Estimation of spectral kurtosis

NASA Astrophysics Data System (ADS)

Sutawanir

2017-03-01

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

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.

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.

Geometry and dynamics in the fractional discrete Fourier transform.

PubMed

Wolf, Kurt Bernardo; Krötzsch, Guillermo

2007-03-01

The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.

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.

A new transform for the analysis of complex fractionated atrial electrograms

PubMed Central

2011-01-01

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

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.

Power Spectral Density and Hilbert Transform

DTIC Science & Technology

2016-12-01

Fourier transform, Hilbert transform, digital filter , SDR 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER...terms. A very good approximation to the ideal Hilbert transform is a low-pass finite impulse response (FIR) filter . In Fig. 7, we show a real signal...220), converted to an analytic signal using a 255-tap Hilbert transform low-pass filter . For an ideal Hilbert

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

DTIC Science & Technology

1995-09-01

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

Probing biological redox chemistry with large amplitude Fourier transformed ac voltammetry

PubMed Central

Adamson, Hope

2017-01-01

Biological electron-exchange reactions are fundamental to life on earth. Redox reactions underpin respiration, photosynthesis, molecular biosynthesis, cell signalling and protein folding. Chemical, biomedical and future energy technology developments are also inspired by these natural electron transfer processes. Further developments in techniques and data analysis are required to gain a deeper understanding of the redox biochemistry processes that power Nature. This review outlines the new insights gained from developing Fourier transformed ac voltammetry as a tool for protein film electrochemistry. PMID:28804798

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.

A Comparative Analysis for Selection of Appropriate Mother Wavelet for Detection of Stationary Disturbances

NASA Astrophysics Data System (ADS)

Kamble, Saurabh Prakash; Thawkar, Shashank; Gaikwad, Vinayak G.; Kothari, D. P.

2017-12-01

Detection of disturbances is the first step of mitigation. Power electronics plays a crucial role in modern power system which makes system operation efficient but it also bring stationary disturbances in the power system and added impurities to the supply. It happens because of the non-linear loads used in modern day power system which inject disturbances like harmonic disturbances, flickers, sag etc. in power grid. These impurities can damage equipments so it is necessary to mitigate these impurities present in the supply very quickly. So, digital signal processing techniques are incorporated for detection purpose. Signal processing techniques like fast Fourier transform, short-time Fourier transform, Wavelet transform etc. are widely used for the detection of disturbances. Among all, wavelet transform is widely used because of its better detection capabilities. But, which mother wavelet has to use for detection is still a mystery. Depending upon the periodicity, the disturbances are classified as stationary and non-stationary disturbances. This paper presents the importance of selection of mother wavelet for analyzing stationary disturbances using discrete wavelet transform. Signals with stationary disturbances of various frequencies are generated using MATLAB. The analysis of these signals is done using various mother wavelets like Daubechies and bi-orthogonal wavelets and the measured root mean square value of stationary disturbance is obtained. The measured value obtained by discrete wavelet transform is compared with the exact RMS value of the frequency component and the percentage differences are presented which helps to select optimum mother wavelet.

A perturbative approach to the redshift space correlation function: beyond the Standard Model

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Koyama, Kazuya

2017-08-01

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with <= 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpch <= s <= 180Mpc/h. Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.

Detection and volume estimation of embolic air in the middle cerebral artery using transcranial Doppler sonography.

PubMed

Bunegin, L; Wahl, D; Albin, M S

1994-03-01

Cerebral embolism has been implicated in the development of cognitive and neurological deficits following bypass surgery. This study proposes methodology for estimating cerebral air embolus volume using transcranial Doppler sonography. Transcranial Doppler audio signals of air bubbles in the middle cerebral artery obtained from in vivo experiments were subjected to a fast-Fourier transform analysis. Audio segments when no air was present as well as artifact resulting from electrocautery and sensor movement were also subjected to fast-Fourier transform analysis. Spectra were compared, and frequency and power differences were noted and used for development of audio band-pass filters for isolation of frequencies associated with air emboli. In a bench model of the middle cerebral artery circulation, repetitive injections of various air volumes between 0.5 and 500 microL were made. Transcranial Doppler audio output was band-pass filtered, acquired digitally, then subjected to a fast-Fourier transform power spectrum analysis and power spectrum integration. A linear least-squares correlation was performed on the data. Fast-Fourier transform analysis of audio segments indicated that frequencies between 250 and 500 Hz are consistently dominant in the spectrum when air emboli are present. Background frequencies appear to be below 240 Hz, and artifact resulting from sensor movement and electrocautery appears to be below 300 Hz. Data from the middle cerebral artery model filtered through a 307- to 450-Hz band-pass filter yielded a linear relation between emboli volume and the integrated value of the power spectrum near 40 microL. Detection of emboli less than 0.5 microL was inconsistent, and embolus volumes greater than 40 microL were indistinguishable from one another. The preliminary technique described in this study may represent a starting point from which automated detection and volume estimation of cerebral emboli might be approached.

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.

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.

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

Hudgins, L.H.

After a brief review of the elementary properties of Fourier Transforms, the Wavelet Transform is defined in Part I. Basic results are given for admissable wavelets. The Multiresolution Analysis, or MRA (a mathematical structure which unifies a large class of wavelets with Quadrature Mirror Filters) is then introduced. Some fundamental aspects of wavelet design are then explored. The Discrete Wavelet Transform is discussed and, in the context of an MRA, is seen to supply a Fast Wavelet Transform which competes with the Fast Fourier Transform for efficiency. In Part II, the Wavelet Transform is developed in terms of the scalemore » number variable s instead of the scale length variable a where a = 1/s. Basic results such as the admissibility condition, conservation of energy, and the reconstruction theorem are proven in this context. After reviewing some motivation for the usual Fourier power spectrum, a definition is given for the wavelet power spectrum. This `spectral density` is then intepreted in the context of spectral estimation theory. Parseval`s theorem for Wavelets then leads naturally to the Wavelet Cross Spectrum, Wavelet Cospectrum, and Wavelet Quadrature Spectrum. Wavelet Transforms are then applied in Part III to the analysis of atmospheric turbulence. Data collected over the ocean is examined in the wavelet transform domain for underlying structure. A brief overview of atmospheric turbulence is provided. Then the overall method of applying Wavelet Transform techniques to time series data is described. A trace study is included, showing some of the aspects of choosing the computational algorithm, and selection of a specific analyzing wavelet. A model for generating synthetic turbulence data is developed, and seen to yield useful results in comparing with real data for structural transitions. Results from the theory of Wavelet Spectral Estimation and Wavelength Cross-Transforms are applied to studying the momentum transport and the heat flux.« less

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.

Characterization of near-terahertz complementary metal-oxide semiconductor circuits using a Fourier-transform interferometer

DOE PAGES

Arenas, D. J.; Shim, Dongha; Koukis, D. I.; ...

2011-10-24

Optical methods for measuring of the emission spectra of oscillator circuits operating in the 400-600 GHz range are described. The emitted power from patch antennas included in the circuits is measured by placing the circuit in the source chamber of a Fourier-transform interferometric spectrometer. The results show that this optical technique is useful for measuring circuits pushing the frontier in operating frequency. The technique also allows the characterization of the circuit by measuring the power radiated in the fundamental and in the harmonics. This capability is useful for oscillator architectures designed to cancel the fundamental and use higher harmonics. Themore » radiated power was measured using two techniques: direct measurement of the power by placing the device in front of a bolometer of known responsivity, and by comparison to the estimated power from blackbody sources. The latter technique showed that these circuits have higher emission than blackbody sources at the operating frequencies, and, therefore, offer potential spectroscopy applications.« less

Planar metasurface retroreflector

NASA Astrophysics Data System (ADS)

Arbabi, Amir; Arbabi, Ehsan; Horie, Yu; Kamali, Seyedeh Mahsa; Faraon, Andrei

2017-07-01

Metasurfaces are two-dimensional arrangements of subwavelength scatterers that control the propagation of optical waves. Here, we show that cascaded metasurfaces, each performing a predefined mathematical transformation, provide a new optical design framework that enables new functionalities not yet demonstrated with single metasurfaces. Specifically, we demonstrate that retroreflection can be achieved with two vertically stacked planar metasurfaces, the first performing a spatial Fourier transform and its inverse, and the second imparting a spatially varying momentum to the Fourier transform of the incident light. Using this concept, we fabricate and test a planar monolithic near-infrared retroreflector composed of two layers of silicon nanoposts, which reflects light along its incident direction with a normal incidence efficiency of 78% and a large half-power field of view of 60°. The metasurface retroreflector demonstrates the potential of cascaded metasurfaces for implementing novel high-performance components, and enables low-power and low-weight passive optical transmitters.

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.

Fourier plane image amplifier

DOEpatents

Hackel, Lloyd A.; Hermann, Mark R.; Dane, C. Brent; Tiszauer, Detlev H.

1995-01-01

A solid state laser is frequency tripled to 0.3 .mu.m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only .about.1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power.

Fourier plane image amplifier

DOEpatents

Hackel, L.A.; Hermann, M.R.; Dane, C.B.; Tiszauer, D.H.

1995-12-12

A solid state laser is frequency tripled to 0.3 {micro}m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only about 1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power. 1 fig.

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

NASA Technical Reports Server (NTRS)

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

1974-01-01

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

Joint transform correlator optical encryption system: Extensions of the recorded encrypted signal and its inverse Fourier transform

NASA Astrophysics Data System (ADS)

Galizzi, Gustavo E.; Cuadrado-Laborde, Christian

2015-10-01

In this work we study the joint transform correlator setup, finding two analytical expressions for the extensions of the joint power spectrum and its inverse Fourier transform. We found that an optimum efficiency is reached, when the bandwidth of the key code is equal to the sum of the bandwidths of the image plus the random phase mask (RPM). The quality of the decryption is also affected by the ratio between the bandwidths of the RPM and the input image, being better as this ratio increases. In addition, the effect on the decrypted image when the detection area is lower than the encrypted signal extension was analyzed. We illustrate these results through several numerical examples.

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

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

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…

A perturbative approach to the redshift space correlation function: beyond the Standard Model

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model whichmore » is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ≤ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpc h ≤ s ≤ 180Mpc/ h . Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.« less

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.

Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals

DOE PAGES

Schmittfull, Marcel; Vlah, Zvonimir

2016-11-28

Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve this is to model nonlinear scales perturbatively. Unfortunately, this involves high-dimensional loop integrals that are cumbersome to evaluate. Here, trying to simplify this, we show how two-loop (next-to-next-to-leading order) corrections to the density power spectrum can be reduced to low-dimensional, radial integrals. Many of those can be evaluated with a one-dimensional fast Fourier transform, which is significantly faster than the five-dimensional Monte-Carlo integrals thatmore » are needed otherwise. The general idea of this fast fourier transform perturbation theory method is to switch between Fourier and position space to avoid convolutions and integrate over orientations, leaving only radial integrals. This reformulation is independent of the underlying shape of the initial linear density power spectrum and should easily accommodate features such as those from baryonic acoustic oscillations. We also discuss how to account for halo bias and redshift space distortions.« less

Four Forms of the Fourier Transform - for Freshmen, using Matlab

NASA Astrophysics Data System (ADS)

Simons, F. J.; Maloof, A. C.

2016-12-01

In 2015, a Fall "Freshman Seminar" at Princeton University (http://geoweb.princeton.edu/people/simons/FRS-SESC.html) taught students to combine field observations of the natural world with quantitative modeling and interpretation, to answer questions like: "How have Earth and human histories been recorded in the geology of Princeton, the Catskills, France and Spain?" (where we took the students on a data-gathering field trip during Fall Break), and "What experiments and analysis can a first-year (possibly non-future-major) do to query such archives of the past?" In the classroom, through problem sets, and around campus, students gained practical experience collecting geological and geophysical data in a geographic context, and analyzing these data using statistical techniques such as regression, time-series and image analysis, with the programming language Matlab. In this presentation I will detail how we instilled basic Matlab skills for quantitative geoscience data analysis through a 6-week progression of topics and exercises. In the 6 weeks after the Fall Break trip, we strengthened these competencies to make our students fully proficient for further learning, as evidenced by their end-of-term independent research work.The particular case study is focused on introducing power-spectral analysis to Freshmen, in a way that even the least quantitative among them could functionally understand. Not counting (0) "inspection", the four ways by which we have successfully instilled the concept of power-spectral analysis in a hands-on fashion are (1) "correlation", (2) "inversion", (3) "stacking", and formal (4) "Fourier transformation". These four provide the main "mappings". Along the way, of course, we also make sure that the students understand that "power-spectral density estimation" is not the same as "Fourier transformation", nor that every Fourier transform has to be "Fast". Hence, concepts from analysis-of-variance techniques, regression, and hypothesis testing, arise in this context, and will be discussed.

Absorption Mode FT-ICR Mass Spectrometry Imaging

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

Smith, Donald F.; Kilgour, David P.; Konijnenburg, Marco

2013-12-03

Fourier transform ion cyclotron resonance mass spectrometry offers the highest mass resolving power for molecular imaging experiments. This high mass resolving power ensures that closely spaced peaks at the same nominal mass are resolved for proper image generation. Typically higher magnetic fields are used to increase mass resolving power. However, a gain in mass resolving power can also be realized by phase correction of the data for absorption mode display. In addition to mass resolving power, absorption mode offers higher mass accuracy and signal-to-noise ratio over the conventional magnitude mode. Here we present the first use of absorption mode formore » Fourier transform ion cyclotron resonance mass spectrometry imaging. The Autophaser algorithm is used to phase correct each spectrum (pixel) in the image and then these parameters are used by the Chameleon work-flow based data processing software to generate absorption mode ?Datacubes? for image and spectral viewing. Absorption mode reveals new mass and spatial features that are not resolved in magnitude mode and results in improved selected ion image contrast.« less

The Simulation Realization of Pavement Roughness in the Time Domain

NASA Astrophysics Data System (ADS)

XU, H. L.; He, L.; An, D.

2017-10-01

As the needs for the dynamic study on the vehicle-pavement system and the simulated vibration table test, how to simulate the pavement roughness actually is important guarantee for whether calculation and test can reflect the actual situation or not. Using the power spectral density function, the simulation of pavement roughness can be realized by Fourier inverse transform. The main idea of this method was that the spectrum amplitude and random phase were obtained separately according to the power spectrum, and then the simulation of pavement roughness was obtained in the time domain through the Fourier inverse transform (IFFT). In the process, the sampling interval (Δl) was 0.1m, and the sampling points(N) was 4096, which satisfied the accuracy requirements. Using this method, the simulate results of pavement roughness (A~H grades) were obtain in the time domain.

Incipient fault diagnosis of power transformers using optical spectro-photometric technique

NASA Astrophysics Data System (ADS)

Hussain, K.; Karmakar, Subrata

2015-06-01

Power transformers are the vital equipment in the network of power generation, transmission and distribution. Mineral oil in oil-filled transformers plays very important role as far as electrical insulation for the winding and cooling of the transformer is concerned. As transformers are always under the influence of electrical and thermal stresses, incipient faults like partial discharge, sparking and arcing take place. As a result, mineral oil deteriorates there by premature failure of the transformer occurs causing huge losses in terms of revenue and assets. Therefore, the transformer health condition has to be monitored continuously. The Dissolved Gas Analysis (DGA) is being extensively used for this purpose, but it has some drawbacks like it needs carrier gas, regular instrument calibration, etc. To overcome these drawbacks, Ultraviolet (UV) -Visible and Fourier Transform Infrared (FTIR) Spectro-photometric techniques are used as diagnostic tools for investigating the degraded transformer oil affected by electrical, mechanical and thermal stresses. The technique has several advantages over the conventional DGA technique.

Suppression law of quantum states in a 3D photonic fast Fourier transform chip

PubMed Central

Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio

2016-01-01

The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135

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…

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

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.

An evaluation of random analysis methods for the determination of panel damping

NASA Technical Reports Server (NTRS)

Bhat, W. V.; Wilby, J. F.

1972-01-01

An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.

Assessment of Power Quality based on Fuzzy Logic and Discrete Wavelet Transform for Nonstationary Disturbances

NASA Astrophysics Data System (ADS)

Sinha, Pampa; Nath, Sudipta

2010-10-01

The main aspects of power system delivery are reliability and quality. If all the customers of a power system get uninterrupted power through the year then the system is considered to be reliable. The term power quality may be referred to as maintaining near sinusoidal voltage at rated frequency at the consumers end. The power component definitions are defined according to the IEEE Standard 1459-2000 both for single phase and three phase unbalanced systems based on Fourier Transform (FFT). In the presence of nonstationary power quality (PQ) disturbances results in accurate values due to its sensitivity to the spectral leakage problem. To overcome these limitations the power quality components are calculated using Discrete Wavelet Transform (DWT). In order to handle the uncertainties associated with electric power systems operations fuzzy logic has been incorporated in this paper. A new power quality index has been introduced here which can assess the power quality under nonstationary disturbances.

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.

Fourier transform spectroscopy for future planetary missions

NASA Astrophysics Data System (ADS)

Brasunas, John; Kolasinski, John; Kostiuk, Ted; Hewagama, Tilak

2017-01-01

Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system. Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, we have developed CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. We discuss the roadmap for making CIRS-lite a viable candidate for future planetary missions, including the recent increased emphasis on ocean worlds (Europa, Encelatus, Titan) and also on smaller payloads such as CubeSats and SmallSats.

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.

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.

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.

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.

Response of Autonomic Nervous System to Body Positions:

NASA Astrophysics Data System (ADS)

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

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

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.

Measurements of Wave Power in Wave Energy Converter Effectiveness Evaluation

NASA Astrophysics Data System (ADS)

Berins, J.; Berins, J.; Kalnacs, A.

2017-08-01

The article is devoted to the technical solution of alternative budget measuring equipment of the water surface gravity wave oscillation and the theoretical justification of the calculated oscillation power. This solution combines technologies such as lasers, WEB-camera image digital processing, interpolation of defined function at irregular intervals, volatility of discrete Fourier transformation for calculating the spectrum.

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…

Phase retrieval by constrained power inflation and signum flipping

NASA Astrophysics Data System (ADS)

Laganà, A. R.; Morabito, A. F.; Isernia, T.

2016-12-01

In this paper we consider the problem of retrieving a signal from the modulus of its Fourier transform (or other suitable transformations) and some additional information, which is also known as "Phase Retrieval" problem. The problem arises in many areas of applied Sciences such as optics, electron microscopy, antennas, and crystallography. In particular, we introduce a new approach, based on power inflation and tunneling, allowing an increased robustness with respect to the possible occurrence of false solutions. Preliminary results are presented for the simple yet relevant case of one-dimensional arrays and noisy data.

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.

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.

Robust Features Of Surface Electromyography Signal

NASA Astrophysics Data System (ADS)

Sabri, M. I.; Miskon, M. F.; Yaacob, M. R.

2013-12-01

Nowadays, application of robotics in human life has been explored widely. Robotics exoskeleton system are one of drastically areas in recent robotic research that shows mimic impact in human life. These system have been developed significantly to be used for human power augmentation, robotics rehabilitation, human power assist, and haptic interaction in virtual reality. This paper focus on solving challenges in problem using neural signals and extracting human intent. Commonly, surface electromyography signal (sEMG) are used in order to control human intent for application exoskeleton robot. But the problem lies on difficulty of pattern recognition of the sEMG features due to high noises which are electrode and cable motion artifact, electrode noise, dermic noise, alternating current power line interface, and other noise came from electronic instrument. The main objective in this paper is to study the best features of electromyography in term of time domain (statistical analysis) and frequency domain (Fast Fourier Transform).The secondary objectives is to map the relationship between torque and best features of muscle unit activation potential (MaxPS and RMS) of biceps brachii. This project scope use primary data of 2 male sample subject which using same dominant hand (right handed), age between 20-27 years old, muscle diameter 32cm to 35cm and using single channel muscle (biceps brachii muscle). The experiment conduct 2 times repeated task of contraction and relaxation of biceps brachii when lifting different load from no load to 3kg with ascending 1kg The result shows that Fast Fourier Transform maximum power spectrum (MaxPS) has less error than mean value of reading compare to root mean square (RMS) value. Thus, Fast Fourier Transform maximum power spectrum (MaxPS) show the linear relationship against torque experience by elbow joint to lift different load. As the conclusion, the best features is MaxPS because it has the lowest error than other features and show the linear relationship with torque experience by elbow joint to lift different load.

An improved model for whole genome phylogenetic analysis by Fourier transform.

PubMed

Yin, Changchuan; Yau, Stephen S-T

2015-10-07

DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees and demonstrates that the improved DFT dissimilarity measure is an efficient and effective similarity measure of DNA sequences. Due to its high efficiency and accuracy, the proposed DFT similarity measure is successfully applied on phylogenetic analysis for individual genes and large whole bacterial genomes. Copyright © 2015 Elsevier Ltd. All rights reserved.

The fractional Fourier transform and applications

NASA Technical Reports Server (NTRS)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

The τq-Fourier transform: Covariance and uniqueness

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-05-01

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

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.

The effect of a hot, spherical scattering cloud on quasi-periodic oscillation behavior

NASA Astrophysics Data System (ADS)

Bussard, R. W.; Weisskopf, M. C.; Elsner, R. F.; Shibazaki, N.

1988-04-01

A Monte Carlo technique is used to investigate the effects of a hot electron scattering cloud surrounding a time-dependent X-ray source. Results are presented for the time-averaged emergent energy spectra and the mean residence time in the cloud as a function of energy. Moreover, after Fourier transforming the scattering Green's function, it is shown how the cloud affects both the observed power spectrum of a time-dependent source and the cross spectrum (Fourier transform of a cross correlation between energy bands). It is found that the power spectra intrinsic to the source are related to those observed by a relatively simple frequency-dependent multiplicative factor (a transmission function). The cloud can severely attenuate high frequencies in the power spectra, depending on optical depth, and, at lower frequencies, the transmission function has roughly a Lorentzian shape. It is also found that if the intrinsic energy spectrum is constant in time, the phase of the cross spectrum is determined entirely by scattering. Finally, the implications of the results for studies of the X-ray quasi-periodic oscillators are discussed.

