform, and Daubechies wavelets are discussed. High-definition television is described. The use of wavelets in identifying fingerprints in the future is related.

Secure multi-party quantum summation based on quantum Fourier transform

NASA Astrophysics Data System (ADS)

Yang, Hui-Yi; Ye, Tian-Yu

2018-06-01

In this paper, we propose a novel secure multi-party quantum summation protocol based on quantum Fourier transform, where the traveling particles are transmitted in a tree-type mode. The party who prepares the initial quantum states is assumed to be semi-honest, which means that she may misbehave on her own but will not conspire with anyone. The proposed protocol can resist both the outside attacks and the participant attacks. Especially, one party cannot obtain other parties' private integer strings; and it is secure for the colluding attack performed by at most n - 2 parties, where n is the number of parties. In addition, the proposed protocol calculates the addition of modulo d and implements the calculation of addition in a secret-by-secret way rather than a bit-by-bit way.

Nanowire humidity optical sensor system based on fast Fourier transform technique

NASA Astrophysics Data System (ADS)

Rota-Rodrigo, S.; Pérez-Herrera, R.; Lopez-Aldaba, A.; López Bautista, M. C.; Esteban, O.; López-Amo, M.

2015-09-01

In this paper, a new sensor system for relative humidity measurements based on its interaction with the evanescent field of a nanowire is presented. The interrogation of the sensing head is carried out by monitoring the fast Fourier transform phase variations of one of the nanowire interference frequencies. This method is independent of the signal amplitude and also avoids the necessity of tracking the wavelength evolution in the spectrum, which can be a handicap when there are multiple interference frequency components with different sensitivities. The sensor is operated within a wide humidity range (20%-70% relative humidity) with a maximum sensitivity achieved of 0.14rad/% relative humidity. Finally, due to the system uses an optical interrogator as unique active element, the system presents a cost-effective feature.

Time efficient Gabor fused master slave optical coherence tomography

NASA Astrophysics Data System (ADS)

Cernat, Ramona; Bradu, Adrian; Rivet, Sylvain; Podoleanu, Adrian

2018-02-01

In this paper the benefits in terms of operation time that Master/Slave (MS) implementation of optical coherence tomography can bring in comparison to Gabor fused (GF) employing conventional fast Fourier transform based OCT are presented. The Gabor Fusion/Master Slave Optical Coherence Tomography architecture proposed here does not need any data stitching. Instead, a subset of en-face images is produced for each focus position inside the sample to be imaged, using a reduced number of theoretically inferred Master masks. These en-face images are then assembled into a final volume. When the channelled spectra are digitized into 1024 sampling points, and more than 4 focus positions are required to produce the final volume, the Master Slave implementation of the instrument is faster than the conventional fast Fourier transform based procedure.

Coherent field propagation between tilted planes.

PubMed

Stock, Johannes; Worku, Norman Girma; Gross, Herbert

2017-10-01

Propagating electromagnetic light fields between nonparallel planes is of special importance, e.g., within the design of novel computer-generated holograms or the simulation of optical systems. In contrast to the extensively discussed evaluation between parallel planes, the diffraction-based propagation of light onto a tilted plane is more burdensome, since discrete fast Fourier transforms cannot be applied directly. In this work, we propose a quasi-fast algorithm (O(N 3  log N)) that deals with this problem. Based on a proper decomposition into three rotations, the vectorial field distribution is calculated on a tilted plane using the spectrum of plane waves. The algorithm works on equidistant grids, so neither nonuniform Fourier transforms nor an explicit complex interpolation is necessary. The proposed algorithm is discussed in detail and applied to several examples of practical interest.

Remote sensing of GHG over Paris megacity and Orléans forest using ground-based QualAir FTS and TCCON-Orléans

NASA Astrophysics Data System (ADS)

Te, Y.; Jeseck, P.; Da Costa, J.; Deutscher, N. M.; Warneke, T.; Notholt, J.

2012-04-01

In a growing world with more than 7 billion inhabitants and big emerging countries such as China, Brazil and India, emissions of anthropogenic pollutants are increasing continuously. Monitoring and control of atmospheric pollutants in megacities have become a major challenge for scientists and public health authorities in environmental research area. The QualAir platform at University Pierre et Marie Curie (UPMC), is an innovating experimental research platform dedicated to survey greenhouse gases (GHGs) and urban air quality. As one of the major instruments of the QualAir platform, the ground-based Fourier transform spectrometer (QualAir FTS, IFS 125HR model) analyses the composition of the urban atmosphere of Paris, which is the third European megacity. The continuous monitoring of atmospheric pollutants is essential to improve the understanding of urban air pollution processes. Associated with a sun-tracker, the QualAir remote sensing FTS operates in solar infrared absorption and enables to monitor many trace gases, and to follow up their variability in the Ile-de-France region. A description of the QualAir FTS will be given. Concentrations of atmospheric GHG, especially CO2 and CH4, are retrieved by the radiative transfer model PROFFIT. Located in the centre of Paris, the QualAir FTS can provide new and complementary urban measurements as compared to unpolluted ground-based stations of existing networks (NDACC and TCCON). The work made by LPMAA to join the TCCON network will also be presented. TCCON-Orléans is a ground-based FTS of the TCCON network located in the forest of Orléans (100 km south of Paris). Preliminary comparisons of GHGs measurements from both sites will be shown. Such ground-based information will help to better characterize regional GHGs, especially regarding anthropogenic emissions and trends.

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.

A Comparison of FTNMR and FTIR Techniques.

ERIC Educational Resources Information Center

Ahn, Myong-Ku

1989-01-01

Nuclear magnetic resonance and infrared are two spectroscopic methods that commonly use the Fourier transform technique. Discussed are the similarities and differences in the use of the Fourier transform in these two spectroscopic techniques. (CW)

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.

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.

Rotation-vibration interactions in the spectra of polycyclic aromatic hydrocarbons: Quinoline as a test-case species

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

Pirali, O.; Gruet, S.; Institut des Sciences Moléculaires d’Orsay, UMR8214 CNRS – Université Paris-Sud, Bât. 210, 91405 Orsay cedex

2015-03-14

Polycyclic aromatic hydrocarbons (PAHs) are highly relevant for astrophysics as possible, though controversial, carriers of the unidentified infrared emission bands that are observed in a number of different astronomical objects. In support of radio-astronomical observations, high resolution laboratory spectroscopy has already provided the rotational spectra in the vibrational ground state of several molecules of this type, although the rotational study of their dense infrared (IR) bands has only recently become possible using a limited number of experimental set-ups. To date, all of the rotationally resolved data have concerned unperturbed spectra. We presently report the results of a high resolution studymore » of the three lowest vibrational states of quinoline C{sub 9}H{sub 7}N, an N-bearing naphthalene derivative. While the pure rotational ground state spectrum of quinoline is unperturbed, severe complications appear in the spectra of the ν{sub 45} and ν{sub 44} vibrational modes (located at about 168 cm{sup −1} and 178 cm{sup −1}, respectively). In order to study these effects in detail, we employed three different and complementary experimental techniques: Fourier-transform microwave spectroscopy, millimeter-wave spectroscopy, and Fourier-transform far-infrared spectroscopy with a synchrotron radiation source. Due to the high density of states in the IR spectra of molecules as large as PAHs, perturbations in the rotational spectra of excited states should be ubiquitous. Our study identifies for the first time this effect and provides some insights into an appropriate treatment of such perturbations.« less

Fourier transform synchrotron spectroscopy of the in-plane methyl-rocking band of CD3OH

NASA Astrophysics Data System (ADS)

Lees, R. M.; Xu, Li-Hong; Gao, Song; Billinghurst, B. E.

