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.

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.

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

PubMed

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

2017-04-10

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

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

PubMed Central

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

2017-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2017-01-01

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

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.

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.

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.

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.

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

PubMed

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

2015-03-01

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

A Constant Percentage Bandwidth Transform for Acoustic Signal Processing

DTIC Science & Technology

1980-01-01

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

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

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

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net

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

A hybrid silicon membrane spatial light modulator for optical information processing

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Decision-feedback detection strategy for nonlinear frequency-division multiplexing

NASA Astrophysics Data System (ADS)

Civelli, Stella; Forestieri, Enrico; Secondini, Marco

2018-04-01

By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previously adopted techniques in terms of Q-factor. The obtained improvement demonstrates that, by tailoring the detection strategy to the peculiar properties of the nonlinear Fourier transform, it is possible to boost the performance of NFDM systems and overcome current limitations imposed by the use of more conventional detection techniques suitable for the linear regime.

(q,{mu}) and (p,q,{zeta})-exponential functions: Rogers-Szego'' polynomials and Fourier-Gauss transform

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

Hounkonnou, Mahouton Norbert; Nkouankam, Elvis Benzo Ngompe

2010-10-15

From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szego polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.

A practical Hadamard transform spectrometer for astronomical application

NASA Technical Reports Server (NTRS)

Tai, M. H.

1977-01-01

The mathematical properties of Hadamard matrices and their application to spectroscopy are discussed. A comparison is made between Fourier and Hadamard transform encoding in spectrometry. The spectrometer is described and its laboratory performance evaluated. The algorithm and programming of inverse transform are given. A minicomputer is used to recover the spectrum.

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.

Solubilization of spider silk proteins and its structural analysis using Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Osbin, K.; Jayan, Manuel; Bhadrakumari, S.; Predeep, P.

2017-06-01

This study investigates the presence of various amide bands present in different spider silk species, which provides extraordinary physical properties. Three different spider silks were collected from Western Ghats region. The collected spider silks samples belonging to the spider Heteropoda venatoria (species 1), Hersilia savignyi (species 2) and Pholcus phalangioides (species 3). Fourier transform infrared (FTIR) spectra reveals the protein peaks in the amide I, II, and III regions in all the three types of spider silk species.

Secret sharing based on quantum Fourier transform

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.

PubMed

Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai

2015-12-01

The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. Copyright © 2015 Elsevier Ltd. All rights reserved.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

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…

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.

A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis

NASA Technical Reports Server (NTRS)

Ioup, G. E.

1980-01-01

Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.

Trigonometric Transforms for Image Reconstruction

DTIC Science & Technology

1998-06-01

applying trigo - nometric transforms to image reconstruction problems. Many existing linear image reconstruc- tion techniques rely on knowledge of...ancestors. The research performed for this dissertation represents the first time the symmetric convolution-multiplication property of trigo - nometric...Fourier domain. The traditional representation of these filters will be similar to new trigo - nometric transform versions derived in later chapters

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

PubMed

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

2015-10-26

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

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

NASA Astrophysics Data System (ADS)

Bekkouche, Toufik; Bouguezel, Saad

2018-03-01

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

Application of the Ramanujan Fourier Transform for the analysis of secondary structure content in amino acid sequences.

PubMed

Mainardi, L T; Pattini, L; Cerutti, S

2007-01-01

A novel method is presented for the investigation of protein properties of sequences using Ramanujan Fourier Transform (RFT). The new methodology involves the preprocessing of protein sequence data by numerically encoding it and then applying the RFT. The RFT is based on projecting the obtained numerical series on a set of basis functions constituted by Ramanujan sums (RS). In RS components, periodicities of finite integer length, rather than frequency, (as in classical harmonic analysis) are considered. The potential of the new approach is documented by a few examples in the analysis of hydrophobic profiles of proteins in two classes including abundance of alpha-helices (group A) or beta-strands (group B). Different patterns are provided as evidence. RFT can be used to characterize the structural properties of proteins and integrate complementary information provided by other signal processing transforms.

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.

Ultrafast and versatile spectroscopy by temporal Fourier transform

NASA Astrophysics Data System (ADS)

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

2014-06-01

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

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.