A blind transform based approach for the detection of isolated astrophysical pulses

NASA Astrophysics Data System (ADS)

Alkhweldi, Marwan; Schmid, Natalia A.; Prestage, Richard M.

2017-06-01

This paper presents a blind algorithm for the automatic detection of isolated astrophysical pulses. The detection algorithm is applied to spectrograms (also known as "filter bank data" or "the (t,f) plane"). The detection algorithm comprises a sequence of three steps: (1) a Radon transform is applied to the spectrogram, (2) a Fourier transform is applied to each projection parametrized by an angle, and the total power in each projection is calculated, and (3) the total power of all projections above 90° is compared to the total power of all projections below 90° and a decision in favor of an astrophysical pulse present or absent is made. Once a pulse is detected, its Dispersion Measure (DM) is estimated by fitting an analytically developed expression for a transformed spectrogram containing a pulse, with varying value of DM, to the actual data. The performance of the proposed algorithm is numerically analyzed.

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

Quaternion-valued single-phase model for three-phase power system

NASA Astrophysics Data System (ADS)

Gou, Xiaoming; Liu, Zhiwen; Liu, Wei; Xu, Yougen; Wang, Jiabin

2018-03-01

In this work, a quaternion-valued model is proposed in lieu of the Clarke's α, β transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion detection in three-phase power systems. In particular, the proposed model maps all the harmonic frequencies into frequencies in the quaternion domain, while the Clarke's transformation-based methods will fail to detect the zero sequence voltages. Based on the quaternion-valued model, the Fourier transform, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are presented as examples to detect harmonic distortion. Simulations are provided to demonstrate the potentials of this new modeling method.

Electromagnetic pulse propagation in dispersive planar dielectrics.

PubMed

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

1989-01-01

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

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

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

Improved ion optics for introduction of ions into a 9.4-T Fourier transform ion cyclotron resonance mass spectrometer

DOE PAGES

Chen, Yu; Leach, Franklin E.; Kaiser, Nathan K.; ...

2015-01-19

Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry provides unparalleled mass accuracy and resolving power.[1],[2] With electrospray ionization (ESI), ions are typically transferred into the mass spectrometer through a skimmer, which serves as a conductance-limiting orifice. However, the skimmer allows only a small fraction of incoming ions to enter the mass spectrometer. An ion funnel, originally developed by Smith and coworkers at Pacific Northwest National Laboratory (PNNL)[3-5] provides much more efficient ion focusing and transfer. The large entrance aperture of the ion funnel allows almost all ions emanating from a heated capillary to be efficiently captured and transferred, resulting inmore » nearly lossless transmission.« less

A Fourier transform spectrometer for site testing at Dome A

NASA Astrophysics Data System (ADS)

Li, Xin-Xing; Paine, Scott; Yao, Qi-Jun; Shi, Sheng-Cai; Matsuo, Hiroshi; Yang, Ji; Zhang, Qi-Zhou

2009-07-01

Observations in tera-hertz astronomy can only be done at a site with good atmospheric transmission at millimeter and submillimeter wavelengths. With extremely dry weather and calm atmosphere resulted by high altitude and cold temperature, Dome A (or Dome Argus), Antarctica, is possibly the best site on this earth for THz astronomy. To evaluate the site condition there, we are constructing a Fourier Transform Spectrometer (FTS) based on Martin-Puplett interferometer to measure the atmospheric transmission in the frequency range of 0.75~15THz. The whole FTS system is designed for unattended and outdoor (temperatures even below -70 degrees Celsius) operation. Its total power consumption is estimated to be approximately 200W. This contribution will give a brief overview of this FTS development.

Concerning the Spatial Heterodyne Spectrometer

DOE PAGES

Lenzner, Matthias; Diels, Jean -Claude

2016-01-22

A modified Spatial Heterodyne Spectrometer (SHS) is used for measuring atomic emission spectra with high resolution. This device is basically a Fourier Transform Spectrometer, but the Fourier transform is taken in the directions perpendicular to the optical propagation and heterodyned around one preset wavelength. In recent descriptions of this device, one specific phenomenon - the tilt of the energy front of wave packets when diffracted from a grating - was neglected. This led to an overestimate of the resolving power of this spectrograph, especially in situations when the coherence length of the radiation under test is in the order ofmore » the effective aperture of the device. In conclusion, the limits of usability are shown here together with some measurements of known spectral lines.« less

A study of sound generation in subsonic rotors, volume 2

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

PubMed

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)

NASA Technical Reports Server (NTRS)

Sromovsky, L. A.

2002-01-01

This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).

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.

CF2 Detection in Radio-Frequency Ar/CHF3 Plasmas by Fourier Transform Infrared Spectroscopy

NASA Technical Reports Server (NTRS)

Kim, J. S.; Rao, M. V. V. S.; Cappelli, M. A.; Sharma, S. P.

1999-01-01

CFx radicals, in particular CF2, are instrumental in anisotropic etching of SiO2. In order to optimize the CFx radical population in a given process environment, it is imperative that we understand their production mechanism. Towards this goal, we have conducted a series of quantitative measurements of CF2 radicals in low pressure RF plasmas similar to those used in SiO2 etching. In this study, we present preliminary results for Ar/CHF3 plasmas operating at pressures ranging from 10-50 mTorr and powers ranging from 100-500 W in the GEC reference cell, modified for inductive (transformer) coupling. Fourier transform infrared (FTIR) spectroscop) is used to observe the absorption features of the CF2 radical in the 1114 cm-1 and 1096 cm-1 spectral regions. The FTIR spectrometer is equipped with a high-sensitivity mercury cadmium telluride (MCT) detector and has afixed resolution of 0.125 cm- 1. The CF2 concentrations are measured for a range of operating pressures and discharge power levels, and are compared to measurements of the relative CF2 concentrations made by mass spectrometry using the method of appearance potential for radical selectivity.

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.

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

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 prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

PubMed

Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

2015-09-01

A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

nMoldyn: a program package for a neutron scattering oriented analysis of molecular dynamics simulations.

PubMed

Róg, T; Murzyn, K; Hinsen, K; Kneller, G R

2003-04-15

We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191-214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high-level language, Python, and of modern object-oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean-square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 657-667, 2003

Compact Microwave Fourier Spectrum Analyzer

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry

2009-01-01

A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.

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

PubMed

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

2015-06-01

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

Fourier 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.

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.

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.

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)

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.

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 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.

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.

Effects of data gaps on Fourier Analysis

NASA Astrophysics Data System (ADS)

Negrea, Catalin; Munteanu, Costel; Echim, Marius

2014-05-01

Fourier Analysis is a vital and widely used tool in all branches of science that require advanced data processing. The method is often used via the Fast Fourier Transform (FFT) implementation readily available in most programming languages. This is a valid approach for data sets with equally spaced data points and no gaps. Such conditions are not always met in real situations where corrections and adjustments to the method are needed. We investigate the intrinsic limitations of four such methods when data gaps are present: 1) linear interpolations and FFT, 2) a direct implementation of the Discrete Fourier Transform, 3) a Z-Transform and 4) the Lomb-Scargle algorithm. Theoretical analysis tools can provide an insight as to the likely problems of such methods and we discuss the likely modifications to the computed spectra. Also, a time series with no data gaps and a constant sampling frequency is altered by introducing several gap configurations and the resulting spectra with the four methods are compared to highlight changes with respect to the original spectrum. Effects on the amplitude and phase of the resulting power spectral densities are analyzed for non-uniformly sampled solar wind data provided by the Venus Express spacecraft. Phase effects are also studied in the context of a sliding window approach. Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM, and a grant of the Romanian Ministry of National Education, CNCS - UEFISCDI, project number PN-II-ID-PCE-2012-4-0418.

Understanding Why Researchers Should Use Synchrotron-Enhanced FTIR Instead of Traditional FTIR

ERIC Educational Resources Information Center

Stem, Michelle R.

2008-01-01

A synchrotron-enhanced Fourier transform infrared (SR-FTIR) specializes in combining the tremendous power, brightness, intensity, focusability, and tunability of the photons radiated by a synchrotron with FTIR ability to research the vibrational properties of the lighter elements (i.e., C, N, O, etc.). Infrared (IR) wavelengths correspond to the…

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

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

PubMed

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

2011-03-01

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

Propagation characteristics of optical fiber structures with arbitrary shape and index variation

NASA Technical Reports Server (NTRS)

Manshadi, F.

1990-01-01

The application of the scalar wave-fast Fourier transform (SW-FFT) technique to the computation of the propagation characteristics of some complex optical fiber structures is presented. The SW-FFT technique is based on the numerical solution of the scalar wave equation by a forward-marching fast Fourier transform method. This solution yields the spatial configuration of the fields as well as its modal characteristics in and around the guiding structure. The following are treated by the SW-FFT method: analysis of coupled optical fibers and computation of their odd and even modes and coupling length; the solution of tapered optical waveguides (transitions) and the study of the effect of the slope of the taper on mode conversion; and the analysis of branching optical fibers and demonstration of their mode-filtering and/or power-dividing properties.

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.

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.

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

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)

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

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.

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

[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.

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.

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

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.

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.

A Direction Finding Method with A 3-D Array Based on Aperture Synthesis

NASA Astrophysics Data System (ADS)

Li, Shiwen; Chen, Liangbing; Gao, Zhaozhao; Ma, Wenfeng

2018-01-01

Direction finding for electronic warfare application should provide a wider field of view as possible. But the maximum unambiguous field of view for conventional direction finding methods is a hemisphere. It cannot distinguish the direction of arrival of the signals from the back lobe of the array. In this paper, a full 3-D direction finding method based on aperture synthesis radiometry is proposed. The model of the direction finding system is illustrated, and the fundamentals are presented. The relationship between the outputs of the measurements of a 3-D array and the 3-D power distribution of the point sources can be represented by a 3-D Fourier transform, and then the 3-D power distribution of the point sources can be reconstructed by an inverse 3-D Fourier transform. And in order to display the 3-D power distribution of the point sources conveniently, the whole spherical distribution is represented by two 2-D circular distribution images, one of which is for the upper hemisphere, and the other is for the lower hemisphere. Then a numeric simulation is designed and conducted to demonstrate the feasibility of the method. The results show that the method can estimate the arbitrary direction of arrival of the signals in the 3-D space correctly.

Swept sine testing of rotor-bearing system for damping estimation

NASA Astrophysics Data System (ADS)

Chandra, N. Harish; Sekhar, A. S.

2014-01-01

Many types of rotating components commonly operate above the first or second critical speed and they are subjected to run-ups and shutdowns frequently. The present study focuses on developing FRF of rotor bearing systems for damping estimation from swept-sine excitation. The principle of active vibration control states that with increase in angular acceleration, the amplitude of vibration due to unbalance will reduce and the FRF envelope will shift towards the right (or higher frequency). The frequency response function (FRF) estimated by tracking filters or Co-Quad analyzers was proved to induce an error into the FRF estimate. Using Fast Fourier Transform (FFT) algorithm and stationary wavelet transform (SWT) decomposition FRF distortion can be reduced. To obtain a theoretical clarity, the shifting of FRF envelope phenomenon is incorporated into conventional FRF expressions and validation is performed with the FRF estimated using the Fourier Transform approach. The half-power bandwidth method is employed to extract damping ratios from the FRF estimates. While deriving half-power points for both types of responses (acceleration and displacement), damping ratio (ζ) is estimated with different approximations like classical definition (neglecting damping ratio of order higher than 2), third order (neglecting damping ratios with order higher than 4) and exact (no assumptions on damping ratio). The use of stationary wavelet transform to denoise the noise corrupted FRF data is explained. Finally, experiments are performed on a test rotor excited with different sweep rates to estimate the damping ratio.

[FREQUENCY-TEMPORAL STRUCTURE OF HUMAN ELECTROENCEPHALOGRAM IN THE CONDITION OF ARTIFICIAL HYPOGRAVITY: DRY IMMERSION MODEL].

PubMed

Kuznetsova, G D; Gabova, A V; Lazarev, I E; Obukhov, Iu V; Obukhov, K Iu; Morozov, A A; Kulikov, M A; Shchatskova, A B; Vasil'eva, O N; Tomilovskaia, E S

2015-01-01

Frequency-temporal electroencephalogram (EEG) reactions to hypogravity were studied in 7 male subjects at the age of 20 to 27 years. The experiment was conducted using dry immersion (DI) as the best known method of simulating the space microgravity effects on the Earth. This hypogravity model reproduces hypokinesia, i.e. the weight-bearing and mechanic load removal, which is typical of microgravity. EEG was recorded by Neuroscan-2 (Compumedics) before the experiment (baseline data) and at the end of day 2 in DI. Comparative analysis of the EEG frequency-temporal structure was performed with the use of 2 techniques: Fourier transform and modified wavelet analysis. The Fourier transform elicited that after 2 days in DI the main shifts occurring to the EEG spectral composition are a decline in the alpha power and a slight though reliable growth of theta power. Similar frequency shifts were detected in the same records analyzed using the wavelet transform. According to wavelet analysis, during DI shifts in EEG frequency spectrum are accompanied by frequency desorganization of the EEG dominant rhythm and gross impairment of total stability of the electrical activity with time. Wavelet transform provides an opportunity to quantify changes in the frequency-temporal structure of the electrical activity of the brain. Quantitative evidence of frequency desorganization and temporal instability of EEG wavelet spectrograms may be the key to the understanding of mechanisms that drive functional disorders in the brain cortex in the conditions of hypogravity.

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.

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.

Using Extractive FTIR to Measure N2O from Medium Heavy Duty Vehicles Powered with Diesel and Biodiesel Fuels

EPA Science Inventory

A Fourier Transform Infrared (FTIR) spectrometer was used to measure N2O and other pollutant gases during an evaluation of two medium heavy-duty diesel trucks equipped with a Diesel Particulate Filter (DPF). The emissions of these trucks were characterized under a variety of oper...

Optical Characterization of IV-VI Mid-Infrared VCSEL

DTIC Science & Technology

2002-01-01

vertical cavity surface emitting laser ( VCSEL ). A power...il quantum well (QW) devices [5], there has little progress until recently in developing mid-IR vertical cavity surface emitting laser ( VCSEL ). This...structures and PbSrSe thin films were grown on Bat; (111) substrates by molecular beam epitaxy ( MBE ) and characterized by Fourier transform infi-ared

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

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.

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.

Astigmatism error modification for absolute shape reconstruction using Fourier transform method

NASA Astrophysics Data System (ADS)

He, Yuhang; Li, Qiang; Gao, Bo; Liu, Ang; Xu, Kaiyuan; Wei, Xiaohong; Chai, Liqun

2014-12-01

A method is proposed to modify astigmatism errors in absolute shape reconstruction of optical plane using Fourier transform method. If a transmission and reflection flat are used in an absolute test, two translation measurements lead to obtain the absolute shapes by making use of the characteristic relationship between the differential and original shapes in spatial frequency domain. However, because the translation device cannot guarantee the test and reference flats rigidly parallel to each other after the translations, a tilt error exists in the obtained differential data, which caused power and astigmatism errors in the reconstructed shapes. In order to modify the astigmatism errors, a rotation measurement is added. Based on the rotation invariability of the form of Zernike polynomial in circular domain, the astigmatism terms are calculated by solving polynomial coefficient equations related to the rotation differential data, and subsequently the astigmatism terms including error are modified. Computer simulation proves the validity of the proposed method.

Application of Fourier-transform ion cyclotron resonance mass spectrometry to metabolic profiling and metabolite identification.

PubMed

Ohta, Daisaku; Kanaya, Shigehiko; Suzuki, Hideyuki

2010-02-01

Metabolomics, as an essential part of genomics studies, intends holistic understanding of metabolic networks through simultaneous analysis of a myriad of both known and unknown metabolites occurring in living organisms. The initial stage of metabolomics was designed for the reproducible analyses of known metabolites based on their comparison to available authentic compounds. Such metabolomics platforms were mostly based on mass spectrometry (MS) technologies enabled by a combination of different ionization methods together with a variety of separation steps including LC, GC, and CE. Among these, Fourier-transform ion cyclotron resonance MS (FT-ICR/MS) is distinguished from other MS technologies by its ultrahigh resolution power in mass to charge ratio (m/z). The potential of FT-ICR/MS as a distinctive metabolomics tool has been demonstrated in nontargeted metabolic profiling and functional characterization of novel genes. Here, we discuss both the advantages and difficulties encountered in the FT-ICR/MS metabolomics studies.

Diffractive optical elements for transformation of modes in lasers

DOEpatents

Sridharan, Arun K.; Pax, Paul H.; Heebner, John E.; Drachenberg, Derrek R.; Armstrong, James P.; Dawson, Jay W.

2015-09-01

Spatial mode conversion modules are described, with the capability of efficiently transforming a given optical beam profile, at one plane in space into another well-defined optical beam profile at a different plane in space, whose detailed spatial features and symmetry properties can, in general, differ significantly. The modules are comprised of passive, high-efficiency, low-loss diffractive optical elements, combined with Fourier transform optics. Design rules are described that employ phase retrieval techniques and associated algorithms to determine the necessary profiles of the diffractive optical components. System augmentations are described that utilize real-time adaptive optical techniques for enhanced performance as well as power scaling.

Diffractive optical elements for transformation of modes in lasers

DOEpatents

Sridharan, Arun K; Pax, Paul H; Heebner, John E; Drachenberg, Derrek R.; Armstrong, James P.; Dawson, Jay W.

2016-06-21

Spatial mode conversion modules are described, with the capability of efficiently transforming a given optical beam profile, at one plane in space into another well-defined optical beam profile at a different plane in space, whose detailed spatial features and symmetry properties can, in general, differ significantly. The modules are comprised of passive, high-efficiency, low-loss diffractive optical elements, combined with Fourier transform optics. Design rules are described that employ phase retrieval techniques and associated algorithms to determine the necessary profiles of the diffractive optical components. System augmentations are described that utilize real-time adaptive optical techniques for enhanced performance as well as power scaling.

Fourier Transformation Theory for Averaged Functions, with Application to Very Long Baseline Radio Interferometry.

DTIC Science & Technology

1981-02-01

primary parameters affecting the SNR. For an earth-based interferometer, the physical aperture may usually be constructed adequately large to keep the...bandwidth Av cent--.c. on vo0 by an interferometer with frequency characteristic F(v) and primary power pattern G(s-s ) (defined as the product of the...infinitely narrow beam for the primary power pattern, G(g- 0 ) = (;-S )] we have where we have assumed a flat frequency response and included as a

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

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1981-01-01

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

Fourier 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.

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

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.

AN OPTIMIZED 64X64 POINT TWO-DIMENSIONAL FAST FOURIER TRANSFORM

NASA Technical Reports Server (NTRS)

Miko, J.

1994-01-01

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

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.

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.

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.

The Analysis of Eigenstates of a Few Generalized Quantum Baker’s Maps Using Hadamard and Related Transforms

NASA Astrophysics Data System (ADS)

Meenakshisundaram, N.

Application of the Hadamard and related transforms on a few generalized quantum baker’s maps have been studied. Effectiveness of the Hadamard transform and a new transform which combines the Fourier and the Hadamard transforms, for simplifying the eigenstates or resonances of the quantization of a few generalized baker’s map namely tetradic baker and lazy baker’s map when the Hilbert space dimension is power of 2 has been done by comparing the participation ratios in the transformed basis with respect to the position basis. Several special family of states based on their maximal compression in either Hadamard transform or the new transform are identified and they are related to the ubiquitous Thue-Morse and allied sequences. Evidence is provided that these special family of states as well as average over all eigenstates exhibits multifractal nature.

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.

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.

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.

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.

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

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.

Fourier transform spectroscopy for future planetary missions

NASA Astrophysics Data System (ADS)

Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor

2015-11-01

Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.

Rapid-scan Fourier-transform coherent anti-Stokes Raman scattering spectroscopy with heterodyne detection.

PubMed

Hiramatsu, Kotaro; Luo, Yizhi; Ideguchi, Takuro; Goda, Keisuke

2017-11-01

High-speed Raman spectroscopy has become increasingly important for analyzing chemical dynamics in real time. To address the need, rapid-scan Fourier-transform coherent anti-Stokes Raman scattering (FT-CARS) spectroscopy has been developed to realize broadband CARS measurements at a scan rate of more than 20,000 scans/s. However, the detection sensitivity of FT-CARS spectroscopy is inherently low due to the limited number of photons detected during each scan. In this Letter, we show our experimental demonstration of enhanced sensitivity in rapid-scan FT-CARS spectroscopy by heterodyne detection. Specifically, we implemented heterodyne detection by superposing the CARS electric field with an external local oscillator (LO) for their interference. The CARS signal was amplified by simply increasing the power of the LO without the need for increasing the incident power onto the sample. Consequently, we achieved enhancement in signal intensity and the signal-to-noise ratio by factors of 39 and 5, respectively, compared to FT-CARS spectroscopy with homodyne detection. The sensitivity-improved rapid-scan FT-CARS spectroscopy is expected to enable the sensitive real-time observation of chemical dynamics in a broad range of settings, such as combustion engines and live biological cells.