2015-09-01

Infrared Fourier transform spectra of the 12CD3OH isotopologue of methanol recorded at the Canadian Light Source synchrotron have been investigated in the 750-950 cm-1 region to explore the torsional energy pattern of the in-plane methyl-rocking mode. The in-plane CD3-rocking band is primarily of parallel a-type character with relatively widely spaced K-structure, and the central Q-branch region is well-resolved. Sub-bands have been assigned for the vt = 0 ground torsional state from K = 0 to 15 for both A and E torsional species, as well as a number of sub-bands in the vt = 1 excited torsional state. A variety of perturbations due to asymmetry-induced, anharmonic Fermi and level-crossing resonances is seen in the spectra. Mapping of K-reduced torsional energies determined from the upper-state term values shows that the K-dependence is severely distorted from the usual pattern of smoothly oscillating, near-sinusoidal interlocking τ-curves. Although the K = 0 levels are nominally inverted for vt = 0, the torsional splitting is very small with the A level higher than the E level by only 0.625 cm-1, and the anomalous behavior precludes a definite conclusion about torsional inversion. However, the range of variation with K of the vt = 0 CD3-rocking τ-curves is about half that of the ground vibrational state, similar to previous observations for CH3OH isotopologues, suggesting a comparable reduction of about 25% in the effective torsional barrier height for the in-plane rocking mode.

Fast algorithm for chirp transforms with zooming-in ability and its applications.

PubMed

Deng, X; Bihari, B; Gan, J; Zhao, F; Chen, R T

2000-04-01

A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both x and u space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order 10(-12) for most cases. As an example of its application to scalar diffraction, this algorithm can be used to calculate near-field patterns directly behind the aperture, 0 < or = z < d2/lambda. It compensates another algorithm for Fresnel diffraction that is limited to z > d2/lambdaN [J. Opt. Soc. Am. A 15, 2111 (1998)]. Experimental results from waveguide-output microcoupler diffraction are in good agreement with the calculations.

Image Reconstruction from Data Collected with an Imaging Interferometer

NASA Astrophysics Data System (ADS)

DeSantis, Z. J.; Thurman, S. T.; Hix, T. T.; Ogden, C. E.

The intensity distribution of an incoherent source and the spatial coherence function at some distance away are related by a Fourier transform, via the Van Cittert-Zernike theorem. Imaging interferometers measure the spatial coherence of light propagated from the incoherently illuminated object by combining light from spatially separated points to measure interference fringes. The contrast and phase of the fringe are the amplitude and phase of a Fourier component of the source’s intensity distribution. The Fiber-Coupled Interferometer (FCI) testbed is a visible light, lab-based imaging interferometer designed to test aspects of an envisioned ground-based interferometer for imaging geosynchronous satellites. The front half of the FCI testbed consists of the scene projection optics, which includes an incoherently backlit scene, located at the focus of a 1 m aperture f/100 telescope. The projected light was collected by the back half of the FCI testbed. The collection optics consisted of three 11 mm aperture fiber-coupled telescopes. Light in the fibers was combined pairwise and dispersed onto a sensor to measure the interference fringe as a function of wavelength, which produces a radial spoke of measurements in the Fourier domain. The visibility function was sampled throughout the Fourier domain by recording fringe data at many different scene rotations and collection telescope separations. Our image reconstruction algorithm successfully produced images for the three scenes we tested: asymmetric pair of pinholes, U.S. Air Force resolution bar target, and satellite scene. The bar target reconstruction shows detail and resolution near the predicted resolution limit. This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). The views, opinions and/or findings expressed are those of the author(s) and should not be interpreted as reflecting the official views or policies of the Department of Defense or the U.S. Government.

Local Complex Potential Based Time Dependent Wave Packet Approach to Calculation of Vibrational Excitation Cross-sections in e-N2, e-H2 and e-CO Scattering

NASA Astrophysics Data System (ADS)

Sarma, Manabendra; Singh, Raman K.; Mishra, Manoj K.

2007-12-01

Vibrational excitation cross-sections σn←m(E) in resonant e-N2, e-CO and e-H2 scattering are calculated from transition matrix elements Tn←m(E) obtained using Fourier transform of the cross correlation function <φn(R)|ψm(R,t)> where ψm(R,t); e-iHA-(R)t/ℏφm(R). Time evolution under the influence of the resonance anionic Hamiltonian HA-(A- = N2-/CO/H2-) is effected using Lanczos and fast Fourier transforms and the target (A) vibrational eigenfunctions φm(R) and φn(R) are calculated using Fourier grid Hamiltonian method applied to PE curve of the neutral target. The resulting vibrational excitation cross-section profiles provide reasonable agreement with experimental results and the cross correlation functions offer an unequivocal differentiation between the boomerang and impulse models.

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.

A spectroscopic study of the hydrogen bonding and pi-pi stacking interactions of harmane with quinoline.

PubMed

Balón, M; Guardado, P; Muñoz, M A; Carmona, C

1998-01-01

A spectroscopic (UV-vis, Fourier transform IR, steady state, and time-resolved fluorescence) study of the interactions of the ground and excited singlet states of harmane (1-methyl-9H-pyrido/3,4-b/indole) with quinoline has been carried out in cyclohexane, toluene, and buffered pH=8.7 aqueous solutions. To analyze how the number of rings in the substrate influences these interactions, pyridine and phenanthridine have also been included in this study. In cyclohexane and toluene 1:1 stoichiometric hydrogen-bonded complexes are formed in both the ground and the excited singlet states. As the number of rings of the benzopyridines and the solvent polarity increase hydrogen-bonding interactions weaken and pi-pi van der Waals interactions become apparent.

Airborne mapping of chemical plumes in the aftermath of Hurricanes Katrina and Rita

NASA Astrophysics Data System (ADS)

Lewis, Paul E.; Thomas, Mark J.; Kroutil, Robert T.; Combs, Roger; Cummings, Alan S.; Miller, Dave; Curry, Tim; Shen, Sylvia S.

2006-05-01

Infrared airborne spectral measurements were collected over the Gulf Coast area during the aftermath of Hurricanes Katrina and Rita. These measurements allowed surveillance for potentially hazardous chemical vapor releases from industrial facilities caused by storm damage. Data was collected with a mid-longwave infrared multispectral imager and a hyperspectral Fourier transform infrared spectrometer operating in a low altitude aircraft. Signal processing allowed detection and identification of targeted spectral signatures in the presence of interferents, atmospheric contributions, and thermal clutter. Results confirmed the presence of a number of chemical vapors. All detection results were immediately passed along to emergency first responders on the ground. The chemical identification, location, and vapor species concentration information were used by the emergency response ground teams for identification of critical plume releases and subsequent mitigation.