Properties of starch-polyglutamic acid (PGA) graft copolymer prepared by microwave irradiation - Fourier transform infrared spectroscopy (FTIR) and rheology studies

USDA-ARS?s Scientific Manuscript database

The rheological properties of waxy starch-'-polygutamic acid (PGA) graft copolymers were investigated. Grafting was confirmed by FTIR spectroscopy. The starch-PGA copolymers absorbed water and formed gels, which exhibited concentration-dependent viscoelastic solid properties. Higher starch-PGA conce...

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

PubMed

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

2007-12-01

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

Quantum number theoretic transforms on multipartite finite systems.

PubMed

Vourdas, A; Zhang, S

2009-06-01

A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.

Conormal distributions in the Shubin calculus of pseudodifferential operators

NASA Astrophysics Data System (ADS)

Cappiello, Marco; Schulz, René; Wahlberg, Patrik

2018-02-01

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

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

Structure of Co-Doped Alq3 thin films investigated by grazing incidence X-ray absorption fine structure and Fourier transform infrared spectroscopy.

PubMed

Lin, Liang; Pang, Zhiyong; Fang, Shaojie; Wang, Fenggong; Song, Shumei; Huang, Yuying; Wei, Xiangjun; Yu, Haisheng; Han, Shenghao

2011-02-10

The structural properties of Co-doped tris(8-hydroxyquinoline)aluminum (Alq(3)) have been studied by grazing incidence X-ray absorption fine structure (GIXAFS) and Fourier transform infrared spectroscopy (FTIR). GIXAFS analysis suggests that there are multivalent Co-Alq(3) complexes and the doped Co atoms tend to locate at the attraction center with respect to N and O atoms and bond with them. The FTIR spectra indicate that the Co atoms interact with the meridional (mer) isomer of Alq(3) rather than forming inorganic compounds.

Quantitative determination of dimethicone in commercial tablets and capsules by Fourier transform infrared spectroscopy and antifoaming activity test.

PubMed

Torrado, G; García-Arieta, A; de los Ríos, F; Menéndez, J C; Torrado, S

1999-03-01

Fourier transform infrared (FTIR) spectroscopy and antifoaming activity test have been employed for the quantitative analysis of dimethicone. Linearity, accuracy and precision are presented for both methods. These methods have been also used to compare different dimethicone-containing proprietary medicines. FTIR spectroscopy has shown to be adequate for quantitation of dimethicone in commercial tablets and capsules in order to comply with USP requirements. The antifoaming activity test is able to detect incompatibilities between dimethicone and other constituents. The presence of certain enzymes in some medicinal products increases the defoaming properties of these formulations.

Nucleic Acid analysis by fourier transform ion cyclotron resonance mass spectrometry at the beginning of the twenty-first century.

PubMed

Frahm, J L; Muddiman, D C

2005-01-01

Mass spectrometers measure an intrinsic property (i.e., mass) of a molecule, which makes it an ideal platform for nucleic acid analysis. Importantly, the unparalleled capabilities of Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry further extend its usefulness for nucleic acid analysis. The beginning of the twenty-first century has been marked with notable advances in the field of FT-ICR mass spectrometry analysis of nucleic acids. Some of these accomplishments include fundamental studies of nucleic acid properties, improvements in sample clean up and preparation, better methods to obtain higher mass measurement accuracy, analysis of noncovalent complexes, tandem mass spectrometry, and characterization of peptide nucleic acids. This diverse range of studies will be presented herein.

Structural, chemical and physical properties of pure and La3+ doped L-Threonine acetate crystals

NASA Astrophysics Data System (ADS)

Senthamizhan, A.; Sambathkumar, K.; Nithiyanantham, S.; Venkatachalapathy, M.; Rajkamal, N.