Fourier Transform Infrared Spectroscopy of CF4 on the GEC Reference Cell

NASA Technical Reports Server (NTRS)

Rao, M. V. V. S.; Sharma, S. P.; Meyyappan, M.; Cruden, Brett A.; Arnold, Jim (Technical Monitor)

2001-01-01

Fourier Transform Infrared Spectroscopy (FTIR) has been used to characterize inductively coupled CF4 plasmas in a GEC Reference Cell in-situ In examining these FTIR spectra, several assumptions and approximations of FTIR analysis are addressed. This includes the density dependence of cross-sections, non-linear effects in the addition of overlapping bands and the effect of spatial variations in density and temperature, This analysis demonstrates that temperatures extracted from MR spectra may provide a poor estimate of the true neutral plasma temperature. The FTIR spectra are dominated by unreacted CF, accounting for 40-60% of the gas products. The amount of CF4 consumption is found to have a marked dependence on power, and is nearly independent of pressure in the range of 10-50 mtorr. Small amounts of C2F6 are observed at low power. Also observed are etching products from the quartz window SiF4 COF2 and CO which occur in approximately equal ratios and together account for less than 10% of the gas. The concentrations of these species are nearly independent of pressure. CFx radicals are below the detection limit of this apparatus (approx. 1012/cc).

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.

Optimal Padding for the Two-Dimensional Fast Fourier Transform

NASA Technical Reports Server (NTRS)

Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.

2011-01-01

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

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

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...

Fourier transform (FT)-artifacts and power-function resolution filter in Fourier transform mass spectrometry.

PubMed

Kanawati, Basem; Bader, Theresa M; Wanczek, Karl-Peter; Li, Yan; Schmitt-Kopplin, Philippe

2017-10-15

Peak picking algorithms in mass spectrometry face the challenge of picking the correct signals from a mass spectrum. In some cases signal wiggles (side lobes) are also chosen in the produced mass list as if they were real signals. Constraints which are defined in such algorithms do not always guarantee wiggle-free accurate mass list generation out of raw mass spectra. This problem intensifies with acquisitions, which are accompanied by longer transients. Thus, the problem represents a contemporary issue, which propagates with modern high-memory digitizers and exists in both MS and MS/MS spectra. A solariX FTMS mass spectrometer with an Infinity ICR cell (Bruker Daltonics, Bremen, Germany) coupled to a 12 Tesla magnet (Magnex, UK) was used for the experimental study. Time-domain transients of several different data point lengths 512k, 1M, 2M, 4M, 8M were obtained and were Fourier-transformed to obtain frequency spectra which show the effect of the transient truncation on sinc wiggle developments in FT-ICR-MS. MATLAB simulations were also performed to investigate the origin of the Fourier transform (FT)-artifacts. A new filter has been developed to identify and remove FT-artifacts (sinc side lobes) from both frequency and mass spectra. The newly developed filter is based on distinguishing between the FWHM of the correct frequency/mass signals and the FWHM of their corresponding wiggles. The filter draws a reliable confidence limit of resolution range, within which a correct frequency/mass signal is identified. The filter is applicable over a wide mass range of metabolic interest (100-1200 amu). The origin of FT-artifacts due to time-domain transient truncations was thoroughly investigated both experimentally and by simulations in this study. A new solution for this problem with automatic recognition and elimination of these FT-artifacts (side lobes/wiggles) is provided, which is independent of any intensity thresholds, magnetic field strengths and time-domain transient lengths. Copyright © 2017 John Wiley & Sons, Ltd.

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.

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.

[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 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.

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.

Design and Implementation of a High-Power Resonant DC-DC Converter Module for a Reduced-Scale Prototype Integrated Power System

DTIC Science & Technology

2001-09-01

damping RC network . The filter was designed to have a pole pair (~450 Hz) above the 360 Hz ripple of the six-pulse rectified DC supply but well below the...Circuit With Input Filtering Included. The damping network was designed using the guidance provided in reference [24] and its function is to lower the...converter as a linear network and estimated the spectrum envelope by multiplying the Fourier transform of the current waveform by the transfer

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...

Reduction and coding of synthetic aperture radar data with Fourier transforms

NASA Technical Reports Server (NTRS)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Algorithm for Wavefront Sensing Using an Extended Scene

NASA Technical Reports Server (NTRS)

Sidick, Erkin; Green, Joseph; Ohara, Catherine

2008-01-01

A recently conceived algorithm for processing image data acquired by a Shack-Hartmann (SH) wavefront sensor is not subject to the restriction, previously applicable in SH wavefront sensing, that the image be formed from a distant star or other equivalent of a point light source. That is to say, the image could be of an extended scene. (One still has the option of using a point source.) The algorithm can be implemented in commercially available software on ordinary computers. The steps of the algorithm are the following: 1. Suppose that the image comprises M sub-images. Determine the x,y Cartesian coordinates of the centers of these sub-images and store them in a 2xM matrix. 2. Within each sub-image, choose an NxN-pixel cell centered at the coordinates determined in step 1. For the ith sub-image, let this cell be denoted as si(x,y). Let the cell of another subimage (preferably near the center of the whole extended-scene image) be designated a reference cell, denoted r(x,y). 3. Calculate the fast Fourier transforms of the sub-sub-images in the central NxN portions (where N < N and both are preferably powers of 2) of r(x,y) and si(x,y). 4. Multiply the two transforms to obtain a cross-correlation function Ci(u,v), in the Fourier domain. Then let the phase of Ci(u, v) constitute a phase function, phi(u,v). 5. Fit u and v slopes to phi (u,v) over a small u,v subdomain. 6. Compute the fast Fourier transform, Si(u,v) of the full NxN cell si(x,y). Multiply this transform by the u and phase slopes obtained in step 4. Then compute the inverse fast Fourier transform of the product. 7. Repeat steps 4 through 6 in an iteration loop, cumulating the u and slopes, until a maximum iteration number is reached or the change in image shift becomes smaller than a predetermined tolerance. 8. Repeat steps 4 through 7 for the cells of all other sub-images.

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)

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.

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.

Time-frequency analysis of electric motors

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

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

1995-12-31

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

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...

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.

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.

Induction motors airgap-eccentricity detection through the discrete wavelet transform of the apparent power signal under non-stationary operating conditions.

PubMed

Yahia, K; Cardoso, A J M; Ghoggal, A; Zouzou, S E

2014-03-01

Fast Fourier transform (FFT) analysis has been successfully used for fault diagnosis in induction machines. However, this method does not always provide good results for the cases of load torque, speed and voltages variation, leading to a variation of the motor-slip and the consequent FFT problems that appear due to the non-stationary nature of the involved signals. In this paper, the discrete wavelet transform (DWT) of the apparent-power signal for the airgap-eccentricity fault detection in three-phase induction motors is presented in order to overcome the above FFT problems. The proposed method is based on the decomposition of the apparent-power signal from which wavelet approximation and detail coefficients are extracted. The energy evaluation of a known bandwidth permits to define a fault severity factor (FSF). Simulation as well as experimental results are provided to illustrate the effectiveness and accuracy of the proposed method presented even for the case of load torque variations. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

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...

Fourier Transform Spectroscopy of two trace gases namely Methane and Carbon monoxide for planetary and atmospheric research application

NASA Astrophysics Data System (ADS)

Hashemi, R.; Dudaryonok, A. S.; Lavrentieva, N. N.; Vandaele, A. C.; Vander Auwera, J.; Tyuterev, AV Nikitin G., VI; Sung, K.; Smith, M. A. H.; Devi, V. M.; Predoi-Cross, A.

2017-02-01

Two atmospheric trace gases, namely methane and carbon monoxide have been considered in this study. Fourier transform absorption spectra of the 2-0 band of 12C16O mixed with CO2 have been recorded at total pressures from 156 to 1212 hPa and at 4 different temperatures between 240 K and 283 K. CO2 pressure-induced line broadening and line shift coefficients, and the associated temperature dependence have been measured in an multi-spectrum non-linear least squares analysis using Voigt profiles with an asymmetric profile due to line mixing. The measured CO2-broadening and CO2-shift parameters were compared with theoretical values, calculated by collaborators. In addition, the CO2-broadening and shift coefficients have been calculated for individual temperatures using the Exponential Power Gap (EPG) semi-empirical method. We also discuss the retrieved line shape parameters for Methane transitions in the spectral range known as the Methane Octad. We used high resolution spectra of pure methane and of dilute mixtures of methane in dry air, recorded with high signal to noise ratio at temperatures between 148 K and room temperature using the Bruker IFS 125 HR Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory, Pasadena, California. Theoretical calculations for line parameters have been performed and the results are compared with the previously published values and with the line parameters available in the GEISA2015 [1] and HITRAN2012 [2] databases.

RANKING TEM CAMERAS BY THEIR RESPONSE TO ELECTRON SHOT NOISE

PubMed Central

Grob, Patricia; Bean, Derek; Typke, Dieter; Li, Xueming; Nogales, Eva; Glaeser, Robert M.

2013-01-01

We demonstrate two ways in which the Fourier transforms of images that consist solely of randomly distributed electrons (shot noise) can be used to compare the relative performance of different electronic cameras. The principle is to determine how closely the Fourier transform of a given image does, or does not, approach that of an image produced by an ideal camera, i.e. one for which single-electron events are modeled as Kronecker delta functions located at the same pixels where the electrons were incident on the camera. Experimentally, the average width of the single-electron response is characterized by fitting a single Lorentzian function to the azimuthally averaged amplitude of the Fourier transform. The reciprocal of the spatial frequency at which the Lorentzian function falls to a value of 0.5 provides an estimate of the number of pixels at which the corresponding line-spread function falls to a value of 1/e. In addition, the excess noise due to stochastic variations in the magnitude of the response of the camera (for single-electron events) is characterized by the amount to which the appropriately normalized power spectrum does, or does not, exceed the total number of electrons in the image. These simple measurements provide an easy way to evaluate the relative performance of different cameras. To illustrate this point we present data for three different types of scintillator-coupled camera plus a silicon-pixel (direct detection) camera. PMID:23747527

High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited].

PubMed

Hayashi, Shin'ichiro; Nawata, Koji; Sakai, Hiroshi; Taira, Takunori; Minamide, Hiroaki; Kawase, Kodo

2012-01-30

We report on the development of a high-peak-power, single-longitudinal-mode and tunable injection-seeded terahertz-wave parametric generator using MgO:LiNbO3, which operates at room temperature. The high peak power (> 120 W) is enough to allow easy detection by commercial and calibrated pyroelectric detectors, and the spectral resolution (< 10 GHz) is the Fourier transform limit of the sub-nanosecond terahertz-wave pulse. The tunability (1.2-2.8 THz) and the small footprint size (A3 paper, 29.7 × 42 cm) are suitable for a variety of applications.

Supercritical Fluid Chromatography/Fourier Transform Infrared Spectroscopy Of Food Components

NASA Astrophysics Data System (ADS)

Calvey, Elizabeth M.; Page, Samuel W.; Taylor, Larry T.

1989-12-01

Supercritical fluid (SF) technologies are being investigated extensively for applications in food processing. The number of SF-related patents issued testifies to the level of interest. Among the properties of materials at temperatures and pressures above their critical points (supercritical fluids) is density-dependent solvating power. Supercritical CO2 is of particular interest to the food industry because of its low critical temperature (31.3°C) and low toxicity. Many of the components in food matrices react or degrade at elevated temperatures and may be adversely affected by high temperature extractions. Likewise, these components may not be amenable to GC analyses. Our SF research has been in the development of methods employing supercritical fluid chromatography (SFC) and extraction (SFE) coupled to a Fourier transform infrared (FT-IR) spectrometer to investigate food composition. The effects of processing techniques on the isomeric fatty acid content of edible oils and the analysis of lipid oxidation products using SFC/FT-IR with a flow-cell interface are described.

Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

Two-Dimensional Fourier Transform Electronic Spectroscopy of Peridinin and Peridinin Analogs

NASA Astrophysics Data System (ADS)

Khosravi, Soroush; Bishop, Michael; Obaid, Razib; Whitelock, Hope; Carroll, Ann Marie; Lafountain, Amy; Frank, Harry; Beck, Warren; Gibson, George; Berrah, Nora

2016-05-01

The peridinin chlorophyll- a protein (PCP) is a light harvesting complex in dinoflagellates that exhibits a carotenoid-to-chlorophyll (Chl) a excitation energy transfer (EET) efficiency of 85-95%. Unlike most light harvesting complexes, where the number of carotenoids is less than Chl, each subunit of PCP contains eight tightly-packed peridinins surrounding two Chl a molecules. The unusual solvent polarity dependence of the lowest excited S1 state of peridinin suggests the presence of an intramolecular charge-transfer (ICT) state. The nature of the ICT state, its coupling to the S1 of peridinin, and whether it enables the high EET efficiency is still unclear. Two-dimensional electronic Fourier transform spectroscopy (2DES) is a powerful method capable of examining these issues. The present work examines the ICT state of peridinin and peridinin analogs that have diminished ICT character. 2DES data adding new insight into the spectral signatures and nature of the ICT state in peridinin will be presented. Funded by the DoE-BES, Grant No. DE-SC0012376.

Stepwise Iterative Fourier Transform: The SIFT

NASA Technical Reports Server (NTRS)

Benignus, V. A.; Benignus, G.

1975-01-01

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

Matrix-free mass spectrometric imaging using laser desorption ionisation Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Goodwin, Richard J A; Pitt, Andrew R; Harrison, David; Weidt, Stefan K; Langridge-Smith, Pat R R; Barrett, Michael P; Logan Mackay, C

2011-04-15

Mass spectrometry imaging (MSI) is a powerful tool in metabolomics and proteomics for the spatial localization and identification of pharmaceuticals, metabolites, lipids, peptides and proteins in biological tissues. However, sample preparation remains a crucial variable in obtaining the most accurate distributions. Common washing steps used to remove salts, and solvent-based matrix application, allow analyte spreading to occur. Solvent-free matrix applications can reduce this risk, but increase the possibility of ionisation bias due to matrix adhesion to tissue sections. We report here the use of matrix-free MSI using laser desorption ionisation performed on a 12 T Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. We used unprocessed tissue with no post-processing following thaw-mounting on matrix-assisted laser desorption ionisation (MALDI) indium-tin oxide (ITO) target plates. The identification and distribution of a range of phospholipids in mouse brain and kidney sections are presented and compared with previously published MALDI time-of-flight (TOF) MSI distributions. Copyright © 2011 John Wiley & Sons, Ltd.

An empirical evaluation of three vibrational spectroscopic methods for detection of aflatoxins in maize.

PubMed

Lee, Kyung-Min; Davis, Jessica; Herrman, Timothy J; Murray, Seth C; Deng, Youjun

2015-04-15

Three commercially available vibrational spectroscopic techniques, including Raman, Fourier transform near infrared reflectance (FT-NIR), and Fourier transform infrared (FTIR) were evaluated to help users determine the spectroscopic method best suitable for aflatoxin analysis in maize (Zea mays L.) grain based on their relative efficiency and predictive ability. Spectral differences of Raman and FTIR spectra were more marked and pronounced among aflatoxin contamination groups than those of FT-NIR spectra. From the observations and findings in our current and previous studies, Raman and FTIR spectroscopic methods are superior to FT-NIR method in terms of predictive power and model performance for aflatoxin analysis and they are equally effective and accurate in predicting aflatoxin concentration in maize. The present study is considered as the first attempt to assess how spectroscopic techniques with different physical processes can influence and improve accuracy and reliability for rapid screening of aflatoxin contaminated maize samples. Copyright © 2014 Elsevier Ltd. All rights reserved.

Hosting a Fourier Transform Spectrometer (FTS) on CubeSat Spacecraft Platforms for Global Measurements of Three-Dimensional Winds

NASA Astrophysics Data System (ADS)

Scott, D. K.; Neilsen, T. L.; Weston, C.; Frazier, C.; Smith, T.; Shumway, A.

2015-12-01

Global measurements of vertically-resolved atmospheric wind profiles offer the potential for improved weather forecasts and superior predictions of atmospheric wind patterns. A small-satellite constellation that uses a Fourier Transform Spectrometer (FTS) instrument onboard 12U CubeSats can provide measurements of global tropospheric wind profiles from space at a very low cost. These small satellites are called FTS CubeSats. This presentation will describe a spacecraft concept that provides a stable, robust platform to host the FTS payload. Of importance to the payload are power, data, station keeping, thermal, and accommodations that enable high spectral measurements to be made from a LEO orbit. The spacecraft concept draws on Space Dynamics Laboratory (SDL) heritage and the recent success of the Dynamic Ionosphere Cubesat Experiment (DICE) and HyperAngular Rainbow Polarimeter (HARP) missions. Working with team members, SDL built a prototype observatory (spacecraft and payload) for testing and proof of concept.

Fast neutral beam ion source coupled to a Fourier transform ion cyclotron resonance mass spectrometer

NASA Astrophysics Data System (ADS)

Hill, Nicholas C.; Limbach, Patrick A.; Shomo, Ronald E., II; Marshall, Alan G.; Appelhans, Anthony D.; Delmore, James E.

1991-11-01

The coupling of an autoneutralizing SF-6 fast ion-beam gun to a Fourier transform ion cyclotron resonance (FT/ICR) mass spectrometer is described. The fast neutral beam provides for secondary-ion-type FT/ICR mass analysis [e.g., production of abundant pseudomolecular (M+H)+ ions] of involatile samples without the need for external ion injection, since ions are formed at the entrance to the ICR ion trap. The design, construction, and testing of the hybrid instrument are described. The feasibility of the experiment (for both broadband and high-resolution FT/ICR positive-ion mass spectra) is demonstrated with tetra-butylammonium bromide and a Tylenol■ sample. The ability to analyze high molecular weight polymers with high mass resolution is demonstrated for Teflon■. All of the advantages of the fast neutral beam ion source previously demonstrated with quadrupole mass analysis are preserved, and the additional advantages of FT/ICR mass analysis (e.g., high mass resolving power, ion trapping) are retained.

Simulation of Near-Edge X-ray Absorption Fine Structure with Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

PubMed

Nascimento, Daniel R; DePrince, A Eugene

2017-07-06

An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Padé approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.

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

Is the algorithm used to process heart rate variability data clinically relevant? Analysis in male adolescents.

PubMed

Soares, Antonio Henrique Germano; Farah, Breno Quintella; Cucato, Gabriel Grizzo; Bastos-Filho, Carmelo José Albanez; Christofaro, Diego Giulliano Destro; Vanderlei, Luiz Carlos Marques; Lima, Aluísio Henrique Rodrigues de Andrade; Ritti-Dias, Raphael Mendes

2016-01-01

To analyze whether the algorithm used for the heart rate variability assessment (fast Fourier transform versus autoregressive methods) influenced its association with cardiovascular risk factors in male adolescents. This cross-sectional study included 1,152 male adolescents (aged 14 to 19 years). The low frequency, high frequency components (absolute numbers and normalized units), low frequency/high frequency ratio, and total power of heart rate variability parameters were obtained using the fast Fourier transform and autoregressive methods, while the adolescents were resting in a supine position. All heart rate variability parameters calculated from both methods were different (p<0.05). However, a low effect size (<0.1) was found for all parameters. The intra-class correlation between methods ranged from 0.96 to 0.99, whereas the variation coefficient ranged from 7.4 to 14.8%. Furthermore, waist circumference was negatively associated with high frequency, and positively associated with low frequency and sympatovagal balance (p<0.001 for both fast Fourier transform and autoregressive methods in all associations). Systolic blood pressure was negatively associated with total power and high frequency, whereas it was positively associated with low frequency and sympatovagal balance (p<0.001 for both fast Fourier transform and autoregressive methods in all associations). Body mass index was negatively associated with high frequency, while it was positively associated with low frequency and sympatovagal balance (p values ranged from <0.001 to 0.007). There are significant differences in heart rate variability parameters obtained with the fast Fourier transform and autoregressive methods in male adolescent; however, these differences are not clinically significant. Analisar se o algoritmo usado para avaliação da variabilidade da frequência cardíaca (transformada rápida de Fourier versus autoregressivo) influencia em sua associação com fatores de risco cardiovascular adolescentes do gênero masculino. Estudo transversal, que incluiu 1.152 adolescentes do gênero masculino (14 a 19 anos). Componentes de baixa e alta frequência (absolutos e unidades normalizadas), razão componente de baixa frequência/componente de alta frequência e poder total da variabilidade da frequência cardíaca foram obtidos em repouso, na posição supina, usando os métodos transformada rápida de Fourier e autorregressivo. Todos os parâmetros da variabilidade da frequência cardíaca para ambos os métodos foram diferentes (p<0,05). Entretanto, um pequeno tamanho do efeito (<0,1) foi observado para todos os parâmetros. Os coeficientes de correlação intraclasse entre os métodos variaram de 0,96 a 0,99, enquanto os coeficientes de variação foram de 7,4 a 14,8%. A circunferência abdominal foi negativamente associada com o componente de alta frequência, e positivamente associada com o componente de baixa frequência e o balanço simpatovagal (p<0,001 para a transformada rápida de Fourier e o autorregressivo em todas as associações). A pressão arterial sistólica foi negativamente associada com o poder total e o componente de alta frequência, enquanto foi positivamente associada com o componente de baixa frequência e o balanço simpatovagal (p<0,001 para a transformada rápida de Fourier e o autorregressivo em todas as associações). O índice de massa corporal foi negativamente associado com o componente de alta frequência, enquanto foi positivamente associado com o componente de baixa frequência e o balanço simpatovagal (valores de p variando de <0,001 a 0,007). Houve diferenças significantes nos parâmetros da variabilidade da frequência cardíaca obtidos com os métodos transformada rápida de Fourier e autorregressivo em adolescentes masculinos, mas essas diferenças não foram clinicamente significativas.

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

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.

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.

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.

Fourier transform power spectrum is a potential measure of tissue alignment in standard MRI: A multiple sclerosis study.