Modulated Fourier Transform Raman Fiber-Optic Spectroscopy

NASA Technical Reports Server (NTRS)

Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)

2000-01-01

A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.

Fourier-transform and global contrast interferometer alignment methods

DOEpatents

Goldberg, Kenneth A.

2001-01-01

Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.

The geometry of organophosphonates: Fourier-transform microwave spectroscopy and ab initio study of diethyl methylphosphonate, diethyl ethylphosphonate, and diisopropyl methylphosphonate

NASA Astrophysics Data System (ADS)

DaBell, Ryan S.; Suenram, Richard D.; Lavrich, Richard J.; Lochner, J. Michael; Ellzy, Michael W.; Sumpter, Kenneth; Jensen, James O.; Samuels, Alan C.

2004-12-01

The rotational spectra of diethyl methylphosphonate (DEMP), diethyl ethylphosphonate (DEEP), and diisopropyl methylphosphonate (DIMP) in supersonic expansions have been acquired using Fourier-transform microwave spectroscopy. Spectroscopic constants have been determined for five distinct conformers of the three molecules. Experimental data have been compared to ab initio calculations performed for each species. For both DEMP and DEEP, the calculations indicate the presence of several low-energy conformers (i.e., ⩽˜400 cm -1 above the ground state) may be present at room temperature (300 K) for both DEMP and DEEP. When entrained in a supersonic expansion, the rotational temperatures of the samples are much colder (˜2 K); nonetheless, spectra from three conformers of DEEP are still observed experimentally, whereas only one conformer of DEMP is observed. In contrast, only a single low-energy conformer of DIMP is predicted by theory, and is present in the molecular beam. The relative abundance of low-energy conformers of DEMP and DEEP is attributed to the flexibility of the ethoxy groups within each molecule. The presence of multiple DEEP conformers in the supersonic beam indicates a more complex potential energy surface for this molecule that is directly related to conformational shifts of the PCH 2CH 3 group. Conversely, the absence of low-energy conformers of DIMP is attributed to steric hindrance between isopropoxy groups in the molecule. The internal rotation barrier for the PCH 3 group in DEMP and DIMP is compared to that found in DMMP and several phosphonate-based chemical weapon agents.

High-resolution synchrotron-based Fourier transform spectroscopy of [image omitted] in the 120-350 cm-1 far-infrared region

NASA Astrophysics Data System (ADS)

Moruzzi, G.; Murphy, R. J.; Lees, R. M.; Predoi-Cross, A.; Billinghurst, B. E.

2010-09-01

The Fourier transform spectrum of the ? isotopologue of methanol has been recorded in the 120-350 cm-1 far-infrared region at a resolution of 0.00096 cm-1 using synchrotron source radiation at the Canadian Light Source. The study, motivated by astrophysical applications, is aimed at generating a sufficiently accurate set of energy level term values for the ground vibrational state to allow prediction of the centres of the quadrupole hyperfine multiplets for astronomically observable sub-millimetre transitions to within an uncertainty of a few MHz. To expedite transition identification, a new function was added to the Ritz program in which predicted spectral line positions were generated by an adjustable interpolation between the known assignments for the ? and ? isotopologues. By displaying the predictions along with the experimental spectrum on the computer monitor and adjusting the predictions to match observed features, rapid assignment of numerous ? sub-bands was possible. The least squares function of the Ritz program was then used to generate term values for the identified levels. For each torsion-K-rotation substate, the term values were fitted to a Taylor-series expansion in powers of J(J + 1) to determine the substate origin energy and effective B-value. In this first phase of the study we did not attempt a full global fit to the assigned transitions, but instead fitted the sub-band J-independent origins to a restricted Hamiltonian containing the principal torsional and K-dependent terms. These included structural and torsional potential parameters plus quartic distortional and torsion-rotation interaction terms.

Performance analysis of a finite radon transform in OFDM system under different channel models

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

Dawood, Sameer A.; Anuar, M. S.; Fayadh, Rashid A.

In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resultedmore » in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.« less

Performance analysis of a finite radon transform in OFDM system under different channel models

NASA Astrophysics Data System (ADS)

Dawood, Sameer A.; Malek, F.; Anuar, M. S.; Fayadh, Rashid A.; Abdullah, Farrah Salwani

2015-05-01

In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.

ERS-2 SAR and IRS-1C LISS III data fusion: A PCA approach to improve remote sensing based geological interpretation

NASA Astrophysics Data System (ADS)

Pal, S. K.; Majumdar, T. J.; Bhattacharya, Amit K.

Fusion of optical and synthetic aperture radar data has been attempted in the present study for mapping of various lithologic units over a part of the Singhbhum Shear Zone (SSZ) and its surroundings. ERS-2 SAR data over the study area has been enhanced using Fast Fourier Transformation (FFT) based filtering approach, and also using Frost filtering technique. Both the enhanced SAR imagery have been then separately fused with histogram equalized IRS-1C LISS III image using Principal Component Analysis (PCA) technique. Later, Feature-oriented Principal Components Selection (FPCS) technique has been applied to generate False Color Composite (FCC) images, from which corresponding geological maps have been prepared. Finally, GIS techniques have been successfully used for change detection analysis in the lithological interpretation between the published geological map and the fusion based geological maps. In general, there is good agreement between these maps over a large portion of the study area. Based on the change detection studies, few areas could be identified which need attention for further detailed ground-based geological studies.

A fast D.F.T. algorithm using complex integer transforms

NASA Technical Reports Server (NTRS)

Reed, I. S.; Truong, T. K.

1978-01-01

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

[Detection of Heart Rate of Fetal ECG Based on STFT and BSS].

PubMed

Wang, Xu; Cai, Kun

2016-01-01

Changes in heart rate of fetal is function regulating performance of the circulatory system and the central nervous system, it is significant to detect heart rate of fetus in perinatal fetal. This paper puts forward the fetal heart rate detection method based on short time Fourier transform and blind source separation. First of all, the mixed ECG signal was preprocessed, and then the wavelet transform technique was used to separate the fetal ECG signal with noise from mixed ECG signal, after that, the short-time Fourier transform and the blind separation were carried on it, and then calculated the correlation coefficient of it, Finally, An independent component that it has strongest correlation with the original signal was selected to make FECG peak detection and calculated the fetal instantaneous heart rate. The experimental results show that the method can improve the detection rate of the FECG peak (R), and it has high accuracy in fixing peak(R) location in the case of low signal-noise ratio.

A High Resolution Fourier-Transform Spectrometer for the Measurement of Atmospheric Column Abundances

NASA Technical Reports Server (NTRS)

Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.

2000-01-01

A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).

Technique for the metrology calibration of a Fourier transform spectrometer

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

Spencer, Locke D.; Naylor, David A

2008-11-10

A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, Charles L.