2017-12-01

The pure and La3+ doped L- Threonine crystals can be grown by slow evaporation techniques. The crystal structure were examined through X-Ray diffraction (XRD) analysis, confirmed the P212121 system. The quantitative nature of dopant can be analyzed with Inductively Coupled Plasma (ICP) study. The Fourier Transform Infra-Red (FTIR) and Fourier Transform (FT- Raman) investigations yields the possible stretching/bonding with their functional groups and the qualitative/quantitative nature of both crystals is analyzed. The optical behavior of crystals can be studied through Ultra Violet (UV) - Visible spectrometer. The mechanical, thermal and decomposition studies can be carried out through Vickers hardness test, Thermo Gravometric Analysis (TGA) and Differential Thermal Analysis (DTA). The Non Linear Optical (NLO) properties are found more than Potassium Phosphate (KDP) through Kurtz powders technique. The dielectric and optical absorption studies for both pure and L-doped crystals were studied and interpreted all the properties. The La3+ dopant increases the properties are investigated.

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.

A new fractional wavelet transform

NASA Astrophysics Data System (ADS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

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

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

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2010-02-01

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

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.

Fourier transform spectra of quantum dots

NASA Astrophysics Data System (ADS)

Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.

2009-09-01

Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.

Fourier transform spectra of quantum dots

NASA Astrophysics Data System (ADS)

Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.

2010-05-01

Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.

Influence of site and soil properties on the DRIFT spectra of northern cold-region soils

USDA-ARS?s Scientific Manuscript database

We investigated the influence of site characteristics and soil properties on the chemical composition of organic matter in soils collected from a latitudinal transect across Alaska through analysis of diffuse reflectance infrared Fourier transform mid infrared (MidIR) spectra of bulk soils. The stud...

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

DTIC Science & Technology

1983-05-31

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

Propagation properties of hollow sinh-Gaussian beams through fractional Fourier transform optical systems

NASA Astrophysics Data System (ADS)

Tang, Bin; Jiang, ShengBao; Jiang, Chun; Zhu, Haibin

2014-07-01

A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping.

[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.

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.

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.

Symmetric convolution of asymmetric multidimensional sequences using discrete trigonometric transforms.

PubMed

Foltz, T M; Welsh, B M

1999-01-01

This paper uses the fact that the discrete Fourier transform diagonalizes a circulant matrix to provide an alternate derivation of the symmetric convolution-multiplication property for discrete trigonometric transforms. Derived in this manner, the symmetric convolution-multiplication property extends easily to multiple dimensions using the notion of block circulant matrices and generalizes to multidimensional asymmetric sequences. The symmetric convolution of multidimensional asymmetric sequences can then be accomplished by taking the product of the trigonometric transforms of the sequences and then applying an inverse trigonometric transform to the result. An example is given of how this theory can be used for applying a two-dimensional (2-D) finite impulse response (FIR) filter with nonlinear phase which models atmospheric turbulence.

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

MULTISPECTRAL IDENTIFICATION OF POTENTIALLY HAZARDOUS BYPRODUCTS OF OZONATION AND CHLORINATION - PART I: STUDIES OF CHROMATOGRAPHIC AND SPECTROSCOPIC PROPERTIES OF MX

EPA Science Inventory

The gas chromatographic (GC) and Fourier transform infrared and mass spectroscopic (FT-IR and MS, respectively) properties of (Z)-2-chloro-3-(dichloromethyl)4-oxobutenoic acid (MX) (a highly mutagenic byproduct of drinking water chlorination) and several related compounds were st...

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

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

Structural and magnetic properties of nanocrystalline NiFe2O4 thin film prepared by spray pyrolysis technique

NASA Astrophysics Data System (ADS)

Chavan, Apparao R.; Chilwar, R. R.; Shisode, M. V.; Hivrekar, Mahesh M.; Mande, V. K.; Jadhav, K. M.

2018-05-01

The nanocrystalline NiFe2O4 thin film has been prepared using a spray pyrolysis technique on glass substrate. The prepared thin film was characterized by using X-ray diffraction (XRD), Fourier transform Infrared spectroscopy (FTIR), and Field Emission-Scanning Electron Microscopy (FE-SEM) characterization techniques for the structural and microstructural analysis. The magnetic property was measured using vibrating sample magnetometer (VSM) at room temperature. X-ray diffraction studies show the formation of single phase spinel structure of the thin film. The octahedral and tetrahedral vibration in the sample was studied by Fourier transform infrared (FT-IR) spectra. Magnetic hysteresis loop was recorded for thin film at room temperature. At 15 kOe, saturation magnetization (Ms) was found to increase while coercivity (Hc) decreases with thickness of the NiFe2O4 thin film.