PubMed

Sharma, Shrushrita; Zhang, Yunyan

2017-01-01

Loss of tissue coherency in brain white matter is found in many neurological diseases such as multiple sclerosis (MS). While several approaches have been proposed to evaluate white matter coherency including fractional anisotropy and fiber tracking in diffusion-weighted imaging, few are available for standard magnetic resonance imaging (MRI). Here we present an image post-processing method for this purpose based on Fourier transform (FT) power spectrum. T2-weighted images were collected from 19 patients (10 relapsing-remitting and 9 secondary progressive MS) and 19 age- and gender-matched controls. Image processing steps included: computation, normalization, and thresholding of FT power spectrum; determination of tissue alignment profile and dominant alignment direction; and calculation of alignment complexity using a new measure named angular entropy. To test the validity of this method, we used a highly organized brain white matter structure, corpus callosum. Six regions of interest were examined from the left, central and right aspects of both genu and splenium. We found that the dominant orientation of each ROI derived from our method was significantly correlated with the predicted directions based on anatomy. There was greater angular entropy in patients than controls, and a trend to be greater in secondary progressive MS patients. These findings suggest that it is possible to detect tissue alignment and anisotropy using traditional MRI, which are routinely acquired in clinical practice. Analysis of FT power spectrum may become a new approach for advancing the evaluation and management of patients with MS and similar disorders. Further confirmation is warranted.

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

A wide-band, high-resolution spectrum analyzer

NASA Technical Reports Server (NTRS)

Wilck, H. C.; Quirk, M. P.; Grimm, M. J.

1985-01-01

A million-channel, 20 MHz-bandwidth, digital spectrum analyzer under evelopment for use in the SETI Sky Survey and other applications in the Deep Space Network is described. The analyzer digitizes an analog input, performs a 2(20)-point Radix-2, Fast Fourier Transform, accumulates the output power, and normalizes the output to remove frequency-dependent gain. The effective speed of the real-time hardware is 2.2 GigaFLOPS.

Monolithic liquid crystal waveguide Fourier transform spectrometer for gas species sensing

NASA Astrophysics Data System (ADS)

Chao, Tien-Hsin; Lu, Thomas T.; Davis, Scott R.; Rommel, Scott D.; Farca, George; Luey, Ben; Martin, Alan; Anderson, Michael H.

2011-04-01

Jet Propulsion Lab and Vescent Photonics Inc. and are jointly developing an innovative ultracompact (volume < 10 cm3), ultra-low power (<10-3 Watt-hours per measurement and zero power consumption when not measuring), completely non-mechanical Liquid Crystal Waveguide Fourier Transform Spectrometer (LCWFTS) that will be suitable for a variety of remote-platform, in-situ measurements. These devices are made possible by novel electro-evanescent waveguide architecture, enabling "monolithic chip-scale" Electro Optic-FTS (EO-FTS) sensors. The potential performance of these EO-FTS sensors include: i) a spectral range throughout 0.4-5 μm (25000 - 2000 cm-1), ii) high-resolution (Δλ <= 0.1 nm), iii) high-speed (< 1 ms) measurements, and iv) rugged integrated optical construction. This performance potential enables the detection and quantification of a large number of different atmospheric gases simultaneously in the same air mass and the rugged construction will enable deployment on previously inaccessible platforms. The sensor construction is also amenable for analyzing aqueous samples on remote floating or submerged platforms. We will report a proof-of-principle prototype LCWFTS sensor that has been demonstrated in the near-IR (range of 1450-1700 nm) with a 5 nm resolution. This performance is in good agreement with theoretical models, which are being used to design and build the next generation LCWFTS devices.

First Signal on the Cryogenic Fourier-Transform Ion Cyclotron Resonance Mass Spectrometer

PubMed Central

Lin, Cheng; Mathur, Raman; Aizikov, Kostantin; O'Connor, Peter B.

2009-01-01

The construction and achievement of the first signal on a cryogenic Fourier-transform ion cyclotron resonance mass spectrometer (FT-ICR-MS) are reported here, demonstrating proof-of-concept of this new instrument design. Building the FTICR cell into the cold bore of a superconducting magnet provided advantages over conventional warm bore design. At 4.2 K, the vacuum system cryopumps itself, thus removing the requirement for a large bore to achieve the desired pumping speed for maintaining base pressure. Furthermore, because the bore diameter has been reduced, the amount of magnet wire needed to achieve high field and homogeneity was also reduced, greatly decreasing the cost/Tesla of the magnet. The current instrument implements an actively shielded 14-Tesla magnet of vertical design with an external matrix assisted laser desorption/ionization (MALDI) source. The first signal was obtained by detecting the laser desorbed/ionized (LDI) C60+• ions, with the magnet at 7 Tesla, unshimmed, and the preamplifier mounted outside of the vacuum chamber at room temperature. A subsequent experiment done with the magnet at 14 Tesla and properly shimmed produced a C60 spectrum showing ∼350,000 resolving power at m/z ∼720. Increased magnetic field strength improves many FTMS performance parameters simultaneously, particularly mass resolving power and accuracy. PMID:17931882

Broadband W-band Rapid Frequency Sweep Considerations for Fourier Transform EPR.

PubMed

Strangeway, Robert A; Hyde, James S; Camenisch, Theodore G; Sidabras, Jason W; Mett, Richard R; Anderson, James R; Ratke, Joseph J; Subczynski, Witold K

2017-12-01

A multi-arm W-band (94 GHz) electron paramagnetic resonance spectrometer that incorporates a loop-gap resonator with high bandwidth is described. A goal of the instrumental development is detection of free induction decay following rapid sweep of the microwave frequency across the spectrum of a nitroxide radical at physiological temperature, which is expected to lead to a capability for Fourier transform electron paramagnetic resonance. Progress toward this goal is a theme of the paper. Because of the low Q-value of the loop-gap resonator, it was found necessary to develop a new type of automatic frequency control, which is described in an appendix. Path-length equalization, which is accomplished at the intermediate frequency of 59 GHz, is analyzed. A directional coupler is favored for separation of incident and reflected power between the bridge and the loop-gap resonator. Microwave leakage of this coupler is analyzed. An oversize waveguide with hyperbolic-cosine tapers couples the bridge to the loop-gap resonator, which results in reduced microwave power and signal loss. Benchmark sensitivity data are provided. The most extensive application of the instrument to date has been the measurement of T 1 values using pulse saturation recovery. An overview of that work is provided.

Online quench-flow electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry for elucidating kinetic and chemical enzymatic reaction mechanisms.

PubMed

Clarke, David J; Stokes, Adam A; Langridge-Smith, Pat; Mackay, C Logan

2010-03-01

We have developed an automated quench-flow microreactor which interfaces directly to an electrospray ionization (ESI) mass spectrometer. We have used this device in conjunction with ESI Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) to demonstrate the potential of this approach for studying the mechanistic details of enzyme reactions. For the model system chosen to test this device, namely, the pre-steady-state hydrolysis of p-nitrophenyl acetate by the enzyme chymotrypsin, the kinetic parameters obtained are in good agreement with those in the literature. To our knowledge, this is the first reported use of online quench-flow coupled with FTICR MS. Furthermore, we have exploited the power of FTICR MS to interrogate the quenched covalently bound enzyme intermediate using top-down fragmentation. The accurate mass capabilities of FTICR MS permitted the nature of the intermediate to be assigned with high confidence. Electron capture dissociation (ECD) fragmentation allowed us to locate the intermediate to a five amino acid section of the protein--which includes the known catalytic residue, Ser(195). This experimental approach, which uniquely can provide both kinetic and chemical details of enzyme mechanisms, is a potentially powerful tool for studies of enzyme catalysis.

A new hybrid electrospray Fourier transform mass spectrometer: design and performance characteristics.

PubMed

O'connor, Peter B; Pittman, Jason L; Thomson, Bruce A; Budnik, Bogdan A; Cournoyer, Jason C; Jebanathirajah, Judith; Lin, Cheng; Moyer, Susanne; Zhao, Cheng

2006-01-01

A new hybrid electrospray quadrupole Fourier transform mass spectrometry (FTMS) instrument design is shown and characterized. This instrument involves coupling an electrospray source and mass-resolving quadrupole, ion accumulation, and collision cell linear ion trap system developed by MDS Sciex with a home-built ion guide and ion cyclotron resonance (ICR) cell. The iterative progression of this design is shown. The final design involves a set of hexapole ion guides to transfer the ions from the accumulation/collision trap through the magnetic field gradient and into the cell. These hexapole ion guides are separated by a thin gate valve and two conduction limits to maintain the required <10(-9) mbar vacuum for FTICR. Low-attomole detection limits for a pure peptide are shown, 220 000 resolving power in broadband mode and 820 000 resolving power in narrow-band mode are demonstrated, and mass accuracy in the <2 ppm range is routinely available provided the signal is abundant, cleanly resolved, and internally calibrated. This instrument design provides high experimental flexibility, allowing Q2 CAD, SORI-CAD, IRMPD, and ECD experiments with selected ion accumulation as well as experiments such as nozzle skimmer dissociation. Initial top-down mass spectrometry experiments on a protein is shown using ECD.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

NASA Astrophysics Data System (ADS)

Li, Qiang; Popov, Valentin L.

2018-03-01

Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation.

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

PubMed

Bach, M; Meigen, T

1999-01-01

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

Mosaicking Techniques for Deep Submergence Vehicle Video Imagery - Applications to Ridge2000 Science

NASA Astrophysics Data System (ADS)

Mayer, L.; Rzhanov, Y.; Fornari, D. J.; Soule, A.; Shank, T. M.; Beaulieu, S. E.; Schouten, H.; Tivey, M.

2004-12-01

Severe attenuation of visible light and limited power capabilities of many submersible vehicles require acquisition of imagery from short ranges, rarely exceeding 8-10 meters. Although modern video- and photo-equipment makes high-resolution video surveying possible, the field of view of each image remains relatively narrow. To compensate for the deficiencies in light and field of view researchers have been developing techniques allowing for combining images into larger composite images i.e., mosaicking. A properly constructed, accurate mosaic has a number of well-known advantages in comparison with the original sequence of images, the most notable being improved situational awareness. We have developed software strategies for PC-based computers that permit conversion of video imagery acquired from any underwater vehicle, operated within both absolute (e.g. LBL or USBL) or relative (e.g. Doppler Velocity Log-DVL) navigation networks, to quickly produce a set of geo-referenced photomosaics which can then be directly incorporated into a Geographic Information System (GIS) data base. The timescale of processing is rapid enough to permit analysis of the resulting mosaics between submersible dives thus enhancing the efficiency of deep-sea research. Commercial imaging processing packages usually handle cases where there is no or little parallax - an unlikely situation for undersea world where terrain has pronounced 3D content and imagery is acquired from moving platforms. The approach we have taken is optimized for situations in which there is significant relief and thus parallax in the imagery (e.g. seafloor fault scarps or constructional volcanic escarpments and flow fronts). The basis of all mosaicking techniques is a pair-wise image registration method that finds a transformation relating pixels of two consecutive image frames. We utilize a "rigid affine model" with four degrees of freedom for image registration that allows for camera translation in all directions and camera rotation about its optical axis. The coefficients of the transformation can be determined robustly using the well-established and powerful "featureless Fourier domain-based technique" (FFDT), which is an extension of the FFT-based correlation approach. While calculation of cross-correlation allows the recovery of only two parameters of the transformation (translation in 2D), FFDT uses the "Phase shift" theorem of the Fourier Transform as well as a log-polar transform of the Fourier magnitude spectrum to recover all four transformation coefficients required for the rigid affine model. Examples of results of our video mosaicking data processing for the East Pacific Rise ISS will be presented.

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.

Simulation program of nonlinearities applied to telecommunication systems

NASA Technical Reports Server (NTRS)

Thomas, C.

1979-01-01

In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.

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.

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,...

[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.

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.

Intelligent Controller for a Compact Wide-Band Compositional Infrared Fourier Transform Spectrometer

NASA Astrophysics Data System (ADS)

Yiu, P.; Keymeulen, D.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.

2013-12-01

This paper presents the design and integration of an intelligent controller for CIRIS (Compositional InfraRed Interferometric Spectrometer) on a stand-alone field programmable gate array (FPGA) architecture. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. This design eliminates the need for periodically accelerating/decelerating mirrors inherent to canonical Michelson designs and allows for a compact and robust device that is intrinsically radiation-hard, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 μm) on planetary exploration missions. A traditional Michelson FTS passes a monochromatic light source (incident light from the sample) through a system of refractors/mirrors followed by a mirror moving linearly in the plane of the incident light. This process selectively blocks certain wavelengths and permits measurement of the sample's absorption rates as a function of the wavelengths blocked to produce an 'inteferogram.' This is subsequently processed using a Fourier transform to obtain the sample's spectrum and ascertain the sample's composition. With our prototype CIRIS instrument in development at Design and Prototype Inc. and NASA-JPL, we propose the use of a rotating refractor spinning at a constant velocity to variably phase shift incident light to the detector as an alternative to a linearly moving mirror. This design eliminates sensitivity to vibrations, minimizing path length and non-linear errors due to minor perturbations to the system, in addition to facilitating compact design critical to meeting the strict volume requirements of spacecraft. Further, this is done without sacrificing spectral resolution or throughput when compared to Michelson or diffractive designs. While Michelson designs typically achieve very high wavelength resolution, the intended application of our instrument (spectroscopic investigation of Europa's surface) places higher emphasis on the greater wavelength band sensitivity in the 2-12 μm range provided by a rotating refractor design. The instrument's embedded microcontroller is implemented on a flight-qualified VIRTEX-5 FPGA with the aim of sampling the instrument's detector and optical rotary encoder in order to construct an interferogram. Subsequent signal processing, including a Fast Fourier Transform (FFT), noise reduction/averaging, and spectral calibration techniques are applied in real-time to compose the sample spectrum. Deployment of an FPGA eliminates the instrument's need to share computing resources with the main spacecraft computer and takes advantage of the low power consumption and high-throughput hardware parallelism intrinsic to FPGA applications. This parallelism facilitates the high speed, low latency sampling/signal processing critical to instrument precision with minimal power consumption to achieve highly sensitive spectra within the constraints of available spacecraft resources. The instrument is characterized in simulated space-flight conditions and we demonstrate that this technology is capable of meeting the strict volume, sensitivity, and power consumption requirements for implementation in scientific space systems.

Classification of footwear outsole patterns using Fourier transform and local interest points.

PubMed

Richetelli, Nicole; Lee, Mackenzie C; Lasky, Carleen A; Gump, Madison E; Speir, Jacqueline A

2017-06-01

Successful classification of questioned footwear has tremendous evidentiary value; the result can minimize the potential suspect pool and link a suspect to a victim, a crime scene, or even multiple crime scenes to each other. With this in mind, several different automated and semi-automated classification models have been applied to the forensic footwear recognition problem, with superior performance commonly associated with two different approaches: correlation of image power (magnitude) or phase, and the use of local interest points transformed using the Scale Invariant Feature Transform (SIFT) and compared using Random Sample Consensus (RANSAC). Despite the distinction associated with each of these methods, all three have not been cross-compared using a single dataset, of limited quality (i.e., characteristic of crime scene-like imagery), and created using a wide combination of image inputs. To address this question, the research presented here examines the classification performance of the Fourier-Mellin transform (FMT), phase-only correlation (POC), and local interest points (transformed using SIFT and compared using RANSAC), as a function of inputs that include mixed media (blood and dust), transfer mechanisms (gel lifters), enhancement techniques (digital and chemical) and variations in print substrate (ceramic tiles, vinyl tiles and paper). Results indicate that POC outperforms both FMT and SIFT+RANSAC, regardless of image input (type, quality and totality), and that the difference in stochastic dominance detected for POC is significant across all image comparison scenarios evaluated in this study. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Characteristics of motive force derived from trajectory analysis of Amoeba proteus.

PubMed

Masaki, Noritaka; Miyoshi, Hiromi; Tsuchiya, Yoshimi

2007-01-01

We used a monochromatic charge-coupled-device camera to observe the migration behavior of Amoeba proteus every 5 s over a time course of 10000 s in order to investigate the characteristics of its centroid movement (cell velocity) over the long term. Fourier transformation of the time series of the cell velocity revealed that its power spectrum exhibits a Lorentz type profile with a relaxation time of a few hundred seconds. Moreover, some sharp peaks were found in the power spectrum, where the ratios of any two frequencies corresponding to the peaks were expressed as simple rational numbers. Analysis of the trajectory using a Langevin equation showed that the power spectrum reflects characteristics of the cell's motive force. These results suggest that some phenomena relating to the cell's motility, such as protoplasmic streaming and the sol-gel transformation of actin filaments, which seem to be independent phenomena and have different relaxation times, interact with each other and cooperatively participate in the generation process of the motive force.

Fourier Transfrom Ion Cyclotron Resonance Mass Spectrometry at High Magnetic Field

NASA Astrophysics Data System (ADS)

Marshall, Alan G.

1998-03-01

At high magnetic field (9.4 tesla at NHMFL), Fourier transform ion cyclotron resonance mass spectrometry performance improves dramatically: mass resolving power, axialization efficiency, and scan speed (each proportional to B), maximum ion mass, dynamic range, ion trapping period, kinetic energy, and electron self-cooling rate for sympathetic cooling (each proportional to B^2), and ion coalescence tendency (proportional 1/B^2). These advantages may apply singly (e.g., unit mass resolution for proteins of >100,000 Da), or compound (e.g., 10-fold improvement in S/N ratio for 9.4 T vs. 6 T at the same resolving power). Examples range from direct determination of molecular formulas of diesel fuel components by accurate mass measurement (=B10.1 ppm) to protein structure and dynamics probed by H/D exchange. This work was supported by N.S.F. (CHE-93-22824; CHE-94-13008), N.I.H. (GM-31683), Florida State University, and the National High Magnetic Field Laboratory in Tallahassee, FL.

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...

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.

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.

Development of a High-Throughput Microwave Imaging System for Concealed Weapons Detection

DTIC Science & Technology

2016-07-15

hardware. Index Terms—Microwave imaging, multistatic radar, Fast Fourier Transform (FFT). I. INTRODUCTION Near-field microwave imaging is a non-ionizing...configuration, but its computational demands are extreme. Fast Fourier Transform (FFT) imaging has long been used to efficiently construct images sampled with...Simulated image of 25 point scatterers imaged at range 1.5m, with array layout depicted in Fig. 3. Left: image formed with Equation (5) ( Fourier

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.

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

DTIC Science & Technology

1982-09-17

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

EVALUATION OF A PORTABLE FOURIER TRANSFORM INFRARED GAS ANALYZER FOR MEASUREMENTS OF AIR TOXICS IN POLLUTION PREVENTION RESEARCH

EPA Science Inventory

A portable Fourier transform infrared gas analyzer with a photoacoustic detector performed reliably during pollution prevention research at two industrial facilities. It exhibited good agreement (within approximately 6%) with other analytical instruments (dispersive infrared and ...

PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

EPA Science Inventory

Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...

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.

Construction of high frame rate images with Fourier transform

NASA Astrophysics Data System (ADS)

Peng, Hu; Lu, Jian-Yu

2002-05-01

Traditionally, images are constructed with a delay-and-sum method that adjusts the phases of received signals (echoes) scattered from the same point in space so that they are summed in phase. Recently, the relationship between the delay-and-sum method and the Fourier transform is investigated [Jian-yu Lu, Anjun Liu, and Hu Peng, ``High frame rate and delay-and-sum imaging methods,'' IEEE Trans. Ultrason. Ferroelectr. Freq. Control (submitted)]. In this study, a generic Fourier transform method is developed. Two-dimensional (2-D) or three-dimensional (3-D) high frame rate images can be constructed using the Fourier transform with a single transmission of an ultrasound pulse from an array as long as the transmission field of the array is known. To verify our theory, computer simulations have been performed with a linear array, a 2-D array, a convex curved array, and a spherical 2-D array. The simulation results are consistent with our theory. [Work supported in part by Grant 5RO1 HL60301 from NIH.

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

The limit distribution in the q-CLT for q\\,\\geqslant \\,1 is unique and can not have a compact support

NASA Astrophysics Data System (ADS)

Umarov, Sabir; Tsallis, Constantino

2016-10-01

In a paper by Umarov et al (2008 Milan J. Math. 76 307-28), a generalization of the Fourier transform, called the q-Fourier transform, was introduced and applied for the proof of a q-generalized central limit theorem (q-CLT). Subsequently, Hilhorst illustrated (2009 Braz. J. Phys. 39 371-9 2010 J. Stat. Mech. P10023) that the q-Fourier transform for q\\gt 1, is not invertible in the space of density functions. Indeed, using an invariance principle, he constructed a family of densities with the same q-Fourier transform and noted that ‘as a consequence, the q-CLT falls short of achieving its stated goal’. The distributions constructed there have compact support. We prove now that the limit distribution in the q-CLT is unique and can not have a compact support. This result excludes all the possible counterexamples which can be constructed using the invariance principle and fills the gap mentioned by Hilhorst.

Application of the fractional Fourier transform to image reconstruction in MRI.

PubMed

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

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.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

PubMed

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

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

PubMed

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

2012-06-01

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

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Direct generation of abruptly focusing vortex beams using a 3/2 radial phase-only pattern.

PubMed

Davis, Jeffrey A; Cottrell, Don M; Zinn, Jonathan M

2013-03-20

Abruptly focusing Airy beams have previously been generated using a radial cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate these abruptly focusing Airy beams using a 3/2 radial phase pattern encoded onto a liquid crystal display. The resulting optical system is much shorter. In addition, we can easily produce vortex patterns at the focal point of these beams. Experimental results match theoretical predictions.

Determination of Structural Parameters from EXAFS (Extended X-Ray Absorption Fine Structure): Application to Solutions and Catalysts.