1996-01-01

An imaging Fourier transform spectrometer (10, 210) having a Fourier transform infrared spectrometer (12) providing a series of images (40) to a focal plane array camera (38). The focal plane array camera (38) is clocked to a multiple of zero crossing occurrences as caused by a moving mirror (18) of the Fourier transform infrared spectrometer (12) and as detected by a laser detector (50) such that the frame capture rate of the focal plane array camera (38) corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer (12). The images (40) are transmitted to a computer (45) for processing such that representations of the images (40) as viewed in the light of an arbitrary spectral "fingerprint" pattern can be displayed on a monitor (60) or otherwise stored and manipulated by the computer (45).

Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

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

Yükçü, Niyazi

Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical propertiesmore » of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.« less

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

Component analyses of urinary nanocrystallites of uric acid stone formers by combination of high-resolution transmission electron microscopy, fast Fourier transformation, energy dispersive X-ray spectroscopy, X-ray diffraction and Fourier transform infrared spectroscopy.

PubMed

Sun, Xin-Yuan; Xue, Jun-Fa; Xia, Zhi-Yue; Ouyang, Jian-Ming

2015-06-01

This study aimed to analyse the components of nanocrystallites in urines of patients with uric acid (UA) stones. X-ray diffraction (XRD), Fourier transform infrared spectroscopy, high-resolution transmission electron microscopy (HRTEM), fast Fourier transformation (FFT) of HRTEM, and energy dispersive X-ray spectroscopy (EDS) were performed to analyse the components of these nanocrystallites. XRD and FFT showed that the main component of urinary nanocrystallites was UA, which contains a small amount of calcium oxalate monohydrate and phosphates. EDS showed the characteristic absorption peaks of C, O, Ca and P. The formation of UA stones was closely related to a large number of UA nanocrystallites in urine. A combination of HRTEM, FFT, EDS and XRD analyses could be performed accurately to analyse the components of urinary nanocrystallites.

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.

1974-01-01

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

Segment density profiles of polyelectrolyte brushes determined by Fourier transform ellipsometry

NASA Astrophysics Data System (ADS)

Biesalski, Markus; Rühe, Jürgen; Johannsmann, Diethelm

1999-10-01

We describe a method for the explicit determination of the segment density profile φ(z) of surface-attached polymer brushes with multiple angle of incidence null-ellipsometry. Because the refractive index contrast between the brush layer and the solvent is weak, multiple reflections are of minor influence and the ellipsometric spectrum is closely related to the Fourier transform of the refractive index profile, thereby allowing for explicit inversion of the ellipsometric data. We chose surface-attached monolayers of polymethacrylic acid (PMAA), a weak polyelectrolyte, as a model system and determined the segment density profile of this system as a function of the pH value of the surrounding medium by the Fourier method. Complementary to the Fourier analysis, fits with error functions are given as well. The brushes were prepared on the bases of high refractive index prisms with the "grafting-from" technique. In water, the brushes swell by more than a factor of 30. The swelling increases with increasing pH because of a growing fraction of dissociated acidic groups leading to a larger electrostatic repulsion.

Advanced satellite communication system

NASA Technical Reports Server (NTRS)

Staples, Edward J.; Lie, Sen

1992-01-01

The objective of this research program was to develop an innovative advanced satellite receiver/demodulator utilizing surface acoustic wave (SAW) chirp transform processor and coherent BPSK demodulation. The algorithm of this SAW chirp Fourier transformer is of the Convolve - Multiply - Convolve (CMC) type, utilizing off-the-shelf reflective array compressor (RAC) chirp filters. This satellite receiver, if fully developed, was intended to be used as an on-board multichannel communications repeater. The Advanced Communications Receiver consists of four units: (1) CMC processor, (2) single sideband modulator, (3) demodulator, and (4) chirp waveform generator and individual channel processors. The input signal is composed of multiple user transmission frequencies operating independently from remotely located ground terminals. This signal is Fourier transformed by the CMC Processor into a unique time slot for each user frequency. The CMC processor is driven by a waveform generator through a single sideband (SSB) modulator. The output of the coherent demodulator is composed of positive and negative pulses, which are the envelopes of the chirp transform processor output. These pulses correspond to the data symbols. Following the demodulator, a logic circuit reconstructs the pulses into data, which are subsequently differentially decoded to form the transmitted data. The coherent demodulation and detection of BPSK signals derived from a CMC chirp transform processor were experimentally demonstrated and bit error rate (BER) testing was performed. To assess the feasibility of such advanced receiver, the results were compared with the theoretical analysis and plotted for an average BER as a function of signal-to-noise ratio. Another goal of this SBIR program was the development of a commercial product. The commercial product developed was an arbitrary waveform generator. The successful sales have begun with the delivery of the first arbitrary waveform generator.

Color image encryption based on color blend and chaos permutation in the reality-preserving multiple-parameter fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

Lang, Jun

2015-03-01

In this paper, we propose a novel color image encryption method by using Color Blend (CB) and Chaos Permutation (CP) operations in the reality-preserving multiple-parameter fractional Fourier transform (RPMPFRFT) domain. The original color image is first exchanged and mixed randomly from the standard red-green-blue (RGB) color space to R‧G‧B‧ color space by rotating the color cube with a random angle matrix. Then RPMPFRFT is employed for changing the pixel values of color image, three components of the scrambled RGB color space are converted by RPMPFRFT with three different transform pairs, respectively. Comparing to the complex output transform, the RPMPFRFT transform ensures that the output is real which can save storage space of image and convenient for transmission in practical applications. To further enhance the security of the encryption system, the output of the former steps is scrambled by juxtaposition of sections of the image in the reality-preserving multiple-parameter fractional Fourier domains and the alignment of sections is determined by two coupled chaotic logistic maps. The parameters in the Color Blend, Chaos Permutation and the RPMPFRFT transform are regarded as the key in the encryption algorithm. The proposed color image encryption can also be applied to encrypt three gray images by transforming the gray images into three RGB color components of a specially constructed color image. Numerical simulations are performed to demonstrate that the proposed algorithm is feasible, secure, sensitive to keys and robust to noise attack and data loss.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Emotion recognition based on multiple order features using fractional Fourier transform

NASA Astrophysics Data System (ADS)

Ren, Bo; Liu, Deyin; Qi, Lin

2017-07-01

In order to deal with the insufficiency of recently algorithms based on Two Dimensions Fractional Fourier Transform (2D-FrFT), this paper proposes a multiple order features based method for emotion recognition. Most existing methods utilize the feature of single order or a couple of orders of 2D-FrFT. However, different orders of 2D-FrFT have different contributions on the feature extraction of emotion recognition. Combination of these features can enhance the performance of an emotion recognition system. The proposed approach obtains numerous features that extracted in different orders of 2D-FrFT in the directions of x-axis and y-axis, and uses the statistical magnitudes as the final feature vectors for recognition. The Support Vector Machine (SVM) is utilized for the classification and RML Emotion database and Cohn-Kanade (CK) database are used for the experiment. The experimental results demonstrate the effectiveness of the proposed method.

Thermal behavior of silicone rubber-based ceramizable composites characterized by Fourier transform infrared (FT-IR) spectroscopy and microcalorimetry.