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

Analysis of the physicochemical properties of post-manufacturing waste derived from production of methyl esters from rapeseed oil

NASA Astrophysics Data System (ADS)

Kachel-Jakubowska, Magdalena; Matwijczuk, Arkadiusz; Gagoś, Mariusz

2017-04-01

The technology of transesterification of biodiesel obtained from many agricultural products, which are often referred to as renewable resources, yields substantial amounts of by-products. They exhibit various properties that prompt scientific research into potential application thereof. Various spectroscopic methods, e.g. Fourier transform infrared spectroscopy, are being increasingly used in the research. In this paper, we present the results of Fourier transform infrared spectroscopy spectroscopy analyses of technical glycerine, distilled glycerine, and matter organic non glycerol, i.e. by-products of biodiesel production. To facilitate the spectroscopic analysis, a number of parameters were determined for all the materials, e.g. the calorific value, water content, sulphated ash content, methanol content, acidity, as well as the contents of esters, heavy metals, aldehydes, nitrogen, and phosphorus. The results indicate that the analysed products are characterised by a comparable calorific value in the range from 11.35 to 16.05 MJ kg-1 in the case of matter organic non glycerol and technical glycerine. Observation of changes in the position of selected peaks in the range of 3700-650 cm-1 in the Fourier transform infrared spectroscopy method facilitates determination of the level of degradation of the analysed material. Changes in the wavelength ranges can be used for monitoring the formation of secondary oxidation products containing carbonyl groups.

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.

Structural, spectral and birefringence studies of semiorganic nonlinear optical single crystal: Calcium5-sulfosalicylate

NASA Astrophysics Data System (ADS)

Shalini, D.; Kalainathan, S.; Ambika, V. Revathi; Hema, N.; Jayalakshmi, D.

2017-11-01

Semi-organic nonlinear optical crystal Calcium5-Sulfosalicylate (CA5SS) was grown by slow evaporation solution growth technique. The cell parameters and molecular structure of the grown crystal were studied by single crystal x-ray diffraction analysis. The presence of various functional groups of the grown crystal was confirmed using Fourier transform infrared (FT-IR), Fourier transform Raman (FT-Raman) analysis. UV-Visible spectrum shows that CA5SS crystals have high transmittance in the range of 330-900 nm. The refractive index, birefringence and transient photoluminescence properties of the grown crystal were analyzed. The frequency doubling of the grown crystal (CA5SS) were studied and compared with that of KDP.

One- and two-center ETF-integrals of first order in relativistic calculation of NMR parameters

NASA Astrophysics Data System (ADS)

Slevinsky, R. M.; Temga, T.; Mouattamid, M.; Safouhi, H.

2010-06-01

The present work focuses on the analytical and numerical developments of first-order integrals involved in the relativistic calculation of the shielding tensor using exponential-type functions as a basis set of atomic orbitals. For the analytical development, we use the Fourier integral transformation and practical properties of spherical harmonics and the Rayleigh expansion of the plane wavefunctions. The Fourier transforms of the operators were derived in previous work and they are used for analytical development. In both the one- and two-center integrals, Cauchy's residue theorem is used in the final developments of the analytical expressions, which are shown to be accurate to machine precision.

Ion beam modification of the structure and properties of hexagonal boron nitride: An infrared and X-ray diffraction study

NASA Astrophysics Data System (ADS)

Aradi, E.; Naidoo, S. R.; Billing, D. G.; Wamwangi, D.; Motochi, I.; Derry, T. E.