DTIC Science & Technology

1984-05-23

the disorder was accurately known. Inverse Transform To isolate the EAFS contribution due to a single feature in the Fourier transform, the inverse ...is associated with setting the "fold" components to 27 zero in r-space. An inverse transform (real part) of the major feature of the Fig. 4 Fourier...phase of the resulting inverse transform represents only any differences between the material being studied and the reference. This residual is

Adaptive DFT-Based Interferometer Fringe Tracking

NASA Astrophysics Data System (ADS)

Wilson, Edward; Pedretti, Ettore; Bregman, Jesse; Mah, Robert W.; Traub, Wesley A.

An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) Observatory at Mount Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier-transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on offline data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse. One example of such an application might be to the field of thin-film measurement by ellipsometry, using a broadband light source and a Fourier-transform spectrometer to detect the resulting fringe patterns.

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

NASA Astrophysics Data System (ADS)

Frere, Noah; Mezzacappa, Anthony; Yakunin, Konstantin

2017-01-01

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

A hybrid method for transient wave propagation in a multilayered solid

NASA Astrophysics Data System (ADS)

Tian, Jiayong; Xie, Zhoumin

2009-08-01

We present a hybrid method for the evaluation of transient elastic-wave propagation in a multilayered solid, integrating reverberation matrix method with the theory of generalized rays. Adopting reverberation matrix formulation, Laplace-Fourier domain solutions of elastic waves in the multilayered solid are expanded into the sum of a series of generalized-ray group integrals. Each generalized-ray group integral containing Kth power of reverberation matrix R represents the set of K-times reflections and refractions of source waves arriving at receivers in the multilayered solid, which was computed by fast inverse Laplace transform (FILT) and fast Fourier transform (FFT) algorithms. However, the calculation burden and low precision of FILT-FFT algorithm limit the application of reverberation matrix method. In this paper, we expand each of generalized-ray group integrals into the sum of a series of generalized-ray integrals, each of which is accurately evaluated by Cagniard-De Hoop method in the theory of generalized ray. The numerical examples demonstrate that the proposed method makes it possible to calculate the early-time transient response in the complex multilayered-solid configuration efficiently.

Double peak-induced distance error in short-time-Fourier-transform-Brillouin optical time domain reflectometers event detection and the recovery method.

PubMed

Yu, Yifei; Luo, Linqing; Li, Bo; Guo, Linfeng; Yan, Jize; Soga, Kenichi

2015-10-01

The measured distance error caused by double peaks in the BOTDRs (Brillouin optical time domain reflectometers) system is a kind of Brillouin scattering spectrum (BSS) deformation, discussed and simulated for the first time in the paper, to the best of the authors' knowledge. Double peak, as a kind of Brillouin spectrum deformation, is important in the enhancement of spatial resolution, measurement accuracy, and crack detection. Due to the variances of the peak powers of the BSS along the fiber, the measured starting point of a step-shape frequency transition region is shifted and results in distance errors. Zero-padded short-time-Fourier-transform (STFT) can restore the transition-induced double peaks in the asymmetric and deformed BSS, thus offering more accurate and quicker measurements than the conventional Lorentz-fitting method. The recovering method based on the double-peak detection and corresponding BSS deformation can be applied to calculate the real starting point, which can improve the distance accuracy of the STFT-based BOTDR system.

Matrix-free mass spectrometric imaging using laser desorption ionisation Fourier transform ion cyclotron resonance mass spectrometry

PubMed Central

Goodwin, Richard J A; Pitt, Andrew R; Harrison, David; Weidt, Stefan K; Langridge-Smith, Pat R R; Barrett, Michael P; Logan Mackay, C

2011-01-01

Mass spectrometry imaging (MSI) is a powerful tool in metabolomics and proteomics for the spatial localization and identification of pharmaceuticals, metabolites, lipids, peptides and proteins in biological tissues. However, sample preparation remains a crucial variable in obtaining the most accurate distributions. Common washing steps used to remove salts, and solvent-based matrix application, allow analyte spreading to occur. Solvent-free matrix applications can reduce this risk, but increase the possibility of ionisation bias due to matrix adhesion to tissue sections. We report here the use of matrix-free MSI using laser desorption ionisation performed on a 12 T Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. We used unprocessed tissue with no post-processing following thaw-mounting on matrix-assisted laser desorption ionisation (MALDI) indium-tin oxide (ITO) target plates. The identification and distribution of a range of phospholipids in mouse brain and kidney sections are presented and compared with previously published MALDI time-of-flight (TOF) MSI distributions. Copyright © 2011 John Wiley & Sons, Ltd. PMID:21416534

Application of phase correction to improve the interpretation of crude oil spectra obtained using 7 T Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Cho, Yunju; Qi, Yulin; O'Connor, Peter B; Barrow, Mark P; Kim, Sunghwan

2014-01-01

In this study, a phase-correction technique was applied to the study of crude oil spectra obtained using a 7 T Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). 7 T FT-ICR MS had not been widely used for oil analysis due to the lower resolving power compared with high field FT-ICR MS. For low field instruments, usage of data that has not been phase-corrected results in an inability to resolve critical mass splits of C3 and SH4 (3.4 mDa), and (13)C and CH (4.5 mDa). This results in incorrect assignments of molecular formulae, and discontinuous double bond equivalents (DBE) and carbon number distributions of S1, S2, and hydrocarbon classes are obtained. Application of phase correction to the same data, however, improves the reliability of assignments and produces continuous DBE and carbon number distributions. Therefore, this study clearly demonstrates that phase correction improves data analysis and the reliability of assignments of molecular formulae in crude oil anlayses.

Radiometric errors in complex Fourier transform spectrometry.

PubMed

Sromovsky, Lawrence A

2003-04-01

A complex spectrum arises from the Fourier transform of an asymmetric interferogram. A rigorous derivation shows that the rms noise in the real part of that spectrum is indeed given by the commonly used relation sigmaR = 2X x NEP/(etaAomega square root(tauN)), where NEP is the delay-independent and uncorrelated detector noise-equivalent power per unit bandwidth, +/- X is the delay range measured with N samples averaging for a time tau per sample, eta is the system optical efficiency, and Aomega is the system throughput. A real spectrum produced by complex calibration with two complex reference spectra [Appl. Opt. 27, 3210 (1988)] has a variance sigmaL2 = sigmaR2 + sigma(c)2 (Lh - Ls)2/(Lh - Lc)2 + sigma(h)2 (Ls - Lc)2/(Lh - Lc)2, valid for sigmaR, sigma(c), and sigma(h) small compared with Lh - Lc, where Ls, Lh, and Lc are scene, hot reference, and cold reference spectra, respectively, and sigma(c) and sigma(h) are the respective combined uncertainties in knowledge and measurement of the hot and cold reference spectra.

Adaptive DFT-Based Interferometer Fringe Tracking

NASA Astrophysics Data System (ADS)

Wilson, Edward; Pedretti, Ettore; Bregman, Jesse; Mah, Robert W.; Traub, Wesley A.

2005-12-01

An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) Observatory at Mount Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier-transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on offline data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately [InlineEquation not available: see fulltext.] milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse. One example of such an application might be to the field of thin-film measurement by ellipsometry, using a broadband light source and a Fourier-transform spectrometer to detect the resulting fringe patterns.

High Grazing Angle and High Resolution Sea Clutter: Correlation and Polarisation Analyses

DTIC Science & Technology

2007-03-01

the azimuthal correlation. The correlation between the HH and VV sea clutter data is low. A CA-CFAR ( cell average constant false-alarm rate...to calculate the power spectra of correlation profiles. The frequency interval of the traditional Discrete Fourier Transform is NT1 Hz, where N and...sea spikes, the Entropy-Alpha decomposition of sea spikes is shown in Figure 30. The process first locates spikes using a cell -average constant false

Symposium U: Thermoelectric Power Generation. Held in Boston, Massachusetts on November 26-29, 2007

DTIC Science & Technology

2008-04-01

including X - ray /electron diffraction, TGA analysis, Raman / Fourier Transform Infrared Spectroscopy, electron microscopy, Rutherford back-scattering and...Energy dispersive X - ray analysis were performed on the treated sample. The results revealed that a surface layer (from 10 nm to up to micron in...nanoparticles into a matrix of bulk Bi2Te 3 material via a hot pressing process. These nanocomposites have been examined by SEM and X - ray powder

Fourier-transform imaging of cotton and botanical and field trash mixtures

USDA-ARS?s Scientific Manuscript database

Botanical and field cotton trash comingled with cotton lint can greatly reduce the marketability and quality of cotton. Trash can be found comingled with cotton lint during harvesting, ginning, and processing, thus this study is of interest. Attenuated Total Reflectance-Fourier Transform Infrared (A...

Detection and classification of salmonella serotypes using spectral signatures collected by fourier transform infrared (FT-IR) spectroscopy

USDA-ARS?s Scientific Manuscript database

Spectral signatures of Salmonella serotypes namely Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky were collected using Fourier transform infrared spectroscopy (FT-IR). About 5-10 µL of Salmonella suspensions with concentrations of 1...

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

USDA-ARS?s Scientific Manuscript database

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

Intermolecular dynamics of substitued benzene and cyclohexane liquids, studied by femtosecond nonlinear-optical polarization spectroscopy

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

Chang, Y.J.; Castner, E.W. Jr.

Femtosecond time-resolved optical-heterodyne detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) is shown to be a powerful and comprehensive tool for studying the intermolecular dynamics occurring in liquids. The observed dynamics include both the underdamped or coherent inertial motions, and the longer time scale diffusive relaxation. The inertial dynamics include phonon-like intermolecular vibrations, intermolecular collisions, and librational caging motions. Data are presented and analyzed for a series of five liquids: cyclohexane, methylcyclohexane, toluene, benzyl alcohol, and benzonitrile, listed in order of increasing polarity. We explore the effects of aromaticity (e.g., methylcyclohexane vs toluene), symmetry reduction (cyclohexane vs methylcyclohexane), and substitution effects (e.g.,more » substituted benzene series) on the ultrafast intermolecular dynamics, for a group of molecular liquids of similar size and volume. We analyze the intermolecular dynamics in both the time and frequency domains by means of Fourier transformations. When Fourier-transformed into the frequency domain, the OHD-RIKES ultrafast transients of the intermolecular dynamics can be directly compared with the frequency domain spectra obtained from the far-infrared absorption and depolarized Raman techniques. This is done using the Gaussian librational caging model of Lynden-Bell and Steele, which results in a power-law scaling relation between dipole and polarizability time correlation functions. 122 refs., 7 figs., 7 tabs.« less

Compact liquid crystal waveguide Fourier transform spectrometer for real-time gas sensing in NIR spectral band

NASA Astrophysics Data System (ADS)

Chao, Tien-Hsin; Lu, Thomas T.; Davis, Scott R.; Rommel, Scott D.; Farca, George; Luey, Ben; Martin, Alan; Anderson, Michael H.

2012-04-01

Jet Propulsion Lab and Vescent Photonics Inc. and are jointly developing an innovative ultra-compact (volume < 10 cm3), ultra-low power (<10 -3 Watt-hours per measurement and zero power consumption when not measuring), completely non-mechanical Liquid Crystal Waveguide Fourier Transform Spectrometer (LCWFTS) that will be suitable for a variety of remote-platform, in-situ measurements. These devices are made possible by novel electro-evanescent waveguide architecture, enabling "monolithic chip-scale" Electro Optic-FTS (EO-FTS) sensors. The potential performance of these EO-FTS sensors include: i) a spectral range throughout 0.4-5 μm (25000 - 2000 cm-1), ii) highresolution (Δλ<= 0.1 nm), iii) high-speed (< 1 ms) measurements, and iv) rugged integrated optical construction. This performance potential enables the detection and quantification of a large number of different atmospheric gases simultaneously in the same air mass and the rugged construction will enable deployment on previously inaccessible platforms. The sensor construction is also amenable for analyzing aqueous samples on remote floating or submerged platforms. We have reported [1] a proof-of-principle prototype LCWFTS sensor that has been demonstrated in the near- IR (range of 1450-1600 nm) with a 5 nm resolution. In this paper, we will report the recently built and tested LCWFTS test bed and the demonstration of a real-time gas sensing applications.

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

PubMed

Ochs, A L

1979-01-01

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

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

NASA Astrophysics Data System (ADS)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Spatially-Heterodyned Holography

DOEpatents

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

2006-02-21

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

Noise-Enhanced Measurement of Weak Doublet Spectra with a Fourier-Transform Spectrometer and a 1-Bit Analog-to-Digital Converter.

PubMed

Lim, M; Saloma, C

2001-04-10

We demonstrate an efficient noise dithering procedure for measuring the power spectrum of a weak spectral doublet with a Fourier-transform spectrometer in which the subthreshold interferogram is measured by a 1-bit analog-to-digital converter without oversampling. In the absence of noise, no information is obtained regarding the doublet spectrum because the modulation term s(x) of its interferogram is below the instrumental detection limit B, i.e., |s(x)| < B, for all path difference x values. Extensive numerical experiments are carried out concerning the recovery of the doublet power spectrum that is represented by s(x) = (s(0)/2)exp(-pi(2)x(2)/beta)[cos(2pif(1)x) + cos(2pif(2)x)], where s(0) is a constant, beta is the linewidth factor, and ?f? = (f(1) + f(2))/2. Different values of ?f?, s(0), and beta are considered to evaluate thoroughly the accuracy of the procedure to determine the unknown values of f(1) and f(2), the spectral linewidth, and the peak values of the spectral profiles. Our experiments show that, even for short observation times, the resonant frequencies of s(x) could be located with high accuracy over a wide range of ?f? and beta values. Signal-to-noise ratios as high as 50 are also gained for the recovered power spectra. The performance of the procedure is also analyzed with respect to another method that recovers the amplitude values of s(x) directly.

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

DTIC Science & Technology

2008-05-01

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

Multi-frequency data analysis in AFM by wavelet transform

NASA Astrophysics Data System (ADS)

Pukhova, V.; Ferrini, G.

2017-10-01

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

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

USDA-ARS?s Scientific Manuscript database

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

Detection of starch adulteration in onion powder by FT-NIR and FT-IR spectroscopy

USDA-ARS?s Scientific Manuscript database

Adulteration of onion powder with cornstarch was identified by Fourier transform near-infrared (FT-NIR) and Fourier transform infrared (FT-IR) spectroscopy. The reflectance spectra of 180 pure and adulterated samples (1–35 wt% starch) were collected and preprocessed to generate calibration and predi...

Coordinate axes, location of origin, and redundancy for the one and two-dimensional discrete Fourier transform

NASA Technical Reports Server (NTRS)

Ioup, G. E.; Ioup, J. W.

1985-01-01

Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.

3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

Treesearch

Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl

2013-01-01

We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...

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...

Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix

NASA Technical Reports Server (NTRS)

Antoon, M. K.; Starkey, K. M.; Koenig, J. L.

1979-01-01

The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.

The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.

ERIC Educational Resources Information Center

Suslick, Kenneth S.; And Others

1987-01-01

Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)

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

USDA-ARS?s Scientific Manuscript database

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

Machine Learning-Aided, Robust Wideband Spectrum Sensing for Cognitive Radios

DTIC Science & Technology

2015-06-12

to even Approved for public release; distribution is unlimited. 2 on the order of a giga -Hertz (GHz). Due to wide bandwidth and noncontiguous...Frequency Band CS Compressive Sampling DFT Discrete Fourier Transform EMI Electro Magnetic Interference FFT Fast Fourier Transform GHz Giga Hertz Hz Hertz

A robust power spectrum split cancellation-based spectrum sensing method for cognitive radio systems

NASA Astrophysics Data System (ADS)

Qi, Pei-Han; Li, Zan; Si, Jiang-Bo; Gao, Rui

2014-12-01

Spectrum sensing is an essential component to realize the cognitive radio, and the requirement for real-time spectrum sensing in the case of lacking prior information, fading channel, and noise uncertainty, indeed poses a major challenge to the classical spectrum sensing algorithms. Based on the stochastic properties of scalar transformation of power spectral density (PSD), a novel spectrum sensing algorithm, referred to as the power spectral density split cancellation method (PSC), is proposed in this paper. The PSC makes use of a scalar value as a test statistic, which is the ratio of each subband power to the full band power. Besides, by exploiting the asymptotic normality and independence of Fourier transform, the distribution of the ratio and the mathematical expressions for the probabilities of false alarm and detection in different channel models are derived. Further, the exact closed-form expression of decision threshold is calculated in accordance with Neyman—Pearson criterion. Analytical and simulation results show that the PSC is invulnerable to noise uncertainty, and can achive excellent detection performance without prior knowledge in additive white Gaussian noise and flat slow fading channels. In addition, the PSC benefits from a low computational cost, which can be completed in microseconds.

Harmonic analysis of traction power supply system based on wavelet decomposition

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, AC drive electric locomotive and EMU large-scale operation in the country on the ground, the electrified railway has become the main harmonic source of China's power grid. In response to this phenomenon, the need for timely monitoring of power quality problems of electrified railway, assessment and governance. Wavelet transform is developed on the basis of Fourier analysis, the basic idea comes from the harmonic analysis, with a rigorous theoretical model, which has inherited and developed the local thought of Garbor transformation, and has overcome the disadvantages such as window fixation and lack of discrete orthogonally, so as to become a more recently studied spectral analysis tool. The wavelet analysis takes the gradual and precise time domain step in the high frequency part so as to focus on any details of the signal being analyzed, thereby comprehensively analyzing the harmonics of the traction power supply system meanwhile use the pyramid algorithm to increase the speed of wavelet decomposition. The matlab simulation shows that the use of wavelet decomposition of the traction power supply system for harmonic spectrum analysis is effective.

Capacitively coupled EMG detection via ultra-low-power microcontroller STFT.

PubMed

Roland, Theresa; Baumgartner, Werner; Amsuess, Sebastian; Russold, Michael F

2017-07-01

As motion artefacts are a major problem with electromyography sensors, a new algorithm is developed to differentiate artefacts to contraction EMG. The performance of myoelectric prosthesis is increased with this algorithm. The implementation is done for an ultra-low-power microcontroller with limited calculation resources and memory. Short Time Fourier Transformation is used to enable real-time application. The sum of the differences (SOD) of the currently measured EMG to a reference contraction EMG is calculated. The SOD is a new parameter introduced for EMG classification. The satisfactory error rates are determined by measurements done with the capacitively coupling EMG prototype, recently developed by the research group.

A wideband, high-resolution spectrum analyzer

NASA Technical Reports Server (NTRS)

Quirk, M. P.; Wilck, H. C.; Garyantes, M. F.; Grimm, M. J.

1988-01-01

A two-million-channel, 40 MHz bandwidth, digital spectrum analyzer under development at the Jet Propulsion Laboratory is described. The analyzer system will serve as a prototype processor for the sky survey portion of NASA's Search for Extraterrestrial Intelligence program and for other applications in the Deep Space Network. The analyzer digitizes an analog input, performs a 2 (sup 21) point Discrete Fourier Transform, accumulates the output power, normalizes the output to remove frequency-dependent gain, and automates simple signal detection algorithms. Due to its built-in frequency-domain processing functions and configuration flexibility, the analyzer is a very powerful tool for real-time signal analysis.

A wide-band high-resolution spectrum analyzer

NASA Technical Reports Server (NTRS)

Quirk, Maureen P.; Garyantes, Michael F.; Wilck, Helmut C.; Grimm, Michael J.

1988-01-01

A two-million-channel, 40 MHz bandwidth, digital spectrum analyzer under development at the Jet Propulsion Laboratory is described. The analyzer system will serve as a prototype processor for the sky survey portion of NASA's Search for Extraterrestrial Intelligence program and for other applications in the Deep Space Network. The analyzer digitizes an analog input, performs a 2 (sup 21) point Discrete Fourier Transform, accumulates the output power, normalizes the output to remove frequency-dependent gain, and automates simple detection algorithms. Due to its built-in frequency-domain processing functions and configuration flexibility, the analyzer is a very powerful tool for real-time signal analysis.

A wide-band high-resolution spectrum analyzer.

PubMed

Quirk, M P; Garyantes, M F; Wilck, H C; Grimm, M J

1988-12-01

This paper describes a two-million-channel 40-MHz-bandwidth, digital spectrum analyzer under development at the Jet Propulsion Laboratory. The analyzer system will serve as a prototype processor for the sky survey portion of NASA's Search for Extraterrestrial Intelligence program and for other applications in the Deep Space Network. The analyzer digitizes an analog input, performs a 2(21)-point, Discrete Fourier Transform, accumulates the output power, normalizes the output to remove frequency-dependent gain, and automates simple signal detection algorithms. Due to its built-in frequency-domain processing functions and configuration flexibility, the analyzer is a very powerful tool for real-time signal analysis and detection.

The Effect of Substrate Emissivity on the Spectral Emission of a Hot-Gas Overlayer

DTIC Science & Technology

2015-12-30

unlimited. Unclassified Unlimited Unclassified Unlimited Unclassified Unlimited Unclassified Unlimited 19 Harold D. Ladouceur (202) 767-3558 Fourier ...13 REFERENCES………………………………………………………………………………….………..14 E-1 EXECUTIVE SUMMARY Fourier transform infrared...Raman spectroscopy, ambient x-ray photoelectron spectroscopy, near- infrared thermal imaging, and Fourier transform infrared emission spectroscopy

Products of multiple Fourier series with application to the multiblade transformation

NASA Technical Reports Server (NTRS)

Kunz, D. L.

1981-01-01

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

Diffraction Theory and Almost Periodic Distributions

NASA Astrophysics Data System (ADS)

Strungaru, Nicolae; Terauds, Venta

2016-09-01

We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distribution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones. We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lebesgue decomposition, with the Fourier-Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.

A novel power harmonic analysis method based on Nuttall-Kaiser combination window double spectrum interpolated FFT algorithm

NASA Astrophysics Data System (ADS)

Jin, Tao; Chen, Yiyang; Flesch, Rodolfo C. C.