PubMed

Anyszka, Rafał; Bieliński, Dariusz M; Jędrzejczyk, Marcin

2013-12-01

Ceramizable (ceramifiable) silicone rubber-based composites are commonly used for cable insulation. These materials are able to create a protective ceramic layer during fire due to the ceramization process, which occurs at high temperature. When the temperature is increased, the polymer matrix is degraded and filler particles stick together by the fluxing agent, producing a solid, continuous ceramic phase that protects the copper wire from heat and mechanical stress. Despite increasing interest in these materials that has resulted in growing applications in the cable industry, their thermal behavior and ceramization process are still insufficiently described in the literature. In this paper, the thermal behavior of ceramizable silicone rubber-based composites is studied using microcalorimetry and Fourier transform infrared spectroscopy. The analysis of the experimental data made it possible to develop complete information on the mechanism of composite ceramization.

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.

Proposed Application of Fast Fourier Transform in Near Infra Red Based Non Invasive Blood Glucose Monitoring System

NASA Astrophysics Data System (ADS)

Jenie, R. P.; Iskandar, J.; Kurniawan, A.; Rustami, E.; Syafutra, H.; Nurdin, N. M.; Handoyo, T.; Prabowo, J.; Febryarto, R.; Rahayu, M. S. K.; Damayanthi, E.; Rimbawan; Sukandar, D.; Suryana, Y.; Irzaman; Alatas, H.

2017-03-01

Worldwide emergence of glycaemic status related health disorders, such as diabetes and metabolic syndrome, is growing in alarming rate. The objective was to propose new methods for non invasive blood glucose level measurement system, based on implementation of Fast Fourier Transform methods. This was an initial-lab-scale-research. Data on non invasive blood glucose measurement are referred from Scopus, Medline, and Google Scholar, from 2011 until 2016, and was used as design references, combined with in house verification. System was developed in modular fashion, based on aforementioned compiled references. Several preliminary tests to understand relationship between LED and photo-diode responses have been done. Several references were used as non invasive blood glucose measurement tools design basis. Solution is developed in modular fashion. we have proven different sensor responses to water and glucose. Human test for non invasive blood glucose level measurement system is needed.

Choice of optical system is critical for the security of double random phase encryption systems

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Cassidy, Derek; Zhao, Liang; Ryle, James P.; Healy, John J.; Sheridan, John T.

2017-06-01

The linear canonical transform (LCT) is used in modeling a coherent light-field propagation through first-order optical systems. Recently, a generic optical system, known as the quadratic phase encoding system (QPES), for encrypting a two-dimensional image has been reported. In such systems, two random phase keys and the individual LCT parameters (α,β,γ) serve as secret keys of the cryptosystem. It is important that such encryption systems also satisfy some dynamic security properties. We, therefore, examine such systems using two cryptographic evaluation methods, the avalanche effect and bit independence criterion, which indicate the degree of security of the cryptographic algorithms using QPES. We compared our simulation results with the conventional Fourier and the Fresnel transform-based double random phase encryption (DRPE) systems. The results show that the LCT-based DRPE has an excellent avalanche and bit independence characteristics compared to the conventional Fourier and Fresnel-based encryption systems.

Blind third-order dispersion estimation based on fractional Fourier transformation for coherent optical communication

NASA Astrophysics Data System (ADS)

Yang, Lin; Guo, Peng; Yang, Aiying; Qiao, Yaojun

2018-02-01

In this paper, we propose a blind third-order dispersion estimation method based on fractional Fourier transformation (FrFT) in optical fiber communication system. By measuring the chromatic dispersion (CD) at different wavelengths, this method can estimation dispersion slope and further calculate the third-order dispersion. The simulation results demonstrate that the estimation error is less than 2 % in 28GBaud dual polarization quadrature phase-shift keying (DP-QPSK) and 28GBaud dual polarization 16 quadrature amplitude modulation (DP-16QAM) system. Through simulations, the proposed third-order dispersion estimation method is shown to be robust against nonlinear and amplified spontaneous emission (ASE) noise. In addition, to reduce the computational complexity, searching step with coarse and fine granularity is chosen to search optimal order of FrFT. The third-order dispersion estimation method based on FrFT can be used to monitor the third-order dispersion in optical fiber system.

Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses

PubMed Central

Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David

2016-01-01

Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175

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.

Instrument Line Shape Modeling and Correction for Off-Axis Detectors in Fourier Transform Spectrometry

NASA Technical Reports Server (NTRS)

Bowman, K.; Worden, H.; Beer, R.

1999-01-01

Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.

Fourier Transform Mass Spectrometry.

ERIC Educational Resources Information Center

Gross, Michael L.; Rempel, Don L.

1984-01-01

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.

ERIC Educational Resources Information Center

Perkins, W. D.

1987-01-01

This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)

A fast Karhunen-Loeve transform for a class of random processes

NASA Technical Reports Server (NTRS)

Jain, A. K.

1976-01-01

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

Fourier Spectral Filter Array for Optimal Multispectral Imaging.

PubMed

Jia, Jie; Barnard, Kenneth J; Hirakawa, Keigo

2016-04-01

Limitations to existing multispectral imaging modalities include speed, cost, range, spatial resolution, and application-specific system designs that lack versatility of the hyperspectral imaging modalities. In this paper, we propose a novel general-purpose single-shot passive multispectral imaging modality. Central to this design is a new type of spectral filter array (SFA) based not on the notion of spatially multiplexing narrowband filters, but instead aimed at enabling single-shot Fourier transform spectroscopy. We refer to this new SFA pattern as Fourier SFA, and we prove that this design solves the problem of optimally sampling the hyperspectral image data.

Deblurring of Class-Averaged Images in Single-Particle Electron Microscopy.

PubMed

Park, Wooram; Madden, Dean R; Rockmore, Daniel N; Chirikjian, Gregory S

2010-03-01

This paper proposes a method for deblurring of class-averaged images in single-particle electron microscopy (EM). Since EM images of biological samples are very noisy, the images which are nominally identical projection images are often grouped, aligned and averaged in order to cancel or reduce the background noise. However, the noise in the individual EM images generates errors in the alignment process, which creates an inherent limit on the accuracy of the resulting class averages. This inaccurate class average due to the alignment errors can be viewed as the result of a convolution of an underlying clear image with a blurring function. In this work, we develop a deconvolution method that gives an estimate for the underlying clear image from a blurred class-averaged image using precomputed statistics of misalignment. Since this convolution is over the group of rigid body motions of the plane, SE(2), we use the Fourier transform for SE(2) in order to convert the convolution into a matrix multiplication in the corresponding Fourier space. For practical implementation we use a Hermite-function-based image modeling technique, because Hermite expansions enable lossless Cartesian-polar coordinate conversion using the Laguerre-Fourier expansions, and Hermite expansion and Laguerre-Fourier expansion retain their structures under the Fourier transform. Based on these mathematical properties, we can obtain the deconvolution of the blurred class average using simple matrix multiplication. Tests of the proposed deconvolution method using synthetic and experimental EM images confirm the performance of our method.

Stellar Astrophysics with a Dispersed Fourier Transform Spectrograph. II. Orbits of Double-lined Spectroscopic Binaries

NASA Astrophysics Data System (ADS)

Behr, Bradford B.; Cenko, Andrew T.; Hajian, Arsen R.; McMillan, Robert S.; Murison, Marc; Meade, Jeff; Hindsley, Robert

2011-07-01

We present orbital parameters for six double-lined spectroscopic binaries (ι Pegasi, ω Draconis, 12 Boötis, V1143 Cygni, β Aurigae, and Mizar A) and two double-lined triple star systems (κ Pegasi and η Virginis). The orbital fits are based upon high-precision radial velocity (RV) observations made with a dispersed Fourier Transform Spectrograph, or dFTS, a new instrument that combines interferometric and dispersive elements. For some of the double-lined binaries with known inclination angles, the quality of our RV data permits us to determine the masses M 1 and M 2 of the stellar components with relative errors as small as 0.2%.

Multi-dimensional quantum state sharing based on quantum Fourier transform

NASA Astrophysics Data System (ADS)

Qin, Huawang; Tso, Raylin; Dai, Yuewei

2018-03-01

A scheme of multi-dimensional quantum state sharing is proposed. The dealer performs the quantum SUM gate and the quantum Fourier transform to encode a multi-dimensional quantum state into an entanglement state. Then the dealer distributes each participant a particle of the entanglement state, to share the quantum state among n participants. In the recovery, n-1 participants measure their particles and supply their measurement results; the last participant performs the unitary operation on his particle according to these measurement results and can reconstruct the initial quantum state. The proposed scheme has two merits: It can share the multi-dimensional quantum state and it does not need the entanglement measurement.

Motion detection using extended fractional Fourier transform and digital speckle photography.

PubMed

Bhaduri, Basanta; Tay, C J; Quan, C; Sheppard, Colin J R

2010-05-24

Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

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.

Optical computing using optical flip-flops in Fourier processors: use in matrix multiplication and discrete linear transforms.

PubMed

Ando, S; Sekine, S; Mita, M; Katsuo, S

1989-12-15

An architecture and the algorithms for matrix multiplication using optical flip-flops (OFFs) in optical processors are proposed based on residue arithmetic. The proposed system is capable of processing all elements of matrices in parallel utilizing the information retrieving ability of optical Fourier processors. The employment of OFFs enables bidirectional data flow leading to a simpler architecture and the burden of residue-to-decimal (or residue-to-binary) conversion to operation time can be largely reduced by processing all elements in parallel. The calculated characteristics of operation time suggest a promising use of the system in a real time 2-D linear transform.

Experimental Research Into Generation of Acoustic Emission Signals in the Process of Friction of Hadfield Steel Single Crystals

NASA Astrophysics Data System (ADS)

Lychagin, D. V.; Filippov, A. V.; Novitskaia, O. S.; Kolubaev, E. A.; Sizova, O. V.

2016-08-01

The results of experimental research into dry sliding friction of Hadfield steel single crystals involving registration of acoustic emission are presented in the paper. The images of friction surfaces of Hadfield steel single crystals and wear grooves of the counterbody surface made after completion of three serial experiments conducted under similar conditions and friction regimes are given. The relation of the acoustic emission waveform envelope to the changing friction factor is revealed. Amplitude-frequency characteristics of acoustic emission signal frames are determined on the base of Fast Fourier Transform and Short Time Fourier Transform during the run-in stage of tribounits and in the process of stable friction.

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.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

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.

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.

Absolute Rovibrational Intensities for the Chi(sup 1)Sigma(sup +) v=3 <-- 0 Band of (12)C(16)O Obtained with Kitt Peak and BOMEM FTS Instruments

NASA Technical Reports Server (NTRS)

Chackerian, Charles, Jr.; Kshirsagar, R. J.; Giver, L. P.; Brown, L. R.; Condon, Estelle P. (Technical Monitor)

1999-01-01

This work was initiated to compare absolute line intensities retrieved with the Kitt Peak FTS (Fourier Transform Spectrometer) and Ames BOMEM FTS. Since thermal contaminations can be a problem using the BOMEM instrument if proper precautions are not taken it was thought that measurements done at 6300 per cm would more easily result in satisfactory intercomparisons. Very recent measurements of the CO 3 <-- 0 band fine intensities confirms results reported here that the intensities listed in HITRAN (High Resolution Molecular Absorption Database) for this band are on the order of six to seven percent too low. All of the infrared intensities in the current HITRAN tabulation are based on the electric dipole moment function reported fifteen years ago. The latter in turn was partly based on intensities for the 3 <-- 0 band reported thirty years ago. We have, therefore, redetermined the electric dipole moment function of ground electronic state CO.

Adaptive optics; Proceedings of the Meeting, Arlington, VA, April 10, 11, 1985

NASA Astrophysics Data System (ADS)

Ludman, J. E.

Papers are presented on the directed energy program for ballistic missile defense, a self-referencing wavefront interferometer for laser sources, the effects of mirror grating distortions on diffraction spots at wavefront sensors, and the optical design of an all-reflecting, high-resolution camera for active-optics on ground-based telescopes. Also considered are transverse coherence length observations, time dependent statistics of upper atmosphere optical turbulence, high altitude acoustic soundings, and the Cramer-Rao lower bound on wavefront sensor error. Other topics include wavefront reconstruction from noisy slope or difference data using the discrete Fourier transform, acoustooptic adaptive signal processing, the recording of phase deformations on a PLZT wafer for holographic and spatial light modulator applications, and an optical phase reconstructor using a multiplier-accumulator approach. Papers are also presented on an integrated optics wavefront measurement sensor, a new optical preprocessor for automatic vision systems, a model for predicting infrared atmospheric emission fluctuations, and optical logic gates and flip-flops based on polarization-bistable semiconductor lasers.

The ISPM unified radio and plasma wave experiment

NASA Technical Reports Server (NTRS)

Stone, R. G.; Caldwell, J.; Deconchy, Y.; Deschanciaux, C.; Ebbett, R.; Epstein, G.; Groetz, K.; Harvey, C. C.; Hoang, S.; Howard, R.

1983-01-01

Hardware for the International Solar Polar Mission (ISPM) Unified Radio and Plasma (URAP) wave experiment is presented. The URAP determines direction and polarization of distant radio sources for remote sensing of the heliosphere, and studies local wave phenomena which determine the transport coefficients of the ambient plasma. Electric and magnetic field antennas and preamplifiers; the electromagnetic compatibility plan and grounding; radio astronomy and plasma frequency receivers; a fast Fourier transformation data processing unit waveform analyzer; dc voltage measurements; a fast envelope sampler for the solar wind, and plasmas near Jupiter; a sounder; and a power converter are described.

[Spectroscopic methods applied to component determination and species identification for coffee].