2017-11-01

Harmonics pose a great threat to safe and economical operation of power grids. Therefore, it is critical to detect harmonic parameters accurately to design harmonic compensation equipment. The fast Fourier transform (FFT) is widely used for electrical popular power harmonics analysis. However, the barrier effect produced by the algorithm itself and spectrum leakage caused by asynchronous sampling often affects the harmonic analysis accuracy. This paper examines a new approach for harmonic analysis based on deducing the modifier formulas of frequency, phase angle, and amplitude, utilizing the Nuttall-Kaiser window double spectrum line interpolation method, which overcomes the shortcomings in traditional FFT harmonic calculations. The proposed approach is verified numerically and experimentally to be accurate and reliable.

High resolution infrared spectroscopy: Some new approaches and applications to planetary atmospheres

NASA Technical Reports Server (NTRS)

Mumma, M. J.

1978-01-01

The principles of spectral line formation and of techniques for retrieval of atmospheric temperature and constituent profiles are discussed. Applications to the atmospheres of Earth, Mars, Venus, and Jupiter are illustrated by results obtained with Fourier transform and infrared heterodyne spectrometers at resolving powers (lambda/delta hyperon lambda of approximately 10,000 and approximately 10 to the seventh power), respectively, showing the high complementarity of spectroscopy at these two widely different resolving powers. The principles of heterodyne spectroscopy are presented and its applications to atmospheric probing and to laboratory spectroscopy are discussed. Direct absorption spectroscopy with tuneable semiconductor lasers is discussed in terms of precision frequency-and line strength-measurements, showing substantial advances in laboratory infrared spectroscopy.

Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods

NASA Astrophysics Data System (ADS)

Garbanzo-Salas, Marcial; Hocking, Wayne. K.

2015-09-01

In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.

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.

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.

Vibration Power Flow In A Constrained Layer Damping Cylindrical Shell

NASA Astrophysics Data System (ADS)

Wang, Yun; Zheng, Gangtie

2012-07-01

In this paper, the vibration power flow in a constrained layer damping (CLD) cylindrical shell using wave propagation approach is investigated. The dynamic equations of the shell are derived with the Hamilton principle in conjunction with the Donnell shell assumption. With these equations, the dynamic responses of the system under a line circumferential cosine harmonic exciting force is obtained by employing the Fourier transform and the residue theorem. The vibration power flows inputted to the system and transmitted along the shell axial direction are both studied. The results show that input power flow varies with driving frequency and circumferential mode order, and the constrained damping layer can obviously restrict the exciting force from inputting power flow into the base shell especially for a thicker viscoelastic layer, a thicker or stiffer constraining layer (CL), and a higher circumferential mode order, can rapidly attenuate the vibration power flow transmitted along the base shell axial direction.

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.

Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

PubMed

Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

2017-06-01

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

The investigation of the bio-oil produced by hydrothermal liquefaction of Spirulina platensis using ultrahigh resolution Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Kostyukevich, Yury; Vlaskin, Mikhail; Vladimirov, Gleb; Zherebker, Alexander; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

2017-04-01

We report the investigation of the hydrothermal liquefaction products of the Spirulina platensis microalgae by using the Fourier transform ion cyclotron resonance mass spectrometry. The hydrothermal liquefaction produced two fractions: one with boiling temperature below 300℃ and the dense residue that remained in the reactor. It was observed that N 2 and N classes of compounds that dominate in the positive ESI Fourier transform ion cyclotron resonance spectra for both fractions, and that the light fraction is considerably more saturated then the heavy one. The performed hydrogen/deuterium exchange reaction indicated the presence of the onium compounds in the bio-oil.

The application of digital signal processing techniques to a teleoperator radar system

NASA Technical Reports Server (NTRS)

Pujol, A.

1982-01-01

A digital signal processing system was studied for the determination of the spectral frequency distribution of echo signals from a teleoperator radar system. The system consisted of a sample and hold circuit, an analog to digital converter, a digital filter, and a Fast Fourier Transform. The system is interfaced to a 16 bit microprocessor. The microprocessor is programmed to control the complete digital signal processing. The digital filtering and Fast Fourier Transform functions are implemented by a S2815 digital filter/utility peripheral chip and a S2814A Fast Fourier Transform chip. The S2815 initially simulates a low-pass Butterworth filter with later expansion to complete filter circuit (bandpass and highpass) synthesizing.

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.

Metasurface Enabled Wide-Angle Fourier Lens.

PubMed

Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo

2018-06-01

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

SAR image formation with azimuth interpolation after azimuth transform

DOEpatents

Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM

2008-07-08

Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.

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

Identification of geographical origin of Lignosus samples using Fourier transform infrared and two-dimensional infrared correlation spectroscopy

NASA Astrophysics Data System (ADS)

Choong, Yew-Keong; Xu, Chang-Hua; Lan, Jin; Chen, Xiang-Dong; Jamal, Jamia Azdina

2014-07-01

Lignosus spp. is a medicinal mushroom that has been used as a folk remedy for 'clearing heat', eliminating phlegm, 'moistening the lungs' and as an anti-breast cancer agent. The objective of this study was to identify the active chemical constituents of the mushroom limited number of sample by using Fourier transform infrared (FTIR) and two-dimensional correlation Fourier transform infrared spectroscopy (2DIR). The sample M26/08 was purchased from a Chinese medicine shop in Kuala Lumpur, while M49/07 and M23/08 were collected from Semenyih and Kuala Lipis respectively. The three samples have strong absorption peaks corresponding to the stretching vibration of conjugated carbonyl Cdbnd O group. Both fresh sample M49/07 and M23/08 showed an identical peak of 1655 cm-1, whereby M26/08 contained stretching vibration of 1648 cm-1. The peaks from 1260 cm-1 onwards were assignation of carbohydrate content including saccharides. Spectrum of M26/08 showed region from 1260 cm-1 to 950 cm-1 which was 99.4% similar to M23/08. The chemical constitutes of M26/08 and M23/08 were closely correlated (r = 0.97), whereas the correlation coefficient of M26/08 and M49/07 was 0.94. The use of second derivative and 2DIR spectroscopy enhanced the distinct differences to a more significant level. Although the geographical origin of M26/08 was unknown, its origin was determined by comparing with M49/07 and M23/08. The visual and colorful 2DIR spectra provided dynamic structural information of the chemical components analyzed and demonstrated a powerful and useful approach using the spectroscopy of different samples.

Adaptive Controller for Compact Fourier Transform Spectrometer with Space Applications

NASA Astrophysics Data System (ADS)

Keymeulen, D.; Yiu, P.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.; Conroy, M.

2014-12-01

Here we present noise mitigation techniques developed as part of an adaptive controller for a very compact Compositional InfraRed Interferometric Spectrometer (CIRIS) implemented on a stand-alone field programmable gate array (FPGA) architecture with emphasis on space applications in high radiation environments such as Europa. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. The design eschews a monochromatic reference laser typically used for sampling clock generation and instead utilizes constant time-sampling via internally generated clocks. This allows for a compact and robust device, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 µm) on planetary exploration missions. The instrument's embedded microcontroller is implemented on a VIRTEX-5 FPGA and a PowerPC with the aim of sampling the instrument's detector and optical rotary encoder in order to construct interferograms. Subsequent onboard signal processing provides spectral immunity from the noise effects introduced by the compact design's removal of a reference laser and by the radiation encountered during space flight to destinations such as Europa. A variety of signal processing techniques including resampling, radiation peak removal, Fast Fourier Transform (FFT), spectral feature alignment, dispersion correction and calibration processes are applied to compose the sample spectrum in real-time with signal-to-noise-ratio (SNR) performance comparable to laser-based FTS designs in radiation-free environments. The instrument's FPGA controller is demonstrated with the FTS to characterize its noise mitigation techniques and highlight its suitability for implementation in space systems.

Parameterized Spectral Bathymetric Roughness Using the Nonequispaced Fast Fourier Transform

NASA Astrophysics Data System (ADS)

Fabre, David Hanks

The ocean and acoustic modeling community has specifically asked for roughness from bathymetry. An effort has been undertaken to provide what can be thought of as the high frequency content of bathymetry. By contrast, the low frequency content of bathymetry is the set of contours. The two-dimensional amplitude spectrum calculated with the nonequispaced fast Fourier transform (Kunis, 2006) is exploited as the statistic to provide several parameters of roughness following the method of Fox (1996). When an area is uniformly rough, it is termed isotropically rough. When an area exhibits lineation effects (like in a trough or a ridge line in the bathymetry), the term anisotropically rough is used. A predominant spatial azimuth of lineation summarizes anisotropic roughness. The power law model fit produces a roll-off parameter that also provides insight into the roughness of the area. These four parameters give rise to several derived parameters. Algorithmic accomplishments include reviving Fox's method (1985, 1996) and improving the method with the possibly geophysically more appropriate nonequispaced fast Fourier transform. A new composite parameter, simply the overall integral length of the nonlinear parameterizing function, is used to make within-dataset comparisons. A synthetic dataset and six multibeam datasets covering practically all depth regimes have been analyzed with the tools that have been developed. Data specific contributions include possibly discovering an aspect ratio isotropic cutoff level (less than 1.2), showing a range of spectral fall-off values between about -0.5 for a sandybottomed Gulf of Mexico area, to about -1.8 for a coral reef area just outside of the Saipan harbor. We also rank the targeted type of dataset, the best resolution gridded datasets, from smoothest to roughest using a factor based on the kernel dimensions, a percentage from the windowing operation, all multiplied by the overall integration length.

An effective detection algorithm for region duplication forgery in digital images

NASA Astrophysics Data System (ADS)

Yavuz, Fatih; Bal, Abdullah; Cukur, Huseyin

2016-04-01

Powerful image editing tools are very common and easy to use these days. This situation may cause some forgeries by adding or removing some information on the digital images. In order to detect these types of forgeries such as region duplication, we present an effective algorithm based on fixed-size block computation and discrete wavelet transform (DWT). In this approach, the original image is divided into fixed-size blocks, and then wavelet transform is applied for dimension reduction. Each block is processed by Fourier Transform and represented by circle regions. Four features are extracted from each block. Finally, the feature vectors are lexicographically sorted, and duplicated image blocks are detected according to comparison metric results. The experimental results show that the proposed algorithm presents computational efficiency due to fixed-size circle block architecture.

Optical joint transform correlation on the DMD. [deformable mirror device

NASA Technical Reports Server (NTRS)

Knopp, Jerome; Juday, Richard D.

1989-01-01

Initial experimental investigation of the deformable mirror device (DMD) in a joint optical transform correlation is reported. The inverted cloverleaf version of the DMD, in which form the DMD is phase-mostly but of limited phase range, is used. Binarized joint Fourier transforms were calculated for similar and dissimilar objects and written onto the DMD. Inverse Fourier transform was done in a diffraction order for which the DMD shows phase-mostly modulation. Matched test objects produced sharp correlation, distinct objects did not. Further studies are warranted and they are outlined.

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.

Time-Domain Computation Of Electromagnetic Fields In MMICs

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1995-01-01

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

FT-IR and Zeta potential measurements on TiO nanoparticles

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

Singh, Jaiveer; Rathore, Ravi; Kaurav, Netram, E-mail: netramkaurav@yahoo.co.uk

2016-05-23

In the present investigation, ultrafine TiO particles have been synthesized successfully by thermal decomposition method. The sample was characterized by X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy. As-synthesized TiO nanoparticles have a cubic structure as characterized by power X-ray diffraction (XRD), which shows that TiO nanoparticles have narrow size distribution with particle size 11.5 nm. FTIR data shows a strong peak at 1300 cm{sup −1}, assignable to the Ti-O stretching vibrations mode.

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

EPA Science Inventory

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

Turbulence excited frequency domain damping measurement and truncation effects

NASA Technical Reports Server (NTRS)

Soovere, J.

1976-01-01

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

Comparison and validation of Fourier transform infrared spectroscopic methods for monitoring secondary cell wall cellulose from cotton fibers

USDA-ARS?s Scientific Manuscript database

The amount of secondary cell wall (SCW) cellulose in the fiber affects the quality and commercial value of cotton. Accurate assessments of SCW cellulose are essential for improving cotton fibers. Fourier Transform Infrared (FT-IR) spectroscopy enables distinguishing SCW from other cell wall componen...

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

EPA Science Inventory

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

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.

Topics in Chemical Instrumentation: Fourier Transform-Infrared Spectroscopy: Part I. Instrumentation.

ERIC Educational Resources Information Center

Perkins, W. D.

1986-01-01

Discusses: (1) the design of the Fourier Transform-Infrared Spectroscopy (FT-IR) spectrometer; (2) the computation of the spectrum from the interferogram; and (3) the use of apodization. (Part II will discuss advantages of FT-IR over dispersive techniques and show applications of FT-IR to difficult spectroscopic measurements.) (JN)

Diffuse-reflectance fourier-transform mid-infrared spectroscopy as a method of characterizing changes in soil organic matter

USDA-ARS?s Scientific Manuscript database

Diffuse-Reflectance Fourier-Transform Mid-Infrared Spectroscopy (MidIR) can identify the presence of important organic functional groups in soil organic matter (SOM). Soils contain myriad organic and inorganic components that absorb in the MidIR so spectral interpretation needs to be validated in or...

Secondary cell wall development in cotton fibers as examined with attenuated total reflection Fourier transform infrared spectroscopy

USDA-ARS?s Scientific Manuscript database

Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-IR) spectroscopy. The selected harvesting points coincide with secondary cell wall (SCW) development in the fibers. Progressive but moderat...

Development of secondary cell wall in cotton fibers as examined with Fourier transform-infrared spectroscopy

USDA-ARS?s Scientific Manuscript database

Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...

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

NASA Astrophysics Data System (ADS)

Caliari, Marco; Zuccher, Simone

2017-04-01

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

Vibrational spectroscopy and DFT calculations of flavonoid derriobtusone A

NASA Astrophysics Data System (ADS)

Marques, A. N. L.; Mendes Filho, J.; Freire, P. T. C.; Santos, H. S.; Albuquerque, M. R. J. R.; Bandeira, P. N.; Leite, R. V.; Braz-Filho, R.; Gusmão, G. O. M.; Nogueira, C. E. S.; Teixeira, A. M. R.

2017-02-01

Flavonoids are secondary metabolites of plants which perform various functions. One subclass of flavonoid is auronol that can present immunostimulating activity. In this work Fourier-Transform Infrared with Attenuated Total Reflectance (FTIR-ATR) and Fourier-Transform Raman (FT-Raman) spectra of an auronol, derriobtusone A (C18H12O4), were obtained at room temperature. Theoretical calculations using Density Functional Theory (DFT) were performed in order to assign the normal modes and to interpret the spectra of the derriobtusone A molecule. The FTIR-ATR and FT-Raman spectra of the crystal, were recorded at room temperature in the regions 600 cm-1 to 4000 cm-1 and 40 cm-1 to 4000 cm-1, respectively. The normal modes of vibrations were obtained using Density Functional Theory with B3LYP functional and 6-31G+ (d,p) basis set. The calculated frequencies are in good agreement with those obtained experimentally. Detailed assignments of the normal modes present in both the Fourier-Transform infrared and the Fourier-Transform Raman spectra of the crystal are given.

An alternative path to the boundary: The CFT as the Fourier space of AdS

NASA Astrophysics Data System (ADS)

Tolfree, Ian M.

2009-12-01

In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the possible representations of a black hole in the CFT. We find that the black hole micro-states live on the boundary, not on the horizon, and correspond to the possible emission modes of the black hole.

A technique for phase correction in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

Artsang, P.; Pongchalee, P.; Palawong, K.; Buisset, C.; Meemon, P.

2018-03-01

Fourier transform spectroscopy (FTS) is a type of spectroscopy that can be used to analyze components in the sample. The basic setup that is commonly used in this technique is "Michelson interferometer". The interference signal obtained from interferometer can be Fourier transformed into the spectral pattern of the illuminating light source. To experimentally study the concept of the Fourier transform spectroscopy, the project started by setup the Michelson interferometer in the laboratory. The implemented system used a broadband light source in near infrared region (0.81-0.89 μm) and controlled the movable mirror by using computer controlled motorized translation stage. In the early study, there is no sample the interference path. Therefore, the theoretical spectral results after the Fourier transformation of the captured interferogram must be the spectral shape of the light source. One main challenge of the FTS is to retrieve the correct phase information of the inferferogram that relates with the correct spectral shape of the light source. One main source of the phase distortion in FTS that we observed from our system is the non-linear movement of the movable reference mirror of the Michelson interferometer. Therefore, to improve the result, we coupled a monochromatic light source to the implemented interferometer. We simultaneously measured the interferograms of the monochromatic and broadband light sources. The interferogram of the monochromatic light source was used to correct the phase of the interferogram of the broadband light source. The result shows significant improvement in the computed spectral shape.

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.

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns.

PubMed

Xu, Wenjun; Tang, Chen; Gu, Fan; Cheng, Jiajia

2017-04-01

It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

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.

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

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.

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

NASA Technical Reports Server (NTRS)

Elson, Lee S.; Froidevaux, Lucien

1993-01-01

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

Electro-optic imaging Fourier transform spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)

2009-01-01

An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

Using Mathematical Software to Introduce Fourier Transforms in Physical Chemistry to Develop Improved Understanding of Their Applications in Analytical Chemistry

ERIC Educational Resources Information Center

Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.

2016-01-01

This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

ERIC Educational Resources Information Center

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

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

USDA-ARS?s Scientific Manuscript database

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

COMPARISON OF AN INNOVATIVE NONLINEAR ALGORITHM TO CLASSICAL LEAST SQUARES FOR ANALYZING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTRA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

EPA Science Inventory

Open-path Fourier transform infrared (OP/FTIR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric gases at an integrated swine production facility. The concentration-pathlength products of the target gases at this site often exceeded th...

APPLICATION OF STANDARDIZED QUALITY CONTROL PROCEDURES TO OPEN-PATH FOURIER TRANSFORM INFRARED DATA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

EPA Science Inventory

Open-path Fourier transform infrared (OP/FT-IR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric eases at a concentrated swine production facility. A total of 2200 OP/FT-IR spectra were acquired along nine different monitoring paths d...

“Self-absorption” phenomenon in near-infrared Fourier transform Raman spectroscopy of cellulosic and lignocellulosic materials

Treesearch

Umesh P. Agarwal; Nancy Kawai

2005-01-01

While cellulosic and lignocellulosic materials have been studied using conventional Raman spectroscopy, availability of near-infrared (NIR) Fourier transform (FT) Raman instrumentation has made studying these materials much more convenient. This is especially true because the problem of laser-induced fluorescence can be avoided or minimized in FT- Raman (NIR Raman)...

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

Electro-optic Imaging Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin

2005-01-01

JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-O IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 micron (1000-4000/cm) to allow high-resolution, high-speed hyperspectral imaging applications. One application will be the remote sensing of the measurement of a large number of different atmospheric gases simultaneously in the same airmass. Due to the use of a combination of birefringent phase retarders and multiple achromatic phase switches to achieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventional Fourier transform spectrometer but without any moving parts. In this paper, the principle of operations, system architecture and recent experimental progress will be presented.

Electro-optic Imaging Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin

2005-01-01

JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-0IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 pm (1000 -4000 cm-') to allow high-resolution, high-speed hyperspectral imaging applications [l-51. One application will be theremote sensing of the measurement of a large number of different atmospheric gases simultaneously in the sameairmass. Due to the use of a combination of birefiingent phase retarders and multiple achromatic phase switches toachieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventionalFourier transform spectrometer but without any moving parts. In this paper, the principle of operations, systemarchitecture and recent experimental progress will be presen.

Application of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.; Truman, W. M.

1975-01-01

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, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are 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 are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

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

PubMed

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

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

The short time Fourier transform and local signals

NASA Astrophysics Data System (ADS)

Okumura, Shuhei

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

COSMIC SHEAR MEASUREMENT USING AUTO-CONVOLVED IMAGES

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

Li, Xiangchong; Zhang, Jun, E-mail: betajzhang@sjtu.edu.cn

2016-10-20

We study the possibility of using quadrupole moments of auto-convolved galaxy images to measure cosmic shear. The autoconvolution of an image corresponds to the inverse Fourier transformation of its power spectrum. The new method has the following advantages: the smearing effect due to the point-spread function (PSF) can be corrected by subtracting the quadrupole moments of the auto-convolved PSF; the centroid of the auto-convolved image is trivially identified; the systematic error due to noise can be directly removed in Fourier space; the PSF image can also contain noise, the effect of which can be similarly removed. With a large ensemblemore » of simulated galaxy images, we show that the new method can reach a sub-percent level accuracy under general conditions, albeit with increasingly large stamp size for galaxies of less compact profiles.« less

The extended Fourier transform for 2D spectral estimation.

PubMed

Armstrong, G S; Mandelshtam, V A

2001-11-01

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals. Copyright 2001 Academic Press.

Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

NASA Astrophysics Data System (ADS)

de Dominicis, C.; Carlucci, D. M.; Temesvári, T.

1997-01-01

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices M^{α β;γ^δ}, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work. On montre que l'analyse d'objets vivant sur un arbre ultramétrique, en particulier, la diagonalisation par blocs d'une matrice M^{α β;γ^δ} dépendant de 4-répliques, se simplifie de façon dramatique si l'on introduit les opérations appropriées sur ces objets. Ce sont les Transformées de Fourier de Répliques sur un arbre ultramétrique. Ces transformations sont définies et utilisées dans le présent travail.

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.

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

NASA Astrophysics Data System (ADS)

Mazurova, Elena; Lapshin, Aleksey

2013-04-01

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

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

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

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 Imaging Detector Readout Circuits with In-Pixel ADCs for Fourier Transform Imaging Spectrometers

NASA Technical Reports Server (NTRS)

Rider, D.; Blavier, J-F.; Cunningham, T.; Hancock, B.; Key, R.; Pannell, Z.; Sander, S.; Seshadri, S.; Sun, C.; Wrigley, C.