PubMed

Chen, Hua-zhou; Xu, Li-li; Qin, Qiang

2014-06-01

Spectroscopic analysis was applied to the determination of the nutrient quality of ground, instant and chicory coffees. By using inductively coupled plasma atomic emission spectrometry (ICP-ES), nine mineral elements were determined in solid coffee samples. Caffeine was determined by ultraviolet (UV) spectrometry and organic matter was investigated by Fourier transform infrared (FTIR) spectroscopy. Oxidation-reduction titration was utilized for measuring the oxalate. The differences between ground coffee and instant coffee was identified on the basis of the contents of caffeine, oxalate and mineral elements. Experimental evidence showed that, caffeine in instant coffee was 2-3 times higher than in ground coffee. Oxalate in instant coffee was significantly higher in ground coffee. Mineral elements of Mg, P and Zn in ground coffee is lower than in instant coffee, while Cu is several times higher. The mineral content in chicory coffee is overall lower than the instant coffee. In addition, we determined the content of Ti for different types of coffees, and simultaneously detected the elements of Cu, Ti and Zn in chicory coffee. As a fast detection technique, FTIR spectroscopy has the potential of detecting the differences between ground coffee and instant coffee, and is able to verify the presence of caffeine and oxalate.

KAM Tori Construction Algorithms

NASA Astrophysics Data System (ADS)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

Generalized fiber Fourier optics.

PubMed

Cincotti, Gabriella

2011-06-15

A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.

Twilight Intensity Variation of the Infrared Hydroxyl Airglow

NASA Technical Reports Server (NTRS)

Lowe, R. P.; Gilbert, K. L.; Niciejewski, R. J.

1984-01-01

The vibration rotation bands of the hydroxyl radical are the strongest features in the night airglow and are exceeded in intensity in the dayglow only by the infrared atmospheric bands of oxygen. The variation of intensity during evening twilight is discussed. Using a ground-based Fourier Transform Spectrometer (FTS), hydroxyl intensity measurements as early as 3 deg solar depression were made. Models of the twilight behavior show that this should be sufficient to provide measurement of the main portion of the twilight intensity change. The instrument was equipped with a liquid nitrogen-cooled germanium detector whose high sensitivity combined with the efficiency of the FTS technique permits spectra of the region 1.1 to 1.6 microns at high signal-to-noise to be obtained in two minutes. The use of a polarizer at the entrance aperture of the instrument reduces the intensity of scattered sunlight by a factor of at least ten for zenith observations.

O2/1 Delta/ emission in the day and night airglow of Venus

NASA Technical Reports Server (NTRS)

Connes, P.; Noxon, J. F.; Traub, W. A.; Carleton, N. P.

1979-01-01

An intense airglow from O2(1 Delta) at 1.27 microns on both the light and the dark sides of Venus has been detected by using a ground-based high-resolution Fourier-transform spectrometer. Both dayglow and nightglow are roughly 1,000 times brighter than the visible O2 nightglow found by Veneras 9 and 10 in 1975. The column emission rate of O2(1 Delta) from Venus is close to the rate at which fresh O atoms are produced from photolysis of CO2 on the day side. Formation of O2(1 Delta) is thus a major step in the removal of O atoms from the atmosphere, and dynamical processes must carry these atoms to the night side fast enough to yield a maximum density near 90 km, which is almost constant over the planet.

Initial Retrieval Validation from the Joint Airborne IASI Validation Experiment (JAIVEx)

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Liu, Xu; Smith, WIlliam L.; Larar, Allen M.; Taylor, Jonathan P.; Revercomb, Henry E.; Mango, Stephen A.; Schluessel, Peter; Calbet, Xavier

2007-01-01

The Joint Airborne IASI Validation Experiment (JAIVEx) was conducted during April 2007 mainly for validation of the Infrared Atmospheric Sounding Interferometer (IASI) on the MetOp satellite, but also included a strong component focusing on validation of the Atmospheric InfraRed Sounder (AIRS) aboard the AQUA satellite. The cross validation of IASI and AIRS is important for the joint use of their data in the global Numerical Weather Prediction process. Initial inter-comparisons of geophysical products have been conducted from different aspects, such as using different measurements from airborne ultraspectral Fourier transform spectrometers (specifically, the NPOESS Airborne Sounder Testbed Interferometer (NAST-I) and the Scanning-High resolution Interferometer Sounder (S-HIS) aboard the NASA WB-57 aircraft), UK Facility for Airborne Atmospheric Measurements (FAAM) BAe146-301 aircraft insitu instruments, dedicated dropsondes, radiosondes, and ground based Raman Lidar. An overview of the JAIVEx retrieval validation plan and some initial results of this field campaign are presented.

The characterization of canvas painting by the Serbian artist Milo Milunović using X-ray fluorescence, micro-Raman and FTIR spectroscopy

NASA Astrophysics Data System (ADS)

Damjanović, Lj.; Gajić-Kvaščev, M.; Đurđević, J.; Andrić, V.; Marić-Stojanović, M.; Lazić, T.; Nikolić, S.

2015-10-01

A canvas painting by Milo Milunović "The Inspiration of the poet" was studied by energy dispersive X-Ray fluorescence (EDXRF), micro-Raman and Fourier transform infrared (FTIR) spectroscopy in order to identify materials used by the artist and his painting technique. Study is perfomed combining in situ non-destructive method with the preparation and study of cross-section samples and raw fragments of the samples. Milo Milunović, an eminent painter from Balkan region, made a copy of the Nicolas Poussin's original painting in Louvre in 1926/27. Obtained results revealed following pigments on the investigated canvas painting: vermilion, minium, cobalt blue, ultramarine, lead white, zinc white, cadmium yellow, chrome-based green pigment and several earth pigments - red and yellow ocher, green earth and umber. Ground layer was made of lead white mixed with calcium carbonate.

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

EPA Science Inventory

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

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

1969-01-01

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

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.

[Research on spatially modulated Fourier transform imaging spectrometer data processing method].

PubMed

Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan

2010-03-01

Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result.

Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm

NASA Technical Reports Server (NTRS)

Hwang, Chyi; Lu, Ming-Jeng; Shieh, Leang S.

1991-01-01

The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.

Applications of Fourier Transform Ion Cyclotron Resonance (FT-ICR) and Orbitrap Based High Resolution Mass Spectrometry in Metabolomics and Lipidomics.

PubMed

Ghaste, Manoj; Mistrik, Robert; Shulaev, Vladimir

2016-05-25

Metabolomics, along with other "omics" approaches, is rapidly becoming one of the major approaches aimed at understanding the organization and dynamics of metabolic networks. Mass spectrometry is often a technique of choice for metabolomics studies due to its high sensitivity, reproducibility and wide dynamic range. High resolution mass spectrometry (HRMS) is a widely practiced technique in analytical and bioanalytical sciences. It offers exceptionally high resolution and the highest degree of structural confirmation. Many metabolomics studies have been conducted using HRMS over the past decade. In this review, we will explore the latest developments in Fourier transform mass spectrometry (FTMS) and Orbitrap based metabolomics technology, its advantages and drawbacks for using in metabolomics and lipidomics studies, and development of novel approaches for processing HRMS data.