2011-01-01

Focal plane arrays (FPAs) with high frame rates and many pixels benefit several upcoming Earth science missions including GEO-CAPE, GACM, and ACE by enabling broader spatial coverage and higher spectral resolution. FPAs for the PanFTS, a high spatial resolution Fourier transform spectrometer and a candidate instrument for the GEO-CAPE mission are the focus of the developments reported here, but this FPA technology has the potential to enable a variety of future measurements and instruments. The ESTO ACT Program funded the developed of a fast readout integrated circuit (ROIC) based on an innovative in-pixel analog-to-digital converter (ADC). The 128 X 128 pixel ROIC features 60 ?m pixels, a 14-bit ADC in each pixel and operates at a continuous frame rate of 14 kHz consuming only 1.1 W of power. The ROIC outputs digitized data completely eliminating the bulky, power consuming signal chains needed by conventional FPAs. The 128 X 128 pixel ROIC has been fabricated in CMOS and tested at the Jet Propulsion Laboratory. The current version is designed to be hybridized with PIN photodiode arrays via indium bump bonding for light detection in the visible and ultraviolet spectral regions. However, the ROIC design incorporates a small photodiode in each cell to permit detailed characterization of the ROICperformance without the need for hybridization. We will describe the essential features of the ROIC design and present results of ROIC performance measurements.

Compact liquid crystal waveguide based fourier transform spectrometer for in-situ and remote gas and chemical sensing

NASA Astrophysics Data System (ADS)

Chao, Tien-Hsin; Davis, Scott R.; Rommel, Scott D.; Farca, George; Luey, Ben; Martin, Alan; Anderson, Michael H.

2009-11-01

Jet Propulsion Lab and Vescent Photonics Inc. are jointly developing an innovative ultra-compact (volume < 10 cm3), ultra-low power (<10-3 Watt-hours per measurement and zero power consumption when not measuring), completely nonmechanical electro-optic Fourier transform spectrometers (EO-FTS) that will be suitable for a variety of remoteplatform, in-situ measurements. This EO-FTS consists of: i) a novel electro-evanescent waveguide architecture as the solid-state time delay device whose optical path difference (OPD) can be precisely varied utilizing voltage control, ii) a photodetector diode, and iii) an external light/sample collecting devices tailored for either in-situ gas and/or rock sample analysis or for remote atmospheric gas analysis. These devices are made possible by a novel electro-evanescent waveguide architecture, enabling "chip-scale" EO-FTS sensors. The potential performance of these EO-FTS sensors include: i) a spectral range throughout 0.4-5 μm (25000 - 2000 cm-1), ii) high-resolution ▵λ <= 0.1 nm), iii) high-speed (< 1 ms) measurements, and iv) rugged integrated optical construction. This performance potential enables the detection and quantification of a large number of different atmospheric gases simultaneously in the same air mass and the rugged construction will enable deployment on previously inaccessible platforms. In this paper, the up-to-date EO-FTS sensor development status will be presented; initial experimental results will also be demonstrated.

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

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.

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.

Demodulation of micro fiber-optic Fabry-Perot interferometer using subcarrier and dual-wavelength method

NASA Astrophysics Data System (ADS)

Lu, En; Ran, Zengling; Peng, Fei; Liu, Zhiwei; Xu, Fuguo

2012-03-01

Subcarrier technology and dual-wavelength demodulation method are combined for tracking the cavity length variation of a micro fiber-optic Fabry-Perot (F-P). Compared with conventional dual-wavelength demodulation method, two operation wavelengths for demodulation are modulated with two different carrier frequencies, respectively, and then injected into optical link connected with the F-P cavity. Light power reflected for the two wavelengths is obtained by interrogating the powers of Fast Fourier Transform (FFT) spectrum at their carrier frequencies. Because the light at the two wavelengths experiences the same optical and electrical routes, measurement deviation resulting from the drift of optical and electrical links can be entirely eliminated.

Demodulation of micro fiber-optic Fabry-Perot interferometer using subcarrier and dual-wavelength method

NASA Astrophysics Data System (ADS)

Ran, Zengling; Rao, Yunjiang; Liu, Zhiwei; Xu, Fuguo

2011-05-01

Subcarrier technology and dual-wavelength demodulation method are combined for tracking the cavity length variation of a micro fiber-optic fabry-periot (F-P). Compared with conventional dual-wavelength demodulation method, two operation wavelengths for demodulation are modulated with two different carrier frequencies, respectively, and then injected into optical link connected with the F-P cavity. Light power reflected for the two wavelengths is obtained by interrogating the powers of Fast Fourier Transform (FFT) spectrum at their carrier frequencies. Because the light at the two wavelengths experiences the same optical and electrical routes, measurement deviation resulting from the drift of optical and electrical links can be entirely eliminated.

Optimization of training sequence for DFT-spread DMT signal in optical access network with direct detection utilizing DML.

PubMed

Li, Fan; Li, Xinying; Yu, Jianjun; Chen, Lin

2014-09-22

We experimentally demonstrated the transmission of 79.86-Gb/s discrete-Fourier-transform spread 32 QAM discrete multi-tone (DFT-spread 32 QAM-DMT) signal over 20-km standard single-mode fiber (SSMF) utilizing directly modulated laser (DML). The experimental results show DFT-spread effectively reduces Peak-to-Average Power Ratio (PAPR) of DMT signal, and also well overcomes narrowband interference and high frequencies power attenuation. We compared different types of training sequence (TS) symbols and found that the optimized TS for channel estimation is the symbol with digital BPSK/QPSK modulation format due to its best performance against optical link noise during channel estimation.

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.

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.

Support vector machine based classification of fast Fourier transform spectroscopy of proteins

NASA Astrophysics Data System (ADS)

Lazarevic, Aleksandar; Pokrajac, Dragoljub; Marcano, Aristides; Melikechi, Noureddine

2009-02-01

Fast Fourier transform spectroscopy has proved to be a powerful method for study of the secondary structure of proteins since peak positions and their relative amplitude are affected by the number of hydrogen bridges that sustain this secondary structure. However, to our best knowledge, the method has not been used yet for identification of proteins within a complex matrix like a blood sample. The principal reason is the apparent similarity of protein infrared spectra with actual differences usually masked by the solvent contribution and other interactions. In this paper, we propose a novel machine learning based method that uses protein spectra for classification and identification of such proteins within a given sample. The proposed method uses principal component analysis (PCA) to identify most important linear combinations of original spectral components and then employs support vector machine (SVM) classification model applied on such identified combinations to categorize proteins into one of given groups. Our experiments have been performed on the set of four different proteins, namely: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor 2 and Osteopontin. Our proposed method of applying principal component analysis along with support vector machines exhibits excellent classification accuracy when identifying proteins using their infrared spectra.

Dioxin analysis by gas chromatography-Fourier transform ion cyclotron resonance mass spectrometry (GC-FTICRMS).

PubMed

Taguchi, Vince Y; Nieckarz, Robert J; Clement, Ray E; Krolik, Stefan; Williams, Robert

2010-11-01

The feasibility of utilizing a gas chromatograph-tandem quadrupole-Fourier transform ion cyclotron resonance mass spectrometer (GC-MS/MS-FTICRMS) to analyze chlorinated-dioxins/furans (CDDs/CDFs) and mixed halogenated dioxins/furans (HDDs/HDFs) was investigated by operating the system in the GC-FTICRMS mode. CDDs/CDFs and mixed HDDs/HDFs could be analyzed at 50,000 to 100,000 resolving power (RP) on the capillary gas chromatographic time scale. Initial experiments demonstrated that 1 pg of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and 5 pg of 2-bromo-3,7,8-trichlorodibenzo-p-dioxin (BTrCDD) could be detected. The feasibility of utilizing an FTICRMS for screening of CDDs/CDFs, HDDs/HDFs and related compounds was also investigated by analyzing an extract from vegetation exposed to fall-out from an industrial fire. CDDs/CDFs, chlorinated pyrenes and chlorinated tetracenes could be detected from a Kendrick plot analysis of the ultrahigh resolution mass spectra. Mass accuracies were of the order of 0.5 ppm on standards with external mass calibration and 1 ppm on a sample with internal mass calibration. Copyright © 2010 American Society for Mass Spectrometry. Published by Elsevier Inc. All rights reserved.

Vibrational mapping of sinonasal lesions by Fourier transform infrared imaging spectroscopy

NASA Astrophysics Data System (ADS)

Giorgini, Elisabetta; Sabbatini, Simona; Conti, Carla; Rubini, Corrado; Rocchetti, Romina; Re, Massimo; Vaccari, Lisa; Mitri, Elisa; Librando, Vito

2015-12-01

Fourier transform infrared imaging (FTIRI) is a powerful tool for analyzing biochemical changes in tumoral tissues. The head and neck region is characterized by a great variety of lesions, with different degrees of malignancy, which are often difficult to diagnose. Schneiderian papillomas are sinonasal benign neoplasms arising from the Schneiderian mucosa; they can evolve into malignant tumoral lesions (squamous cell carcinoma). In addition, they can sometimes be confused with the more common inflammatory polyps. Therefore, an early and definitive diagnosis of this pathology is mandatory. Progressing in our research on the study of oral cavity lesions, 15 sections consisting of inflammatory sinonasal polyps, benign Schneiderian papillomas, and sinonasal undifferentiated carcinomas were analyzed using FTIRI. To allow a rigorous description of these pathologies and to gain objective diagnosis, the epithelial layer and the adjacent connective tissue of each section were separately investigated by following a multivariate analysis approach. According to the nature of the lesion, interesting modifications were detected in the average spectra of the different tissue components, above all in the lipid and protein patterns. Specific band-area ratios acting as spectral markers of the different pathologies were also highlighted.

Fourier Transform Infrared Absorption Spectroscopy of Gas-Phase and Surface Reaction Products during Si Etching in Inductively Coupled Cl2 Plasmas

NASA Astrophysics Data System (ADS)

Miyata, Hiroki; Tsuda, Hirotaka; Fukushima, Daisuke; Takao, Yoshinori; Eriguchi, Koji; Ono, Kouichi

2011-10-01

A better understanding of plasma-surface interactions is indispensable during etching, including the behavior of reaction or etch products, because the products on surfaces and in the plasma are important in passivation layer formation through their redeposition on surfaces. In practice, the nanometer-scale control of plasma etching would still rely largely on such passivation layer formation as well as ion-enhanced etching on feature surfaces. This paper presents in situ Fourier transform infrared (FTIR) absorption spectroscopy of gas-phase and surface reaction products during inductively coupled plasma (ICP) etching of Si in Cl2. The observation was made in the gas phase by transmission absorption spectroscopy (TAS), and also on the substrate surface by reflection absorption spectroscopy (RAS). The quantum chemical calculation was also made of the vibrational frequency of silicon chloride molecules. The deconvolution of the TAS spectrum revealed absorption features of Si2Cl6 and SiClx (x = 1-3) as well as SiCl4, while that of the RAS spectrum revealed relatively increased absorption features of unsaturated silicon chlorides. A different behavior was also observed in bias power dependence between the TAS and RAS spectra.

Static Magnetic Field Effects on Impaired Peripheral Vasomotion in Conscious Rats

PubMed Central

Okano, Hideyuki; Hatano, Naoya; Tomita, Naohide; Ikada, Yoshito

2013-01-01

We investigated the SMF effects on hemodynamics in the caudal artery-ligated rat as an in vivo ischemia model using noninvasive near-infrared spectroscopy (NIRS) combined with power spectral analysis by fast Fourier transform. Male Wistar rats in the growth stage (10 weeks old) were randomly assigned into four groups: (i) intact and nonoperated cage control (n = 20); (ii) ligated alone (n = 20); (iii) ligated and implanted with a nonmagnetized rod (sham magnet; n = 22); and (vi) ligated and implanted with a magnetized rod (n = 22). After caudal artery ligation, a magnetized or unmagnetized rod (maximum magnetic flux density of 160 mT) was implanted transcortically into the middle diaphysis of the fifth caudal vertebra. During the experimental period of 7 weeks, NIRS measurements were performed in 3- , 5- , and 7-week sessions and the vasomotion amplitude and frequency were analyzed by fast Fourier transform. Exposure for 3–7 weeks to the SMF significantly contracted the increased vasomotion amplitude in the ischemic area. These results suggest that SMF may have a regulatory effect on rhythmic vasomotion in the ischemic area by smoothing the vasomotion amplitude in the early stage of the wound healing process. PMID:24454512

Evaluation of the microscopic distribution of florfenicol in feed pellets for salmon by Fourier Transform infrared imaging and multivariate analysis.

PubMed

Bastidas, Camila Y; von Plessing, Carlos; Troncoso, José; Del P Castillo, Rosario

2018-04-15

Fourier Transform infrared imaging and multivariate analysis were used to identify, at the microscopic level, the presence of florfenicol (FF), a heavily-used antibiotic in the salmon industry, supplied to fishes in feed pellets for the treatment of salmonid rickettsial septicemia (SRS). The FF distribution was evaluated using Principal Component Analysis (PCA) and Augmented Multivariate Curve Resolution with Alternating Least Squares (augmented MCR-ALS) on the spectra obtained from images with pixel sizes of 6.25 μm × 6.25 μm and 1.56 μm × 1.56 μm, in different zones of feed pellets. Since the concentration of the drug was 3.44 mg FF/g pellet, this is the first report showing the powerful ability of the used of spectroscopic techniques and multivariate analysis, especially the augmented MCR-ALS, to describe the FF distribution in both the surface and inner parts of feed pellets at low concentration, in a complex matrix and at the microscopic level. The results allow monitoring the incorporation of the drug into the feed pellets. Copyright © 2018 Elsevier B.V. All rights reserved.

Nondestructive Handheld Fourier Transform Infrared (FT-IR) Analysis of Spectroscopic Changes and Multivariate Modeling of Thermally Degraded Plain Portland Cement Concrete and its Slag and Fly Ash-Based Analogs.

PubMed

Leung Tang, Pik; Alqassim, Mohammad; Nic Daéid, Niamh; Berlouis, Leonard; Seelenbinder, John

2016-05-01

Concrete is by far the world's most common construction material. Modern concrete is a mixture of industrial pozzolanic cement formulations and aggregate fillers. The former acts as the glue or binder in the final inorganic composite; however, when exposed to a fire the degree of concrete damage is often difficult to evaluate nondestructively. Fourier transform infrared (FT-IR) spectroscopy through techniques such as transmission, attenuated total reflectance, and diffuse reflectance have been rarely used to evaluate thermally damaged concrete. In this paper, we report on a study assessing the thermal damage of concrete via the use of a nondestructive handheld FT-IR with a diffuse reflectance sample interface. In situ measurements can be made on actual damaged areas, without the need for sample preparation. Separate multivariate models were developed to determine the equivalent maximal temperature endured for three common industrial concrete formulations. The concrete mixtures were successfully modeled displaying high predictive power as well as good specificity. This has potential uses in forensic investigation and remediation services particularly for fires in buildings. © The Author(s) 2016.

Comparative Variable Temperature Studies of Polyamide II with a Benchtop Fourier Transform and a Miniature Handheld Near-Infrared Spectrometer Using 2D-COS and PCMW-2D Analysis.

PubMed

Unger, Miriam; Pfeifer, Frank; Siesler, Heinz W

2016-07-01

The main objective of this communication is to compare the performance of a miniaturized handheld near-infrared (NIR) spectrometer with a benchtop Fourier transform near-infrared (FT-NIR) spectrometer. Generally, NIR spectroscopy is an extremely powerful analytical tool to study hydrogen-bonding changes of amide functionalities in solid and liquid materials and therefore variable temperature NIR measurements of polyamide II (PAII) have been selected as a case study. The information content of the measurement data has been further enhanced by exploiting the potential of two-dimensional correlation spectroscopy (2D-COS) and the perturbation correlation moving window two-dimensional (PCMW2D) evaluation technique. The data provide valuable insights not only into the changes of the hydrogen-bonding structure and the recrystallization of the hydrocarbon segments of the investigated PAII but also in their sequential order. Furthermore, it has been demonstrated that the 2D-COS and PCMW2D results derived from the spectra measured with the miniaturized NIR instrument are equivalent to the information extracted from the data obtained with the high-performance FT-NIR instrument. © The Author(s) 2016.

Fourier-Transform Infrared Microspectroscopy, a Novel and Rapid Tool for Identification of Yeasts

PubMed Central

Wenning, Mareike; Seiler, Herbert; Scherer, Siegfried

2002-01-01

Fourier-transform infrared (FT-IR) microspectroscopy was used in this study to identify yeasts. Cells were grown to microcolonies of 70 to 250 μm in diameter and transferred from the agar plate by replica stamping to an IR-transparent ZnSe carrier. IR spectra of the replicas on the carrier were recorded using an IR microscope coupled to an IR spectrometer, and identification was performed by comparison to reference spectra. The method was tested by using small model libraries comprising reference spectra of 45 strains from 9 genera and 13 species, recorded with both FT-IR microspectroscopy and FT-IR macrospectroscopy. The results show that identification by FT-IR microspectroscopy is equivalent to that achieved by FT-IR macrospectroscopy but the time-consuming isolation of the organisms prior to identification is not necessary. Therefore, this method also provides a rapid tool to analyze mixed populations. Furthermore, identification of 21 Debaryomyces hansenii and 9 Saccharomyces cerevisiae strains resulted in 92% correct identification at the strain level for S. cerevisiae and 91% for D. hansenii, which demonstrates that the resolution power of FT-IR microspectroscopy may also be used for yeast typing at the strain level. PMID:12324312

Nondestructive surface analysis for material research using fiber optic vibrational spectroscopy

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.

2001-11-01

The advanced methods of fiber optical vibrational spectroscopy (FOVS) has been developed in conjunction with interferometer and low-loss, flexible, and nontoxic optical fibers, sensors, and probes. The combination of optical fibers and sensors with Fourier Transform (FT) spectrometer has been used in the range from 2.5 to 12micrometers . This technique serves as an ideal diagnostic tool for surface analysis of numerous and various diverse materials such as complex structured materials, fluids, coatings, implants, living cells, plants, and tissue. Such surfaces as well as living tissue or plants are very difficult to investigate in vivo by traditional FT infrared or Raman spectroscopy methods. The FOVS technique is nondestructive, noninvasive, fast (15 sec) and capable of operating in remote sampling regime (up to a fiber length of 3m). Fourier transform infrared (FTIR) and Raman fiber optic spectroscopy operating with optical fibers has been suggested as a new powerful tool. These techniques are highly sensitive techniques for structural studies in material research and various applications during process analysis to determine molecular composition, chemical bonds, and molecular conformations. These techniques could be developed as a new tool for quality control of numerous materials as well as noninvasive biopsy.

Kinetics and Product Branching Fractions of Reactions between a Cation and a Radical: Ar+ + CH3 and O2+ + CH3 (Postprint)

DTIC Science & Technology

2015-01-13

Gross group using a Chen nozzle coupled to a Fourier transform ion cyclotron reso- nance (FT-ICR) mass spectrometer for reactions of the benzyl radical...reactions: A Fourier transform ion cyclotron resonance study of allyl radical reacting with aromatic radical cations. Int. J. Mass Spectrom. 2009, 287, 8

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

DTIC Science & Technology

2005-07-01

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

Color and surface chemistry changes of extracted wood flour after heating at 120 °C

Treesearch

Yao Chen; Mandla A. Tshabalala; Jianmin Gao; Nicole M. Stark

2013-01-01

To investigate the effect of heat on color and surface chemistry of wood flour (WF), unextracted, extracted and delignified samples of commercial WF were heated at 120 °C for 24 h and analyzed by colorimetry, diffuse reflectance visible (DRV), attenuated total reflectance Fourier transform infrared (ATR-FTIR) and Fourier transform Raman (FT-Raman) spectroscopies....

Characterization of southern yellow pine bark layers by Attenuated Total Reflectance (ATR) and Fourier Transform Infrared (FT-IR) Spectroscopy

Treesearch

Thomas L. Eberhardt

2009-01-01

The outer bark (rhytidome) of the southern yellow pines is a complex structure comprised of alternating layers of obliterated phloem and periderm tissues, with the latter comprised of three layers, those being phellem, phellogen, and phelloderm. An attenuated total reflectance (ATR) sampling accessory, coupled with a Fourier transform infrared (FTIR) spectrometer,...

Determination of diosmin in pharmaceutical formulations using Fourier transform infrared spectrophotometry

PubMed Central

Bunaciu, Andrei A.; Udristioiu, Gabriela Elena; Ruţă, Lavinia L.; Fleschin, Şerban; Aboul-Enein, Hassan Y.

2009-01-01

A Fourier transform infrared (FT-IR) spectrometric method was developed for the rapid, direct measurement of diosmin in different pharmaceutical drugs. Conventional KBr-spectra were compared for best determination of active substance in commercial preparations. The Beer–Lambert law and two chemometric approaches, partial least squares (PLS) and principal component regression (PCR+) methods, were tried in data processing. PMID:23960715

Effects of aging on the structural, mechanical, and thermal properties of the silicone rubber current transformer insulation bushing for a 500 kV substation.

PubMed

Wang, Zhigao; Zhang, Xinghai; Wang, Fangqiang; Lan, Xinsheng; Zhou, Yiqian

2016-01-01

In order to analyze the cracking and aging reason of the silicone rubber current transformer (CT) insulation bushing used for 8 years from a 500 kV alternating current substation, characteristics including Fourier transform infrared (FTIR) spectroscopy, mechanical properties analysis, hardness, and thermo gravimetric analysis have been carried out. The FTIR results indicated that the external surface of the silicone rubber CT insulation bushing suffered from more serious aging than the internal part, fracture of side chain Si-C bond was much more than the backbone. Mechanical properties and thermal stability results illustrated that the main aging reasons were the breakage of side chain Si-C bond and the excessive cross-linking reaction of the backbone. This study can provide valuable basis for evaluating degradation mechanism and aging state of the silicone rubber insulation bushing in electric power field.