Applications of Fourier Transform Ion Cyclotron Resonance (FT-ICR) and Orbitrap Based High Resolution Mass Spectrometry in Metabolomics and Lipidomics

PubMed Central

Ghaste, Manoj; Mistrik, Robert; Shulaev, Vladimir

2016-01-01

Metabolomics, along with other “omics” approaches, is rapidly becoming one of the major approaches aimed at understanding the organization and dynamics of metabolic networks. Mass spectrometry is often a technique of choice for metabolomics studies due to its high sensitivity, reproducibility and wide dynamic range. High resolution mass spectrometry (HRMS) is a widely practiced technique in analytical and bioanalytical sciences. It offers exceptionally high resolution and the highest degree of structural confirmation. Many metabolomics studies have been conducted using HRMS over the past decade. In this review, we will explore the latest developments in Fourier transform mass spectrometry (FTMS) and Orbitrap based metabolomics technology, its advantages and drawbacks for using in metabolomics and lipidomics studies, and development of novel approaches for processing HRMS data. PMID:27231903

A Preliminary Research on the Development of the Hard X-Ray Imaging Telescope

NASA Astrophysics Data System (ADS)

Zheng, C. X.; Cai, M. S.; Hu, Y. M.; Huang, Y. Y.; Gong, Y. Z.

2014-03-01

Since the 1860s, astronomers have explored a new field with the discovery of X-ray. Instead of the conventional imaging technique by using mirrors or lens, which can not work in the high-energy bands, direct imaging, coded aperture, and Fourier transform are used for the high-energy imaging. It can be implemented in various hardware configurations, among which the spatial modulation collimator are widely used. We adopt the grating collimator based on Fourier transform that is discussed in detail. This paper makes an investigation on the fabrication process of grating. The key components of the hard X-ray telescope based on the spatial modulation are developed, which contains 8 CsI-detector modules, 8-channel shaping amplifiers, and data acquisition system. The preliminary test results of readout electronics system are obtained.

Distributed ISAR Subimage Fusion of Nonuniform Rotating Target Based on Matching Fourier Transform.

PubMed

Li, Yuanyuan; Fu, Yaowen; Zhang, Wenpeng

2018-06-04

In real applications, the image quality of the conventional monostatic Inverse Synthetic Aperture Radar (ISAR) for the maneuvering target is subject to the strong fluctuation of Radar Cross Section (RCS), as the target aspect varies enormously. Meanwhile, the maneuvering target introduces nonuniform rotation after translation motion compensation which degrades the imaging performance of the conventional Fourier Transform (FT)-based method in the cross-range dimension. In this paper, a method which combines the distributed ISAR technique and the Matching Fourier Transform (MFT) is proposed to overcome these problems. Firstly, according to the characteristics of the distributed ISAR, the multiple channel echoes of the nonuniform rotation target from different observation angles can be acquired. Then, by applying the MFT to the echo of each channel, the defocused problem of nonuniform rotation target which is inevitable by using the FT-based imaging method can be avoided. Finally, after preprocessing, scaling and rotation of all subimages, the noncoherent fusion image containing all the RCS information in all channels can be obtained. The accumulation coefficients of all subimages are calculated adaptively according to the their image qualities. Simulation and experimental data are used to validate the effectiveness of the proposed approach, and fusion image with improved recognizability can be obtained. Therefore, by using the distributed ISAR technique and MFT, subimages of high-maneuvering target from different observation angles can be obtained. Meanwhile, by employing the adaptive subimage fusion method, the RCS fluctuation can be alleviated and more recognizable final image can be obtained.

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.

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.

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

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

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

Fourier transform spectroscopy of cotton and cotton trash

USDA-ARS?s Scientific Manuscript database

Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...

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)

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...

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.

Research on fast Fourier transforms algorithm of huge remote sensing image technology with GPU and partitioning technology.

PubMed

Yang, Xue; Li, Xue-You; Li, Jia-Guo; Ma, Jun; Zhang, Li; Yang, Jan; Du, Quan-Ye

2014-02-01

Fast Fourier transforms (FFT) is a basic approach to remote sensing image processing. With the improvement of capacity of remote sensing image capture with the features of hyperspectrum, high spatial resolution and high temporal resolution, how to use FFT technology to efficiently process huge remote sensing image becomes the critical step and research hot spot of current image processing technology. FFT algorithm, one of the basic algorithms of image processing, can be used for stripe noise removal, image compression, image registration, etc. in processing remote sensing image. CUFFT function library is the FFT algorithm library based on CPU and FFTW. FFTW is a FFT algorithm developed based on CPU in PC platform, and is currently the fastest CPU based FFT algorithm function library. However there is a common problem that once the available memory or memory is less than the capacity of image, there will be out of memory or memory overflow when using the above two methods to realize image FFT arithmetic. To address this problem, a CPU and partitioning technology based Huge Remote Fast Fourier Transform (HRFFT) algorithm is proposed in this paper. By improving the FFT algorithm in CUFFT function library, the problem of out of memory and memory overflow is solved. Moreover, this method is proved rational by experiment combined with the CCD image of HJ-1A satellite. When applied to practical image processing, it improves effect of the image processing, speeds up the processing, which saves the time of computation and achieves sound result.

A method to perform a fast fourier transform with primitive image transformations.

PubMed

Sheridan, Phil

2007-05-01

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC.

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

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

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

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fouriermore » transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.« less

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

Spherical 3D isotropic wavelets

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2012-04-01

Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html

Polypeptides Based Molecular Electronics

DTIC Science & Technology

2008-10-06

average of 0.82 nm, corresponding to the theoretical height of a MPTMS monolayer of 0.87nm. Fourier Transform Infrared Spectroscopy (FTIR) spectrum of 3... Infrared Spectroscopy (FTIR) of 3-Mercaptopropyl trimethoxysilane (MPTMS) layer on Si wafer Figure 23a. Topographical image of peptide on MPTMS...transform infrared spectroscopy . Peptide with COOH group is proven to attach to Aminopropyltrimethoxysilane (APTES) functionalized silicon substrate

Information security using multiple reference-based optical joint transform correlation and orthogonal code

NASA Astrophysics Data System (ADS)

Nazrul Islam, Mohammed; Karim, Mohammad A.; Vijayan Asari, K.

2013-09-01

Protecting and processing of confidential information, such as personal identification, biometrics, remains a challenging task for further research and development. A new methodology to ensure enhanced security of information in images through the use of encryption and multiplexing is proposed in this paper. We use orthogonal encoding scheme to encode multiple information independently and then combine them together to save storage space and transmission bandwidth. The encoded and multiplexed image is encrypted employing multiple reference-based joint transform correlation. The encryption key is fed into four channels which are relatively phase shifted by different amounts. The input image is introduced to all the channels and then Fourier transformed to obtain joint power spectra (JPS) signals. The resultant JPS signals are again phase-shifted and then combined to form a modified JPS signal which yields the encrypted image after having performed an inverse Fourier transformation. The proposed cryptographic system makes the confidential information absolutely inaccessible to any unauthorized intruder, while allows for the retrieval of the information to the respective authorized recipient without any distortion. The proposed technique is investigated through computer simulations under different practical conditions in order to verify its overall robustness.