Application of wavelet and Fuorier transforms as powerful alternatives for derivative spectrophotometry in analysis of binary mixtures: A comparative study

NASA Astrophysics Data System (ADS)

Hassan, Said A.; Abdel-Gawad, Sherif A.

2018-02-01

Two signal processing methods, namely, Continuous Wavelet Transform (CWT) and the second was Discrete Fourier Transform (DFT) were introduced as alternatives to the classical Derivative Spectrophotometry (DS) in analysis of binary mixtures. To show the advantages of these methods, a comparative study was performed on a binary mixture of Naltrexone (NTX) and Bupropion (BUP). The methods were compared by analyzing laboratory prepared mixtures of the two drugs. By comparing performance of the three methods, it was proved that CWT and DFT methods are more efficient and advantageous in analysis of mixtures with overlapped spectra than DS. The three signal processing methods were adopted for the quantification of NTX and BUP in pure and tablet forms. The adopted methods were validated according to the ICH guideline where accuracy, precision and specificity were found to be within appropriate limits.

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.

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).

Determination of Spectroscopic Properties of Atmospheric Molecules from High Resolution Vacuum Ultraviolet Cross Section and Wavelength Measurements

NASA Technical Reports Server (NTRS)

Parkinson, W. H.; Yoshino, K.

1997-01-01

An account is given of progress during the period 8/l/96-7/31/97 on work on (a) cross section measurements of O2 S-R using a Fourier transform spectrometer (FTS) at the Photon Factory in Japan; (b) the determination of the predissociation linewidths of the Schumann-Runge bands (S-R) of 02; (c) cross section measurements of 02 Herzberg bands using a Fourier transform spectrometer (FTS) at Imperial College; and (d) cross section measurements of H2O in the wavelength region 120-188 nm. The experimental investigations are effected at high resolution with a 6.65 m scanning spectrometer and with the Fourier transform spectrometer. Below 175 nm, synchrotron radiation is most suitable for cross section measurements in combination with spectrometers at the Photon Factory Japan. Cross section measurements of the Doppler limited bands depend on using the very high resolution, available with the Fourier transform spectrometer, (0.025/cm resolution). All of these spectroscopic measurements are needed for accurate calculations of the production of atomic oxygen, the penetration of solar radiation into the Earth's atmosphere, and photochemistry of minor molecules.

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.

SHOCKS Impulse-Jerk(I-J) Plasticity/Fracture Burst Acoustic-Emission(BAE) NON:``1''/ ω -``Noise'' Power-Law; Universality Power-Spectrum is I-J Time-Series Fourier-Transform: 1687 < < < 1988: VERY-LONG PRE-``Bak''!!!

NASA Astrophysics Data System (ADS)

Chavira, Aldo; Gregson, Victor, Jr.; Green, Sidney; Siegel, Edward

2011-06-01

SHOCKS impulse-jerk(I-J) [apply strain/impulse to get stress/jerk ],{VS. NON-shocks[apply stress to get strain]}, plasticity/fracture BAE[E. S.: MSE 8.,310(71); PSS: (a) 5, 601/607(71); Xl..-Latt. Defects 5, 277(74); Scripta Met.: 6, 785(72); 8, 587/617(74); 3rd Tokyo A.-E. Symp. (76);Acta Met.25,383(77); JMMM 7, 312(78)] NON: ``1''/ ω -``Noise'' Zipf(NON-Pareto); power-law ; universality power-spectrum is manifestly-demonstrated in ONLY ``PURE''-MATHS way to be nothing but d[F(t)=m(t)a(t)=Newton's (3rd) Law of Motion=(I-J)]/dt I-Jderivative d(I-J)/dt=dF(t)/dt=[m(t)da(t)/dt+a(t)dm(t)/dt] REdiscovery!!! A/Siegel NON-shock PHYSICS derivation fails!!!; ''PURE''-MATHS: dF(t)/dt=d2p(t)/dt2=[m(t)da(t)/dt+a(t)dm(t)/dt] TRIPLE-integral [VS. NON -shocks F = ma time-series DOUBLE-integral] Dichotomy: s(t) = [v0+(1/2)a(t)t2+EXTRA-TERM(S)], {VS. s(t) = [v0t+(1/2) at2]}, integral-transform formally defines power-spectrum Dichotomy:

Cell shape characterization and classification with discrete Fourier transforms and self-organizing maps.

PubMed

Kriegel, Fabian L; Köhler, Ralf; Bayat-Sarmadi, Jannike; Bayerl, Simon; Hauser, Anja E; Niesner, Raluca; Luch, Andreas; Cseresnyes, Zoltan

2018-03-01

Cells in their natural environment often exhibit complex kinetic behavior and radical adjustments of their shapes. This enables them to accommodate to short- and long-term changes in their surroundings under physiological and pathological conditions. Intravital multi-photon microscopy is a powerful tool to record this complex behavior. Traditionally, cell behavior is characterized by tracking the cells' movements, which yields numerous parameters describing the spatiotemporal characteristics of cells. Cells can be classified according to their tracking behavior using all or a subset of these kinetic parameters. This categorization can be supported by the a priori knowledge of experts. While such an approach provides an excellent starting point for analyzing complex intravital imaging data, faster methods are required for automated and unbiased characterization. In addition to their kinetic behavior, the 3D shape of these cells also provide essential clues about the cells' status and functionality. New approaches that include the study of cell shapes as well may also allow the discovery of correlations amongst the track- and shape-describing parameters. In the current study, we examine the applicability of a set of Fourier components produced by Discrete Fourier Transform (DFT) as a tool for more efficient and less biased classification of complex cell shapes. By carrying out a number of 3D-to-2D projections of surface-rendered cells, the applied method reduces the more complex 3D shape characterization to a series of 2D DFTs. The resulting shape factors are used to train a Self-Organizing Map (SOM), which provides an unbiased estimate for the best clustering of the data, thereby characterizing groups of cells according to their shape. We propose and demonstrate that such shape characterization is a powerful addition to, or a replacement for kinetic analysis. This would make it especially useful in situations where live kinetic imaging is less practical or not possible at all. © 2017 International Society for Advancement of Cytometry. © 2017 International Society for Advancement of Cytometry.

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

NASA Technical Reports Server (NTRS)

White, Michael J.

2006-01-01

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

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

PubMed Central

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

Multichannel Dynamic Fourier-Transform IR Spectrometer

NASA Astrophysics Data System (ADS)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

Effects of Pulsed Electric Fields (PEF) on Vitamin C and Its Antioxidant Properties.

PubMed

Zhang, Zhi-Hong; Zeng, Xin-An; Brennan, Charles S; Brennan, Margaret; Han, Zhong; Xiong, Xia-Yu

2015-10-13

In this study, pulsed electric fields (PEF) treatments and their effects on the structure of vitamin C (VIT-C) were estimated by fluorescence and Fourier transform infrared (FT-IR) spectroscopy, the relative content of VIT-C was measured by HPLC and the antioxidant properties of treated VIT-C by DPPH radical scavenging as well as reducing power tests. The fluorescence intensity of treated VIT-C increased slightly compared to the untreated VIT-C. Moreover, the effect of PEF on the structure of VIT-C was observed using the FT-IR spectra. These phenomena indicated that the PEF affected the conformation of VIT-C, which promoted the VIT-C isomer transformed enol-form into keto-form. In addition, the PEF treatments did not suffer the damage to VIT-C and could slow down the oxidation process in involving of experimental conditions by HPLC. The antioxidant properties of the treated VIT-C were enhanced, which was proved by radical scavenging and also the reducing power tests.

Effects of Pulsed Electric Fields (PEF) on Vitamin C and Its Antioxidant Properties

PubMed Central

Zhang, Zhi-Hong; Zeng, Xin-An; Brennan, Charles S.; Brennan, Margaret; Han, Zhong; Xiong, Xia-Yu

2015-01-01

In this study, pulsed electric fields (PEF) treatments and their effects on the structure of vitamin C (VIT-C) were estimated by fluorescence and Fourier transform infrared (FT-IR) spectroscopy, the relative content of VIT-C was measured by HPLC and the antioxidant properties of treated VIT-C by DPPH radical scavenging as well as reducing power tests. The fluorescence intensity of treated VIT-C increased slightly compared to the untreated VIT-C. Moreover, the effect of PEF on the structure of VIT-C was observed using the FT-IR spectra. These phenomena indicated that the PEF affected the conformation of VIT-C, which promoted the VIT-C isomer transformed enol-form into keto-form. In addition, the PEF treatments did not suffer the damage to VIT-C and could slow down the oxidation process in involving of experimental conditions by HPLC. The antioxidant properties of the treated VIT-C were enhanced, which was proved by radical scavenging and also the reducing power tests. PMID:26473846

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.

Application of Fourier analysis to multispectral/spatial recognition

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

The New Physical Optics Notebook: Tutorials in Fourier Optics.

ERIC Educational Resources Information Center

Reynolds, George O.; And Others

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

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)

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

NASA Technical Reports Server (NTRS)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

Determination of Carbon Dioxide, Carbon Monoxide, and Methane Concentrations in Cigarette Smoke by Fourier Transform Infrared Spectroscopy

ERIC Educational Resources Information Center

Tan, T. L.; Lebron, G. B.

2012-01-01

The integrated absorbance areas of vibrational bands of CO[subscript 2], CO, and CH[subscript 4] gases in cigarette smoke were measured from Fourier transform infrared (FTIR) spectra to derive the partial pressures of these gases at different smoke times. The quantity of the three gas-phase components of cigarette smoke at different smoke times…

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

ERIC Educational Resources Information Center

Pezzolo, Alessandra De Lorenzi

2011-01-01

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

Double Fourier Series Solution of Poisson’s Equation on a Sphere.

DTIC Science & Technology

1980-10-29

algebraic systems, the solution of these systems, and the inverse transform of the solution in Fourier space back to physi- cal space. 6. Yee, S. Y. K...Multiply each count in steps (2) through (5) by K] 7. Inverse transform um(0j j = 1, J - 1, to obtain u k; set u(P) = u 0 (P). [K(J - 1) log 2 K

Using multiple calibration sets to improve the quantitative accuracy of partial least squares (PLS) regression on open-path fourier transform infrared (OP/FT-IR) spectra of ammonia over wide concentration ranges

USDA-ARS?s Scientific Manuscript database

A technique of using multiple calibration sets in partial least squares regression (PLS) was proposed to improve the quantitative determination of ammonia from open-path Fourier transform infrared spectra. The spectra were measured near animal farms, and the path-integrated concentration of ammonia...

Bit-parallel arithmetic in a massively-parallel associative processor

NASA Technical Reports Server (NTRS)

Scherson, Isaac D.; Kramer, David A.; Alleyne, Brian D.

1992-01-01

A simple but powerful new architecture based on a classical associative processor model is presented. Algorithms for performing the four basic arithmetic operations both for integer and floating point operands are described. For m-bit operands, the proposed architecture makes it possible to execute complex operations in O(m) cycles as opposed to O(m exp 2) for bit-serial machines. A word-parallel, bit-parallel, massively-parallel computing system can be constructed using this architecture with VLSI technology. The operation of this system is demonstrated for the fast Fourier transform and matrix multiplication.

Stretchable and flexible thermoelectric polymer composites

NASA Astrophysics Data System (ADS)

Slobodian, P.; Riha, P.; Matyas, J.; Olejnik, R.

2018-03-01

Polymer composites were manufactured from pristine and oxidized multi-walled carbon nanotubes and ethylene-octene copolymer. The composites had thermoelectric properties and exhibit thermoelectric effect, that is, the conversion of temperature differences into electricity. Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy of the multi-walled carbon nanotubes in ethylene-octene copolymer matrix showed that the oxidation with HNO3 or KMnO4 enhanced its p-type electrical conductivity and that the thermoelectric power increase was proportional to the formation of new oxygen-containing functional groups on the surface of carbon nanotubes.

Discrete Fourier transforms of nonuniformly spaced data

NASA Technical Reports Server (NTRS)

Swan, P. R.

1982-01-01

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

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

A Review of Maximum Entropy Spectral Analysis and Applications to Fourier Spectroscopy.

DTIC Science & Technology

1985-04-03

1 From Pythagoras to Fourier 3 2. 2 The Periodogram as Introduced by Sir Arthur Schuster 6 2. 3 The Slutzky Effect and the Work of Yule 7 2.4 The...Transform 27 4. 2 The Z-Transform Convolution Theorem 29 4. 3 The Wiener -Khintchmne , Theorem 31 4.4 The Z-Transform of el. 3 5. A COMPARISON BETWEEN...the Convolution I’heoreni, the Wiene i-Khintrbitte Theorem , aind the conventional ;pp roach of Il1ac km in and Tuke-,. Finally, it should he

On Weak and Strong 2k- bent Boolean Functions

DTIC Science & Technology

2016-01-01

U.S.A. Email: pstanica@nps.edu Abstract—In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent...denotes the complex conjugate of z. An important tool in our analysis is the discrete Fourier transform , known in Boolean functions literature, as Walsh...Hadamard, or Walsh–Hadamard transform , which is the func- tion Wf : Fn2 → C, defined by Wf (u) = 2− n 2 ∑ x∈Vn (−1)f(x)⊕u·x. Any f ∈ Bn can be

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.

A pipeline design of a fast prime factor DFT on a finite field

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, In-Shek; Shao, H. M.; Reed, Irving S.; Shyu, Hsuen-Chyun

1988-01-01

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.

Qualitative and semiquantitative Fourier transformation using a noncoherent system.

PubMed

Rogers, G L

1979-09-15

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

Parallel β-sheet vibration band increases with proteins dipole moment under exposure to 1765 MHz microwaves.

PubMed

Calabrò, Emanuele; Magazù, Salvatore

2016-02-01

Effects of exposure of 4 h to mobile phones microwaves at 1765 MHz at a power density around 940 mW/m(2) on four typical proteins (hemoglobin in H2 O solution, and myoglobin, bovine serum albumin, and lysozyme in D2 O solution) were studied by means of Fourier Transform Infrared spectroscopy and Fourier self-deconvolution analysis. Increase in intensity of parallel β-sheet component around 1635 cm(-1) was observed after exposure of hemoglobin, myoglobin, and bovine serum albumin, showing that a mechanism of unfolding occurred after exposure, whereas no appreciable change in the amide I region occurred after lysozyme exposure. In addition, a relationship between protein dipole moment and protein unfolding rate was demonstrated with a correlation coefficient r = 0.973 and 95% confidence interval. © 2016 Wiley Periodicals, Inc.

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

PubMed

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

2018-04-01

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

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

PubMed

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

[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.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

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

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.

A novel collinear optical system with annulus mirrors for holographic disc driver

NASA Astrophysics Data System (ADS)

Wang, Ye

2008-12-01

This paper focus on a novel collinear lens system with annulus mirrors for holographic disc driver, both information beam and reference beam are use same laser beam. The expanded and parallel laser beam, center part of it as the information beam then through Fourier transform lens, the beam around center part as a reference beam. On this axis, the ring reference beam reflected by two annulus shaped mirrors, then became a convergent beam, together with the information beam which through the first Fourier transform lens then produce holographic pattern to be write into the holographic disc behind of them, this lens system with two mirrors made the angle between information beam and reference beam more wide, can improved the multiplex level of holographic storage. Pair of Fourier transform lens with advance performance is designed in this paper.

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%.

FFTDC2: a one-dimensional Fourier transform with forward and inverse data conditioning for non-complex data

USGS Publications Warehouse

Bracken, Robert E.

2004-01-01

A subroutine (FFTDC2) coded in Fortran 77 is described, which performs a Fast Fourier Transform or Discrete Fourier Transform together with necessary conditioning steps of trend removal, extension, and windowing. The source code for the entire library of required subroutines is provided with the digital release of this report. But, there is only one required entry point, the subroutine call to FFTDC2; all the other subroutines are operationally transparent to the user. Complete instructions for use of FFTDC2.F (as well as for all the other subroutines) and some practical theoretical discussions are included as comments at the beginning of the source code. This subroutine is intended to be an efficient tool for the programmer in a variety of production-level signal-processing applications.

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.

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

PubMed

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

DOE PAGES

Xu, Kuan; Austin, Anthony P.; Wei, Ke

2017-12-21

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

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

Xu, Kuan; Austin, Anthony P.; Wei, Ke

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

Beyond Fourier

NASA Astrophysics Data System (ADS)

Hoch, Jeffrey C.

2017-10-01

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

Non-contact feature detection using ultrasonic Lamb waves

DOEpatents

Sinha, Dipen N [Los Alamos, NM

2011-06-28

Apparatus and method for non-contact ultrasonic detection of features on or within the walls of hollow pipes are described. An air-coupled, high-power ultrasonic transducer for generating guided waves in the pipe wall, and a high-sensitivity, air-coupled transducer for detecting these waves, are disposed at a distance apart and at chosen angle with respect to the surface of the pipe, either inside of or outside of the pipe. Measurements may be made in reflection or transmission modes depending on the relative position of the transducers and the pipe. Data are taken by sweeping the frequency of the incident ultrasonic waves, using a tracking narrow-band filter to reduce detected noise, and transforming the frequency domain data into the time domain using fast Fourier transformation, if required.

Dielectric Properties and Electrodynamic Process of Natural Ester-Based Insulating Nanofluid

NASA Astrophysics Data System (ADS)

Zou, Ping; Li, Jian; Sun, Cai-Xin; Zhang, Zhao-Tao; Liao, Rui-Jin

Natural ester is currently used as an insulating oil and coolant for medium-power transformers. The biodegradability of insulating natural ester makes it a preferable insulation liquid to mineral oils. In this work, Fe3O4 nanoparticles were used along with oleic acid to improve the performance of insulating natural ester. The micro-morphology of Fe3O4 nanoparticles before and after surface modification was observed through transmission electron microscopy. Attenuated total reflection-Fourier transform infrared spectroscopy, thermal gravimetric analysis, and differential thermal analysis were employed to investigate functional groups and their thermal stability on the surface-modified Fe3O4 nanoparticles. Basic dielectric properties of natural ester-based insulating nanofluid were measured. The electrodynamic process in the natural ester-based insulating nanofluid is also presented.

Characterization of non-polar aromatic hydrocarbons in crude oil using atmospheric pressure laser ionization and Fourier transform ion cyclotron resonance mass spectrometry (APLI FT-ICR MS).

PubMed

Schrader, Wolfgang; Panda, Saroj K; Brockmann, Klaus J; Benter, Thorsten

2008-07-01

We report on the successful application of the recently introduced atmospheric pressure laser ionization (APLI) method as a novel tool for the analysis of crude oil and its components. Using Fourier transform ion cyclotron resonance mass spectrometry, unambiguous determination of key compounds in this complex matrix with unprecedented sensitivity is presented.

Artifacts in Radar Imaging of Moving Targets

DTIC Science & Technology

2012-09-01

CA, USA, 2007. [11] B. Borden, Radar imaging of airborne targets: A primer for Applied mathematicians and Physicists . New York, NY: Taylor and... Project (0704–0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 21 September 2012 3. REPORT TYPE AND DATES COVERED...CW Continuous Wave DAC Digital to Analog Convertor DFT Discrete Fourier Transform FBP Filtered Back Projection FFT Fast Fourier Transform GPS

Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images

NASA Technical Reports Server (NTRS)

Generazio, E. R.

1986-01-01

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer-Indian Ocean METOC Imager (GIFTS-IOMI) Hyperspectral Data

DTIC Science & Technology

2002-09-30

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer-Indian Ocean METOC Imager ( GIFTS -IOMI) Hyperspectral Data...water quality assessment. OBJECTIVES The objective of this DoD research effort is to develop and demonstrate a fully functional GIFTS - IOMI...environment once GIFTS -IOMI is stationed over the Indian Ocean. The system will provide specialized methods for the characterization of the atmospheric

Passive Standoff Detection of Chemical Vapors by Differential FTIR Radiometry

DTIC Science & Technology

2001-01-01

8217 utilisation d’un interferometre infrarouge a transformation de Fourier (FTIR) a double entree optimise pour la soustraction optique. En vue de sa mise...Valcartier (DREV) is currently developing a passive Fourier Transform InfraRed (FTIR) technique for the standoff detection and identification of...chemical vapors. A well-known difficulty associated with this technique is that the recorded signal also contains a large amount of unwanted background

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

NASA Technical Reports Server (NTRS)

Lyubashevskiy, G. S.

1973-01-01

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

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

PubMed

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

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

An algorithm for the basis of the finite Fourier transform

NASA Technical Reports Server (NTRS)

Santhanam, Thalanayar S.

1995-01-01

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.

PubMed

Lange, K

1982-03-01

In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.

Parameter Estimation for the Blind Restoration of Blurred Imagery.

DTIC Science & Technology

1986-09-01

17 Noise Process .... ............. 23 Restoration Methods .... .......... 26 Inverse Filter .... ........... 26 Wiener Filter...of Eq. (155) ....... .................... ... 64 Table 2 Restored Pictures and Noise Variances ........ . 69 v 5𔃼 5- viq °,. r -’ .’S’ .N’% N...restoration system. g(x,y) Degraded image. G(u,v) Discrete Fourier Transform of the degraded image. n(x,y) Noise . N(u,v) Discrete Fourier transform of n

Fourier spectroscopy with a one-million-point transformation

NASA Technical Reports Server (NTRS)

Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.

1972-01-01

A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

NASA Astrophysics Data System (ADS)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

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

A VLSI architecture for simplified arithmetic Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.

1992-01-01

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

Santa Maria, Odilyn L.

1999-01-01

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

Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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

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

PubMed

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

2017-08-01

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