2014-07-01

The vibrational mode for the cubic symmetry of boron nitride (BN) has been produced by boron ion implantation of hexagonal boron nitride (h-BN). The optimum fluence at 150 keV was found to be 5 × 1014 ions/cm2. The presence of the c-BN phase was inferred using glancing incidence XRD (GIXRD) and Fourier Transform Infrared Spectroscopy (FTIR). After implantation, Fourier Transform Infrared Spectroscopy indicated a peak at 1092 cm-1 which corresponds to the vibrational mode for nanocrystalline BN (nc-BN). The glancing angle XRD pattern after implantation exhibited c-BN diffraction peaks relative to the implantation depth of 0.4 μm.

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

PubMed

Hanson, Jeffery A; Yang, Haw

2008-06-07

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

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

PubMed

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

2018-03-14

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

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.

Multichannel Compressive Sensing MRI Using Noiselet Encoding

PubMed Central

Pawar, Kamlesh; Egan, Gary; Zhang, Jingxin

2015-01-01

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

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.

Increasing the quantitative credibility of open-path FT-IR spectroscopic data with focus on several properties of the background spectrum

USDA-ARS?s Scientific Manuscript database

The choice of the type of background spectrum affects the credibility of open-path Fourier transform infrared (OP/FT-IR) spectroscopic data, and consequently the quality of data analysis. We systematically investigated several properties of the background spectrum. The results show that a short-pa...

The Radon cumulative distribution transform and its application to image classification

PubMed Central

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

2016-01-01

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

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

The characterization of hydroxypropyl methylcellulose through the analysis of its substituents

USDA-ARS?s Scientific Manuscript database

The methyl and hydroxypropyl substituents in hydroxypropyl methylcellulose (HPMC) affect the resulting gel properties. These substituents in five HPMC gels were characterized using Fourier transform infrared spectroscopy (FT-IR), Raman spectroscopy, small-amplitude oscillatory shear measurements, a...

Holographic optical elements: Fabrication and testing

NASA Technical Reports Server (NTRS)

Zech, R. G.; Shareck, M.; Ralston, L. M.

1974-01-01

The basic properties and use of holographic optical elements were investigated to design and construct wide-angle, Fourier-transform holographic optical systems for use in a Bragg-effect optical memory. The performance characteristics are described along with the construction of the holographic system.

[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.

Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes

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

Javaloyes, J., E-mail: julien.javaloyes@uib.es; Balle, S.

2015-10-01

This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of broad-area laser diodes and amplifiers. This spectral method can be used in combination with the delay algebraic equations approach developed in [1], which substantially reduces the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in [2] as a particular case. It is also extended to the consideration of index guiding with an arbitrary transverse profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allowmore » handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model.« less

Rainbow Fourier Transform

NASA Technical Reports Server (NTRS)

Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.

2012-01-01

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Influence of Surface Modification on the Microstructure and Thermo-Mechanical Properties of Bamboo Fibers

PubMed Central

Zhang, Xiaoping; Wang, Fang; Keer, Leon M.

2015-01-01

The objective of this study is to investigate the effect of surface treatment on the morphology and thermo-mechanical properties of bamboo fibers. The fibers are subjected to an alkali treatment using 4 wt % sodium hydroxide (NaOH) for 1 h. Mechanical measurements show that the present concentration has an insignificant effect on the fiber tensile strength. In addition, systematic experimental results characterizing the morphological aspects and thermal properties of the bamboo fibers are analyzed by scanning electron microscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis, and differential scanning calorimetry. It is found that an alkali treatment may increase the effective surface area, which is in turn available for superior bonding with the matrix. Fourier transform infrared spectroscopy analysis reveals that the alkali treatment leads to a gradual removal of binding materials, such as hemicellulose and lignin from the bamboo fiber. A comparison of the curve of thermogravimetric analysis and differential scanning calorimetry for the treated and untreated samples is presented to demonstrate that the presence of treatment contributes to a better thermal stability for bamboo fibers. PMID:28793585

Gas sensing properties and in situ diffuse reflectance infrared Fourier transform spectroscopy study of trichloroethylene adsorption and reactions on SnO2 films

NASA Astrophysics Data System (ADS)

Zhang, Zhenxin; Huang, Kaijin; Yuan, Fangli; Xie, Changsheng

2014-05-01

The detection of trichloroethylene has attracted much attention because it has an important effect on human health. The sensitivity of the SnO2 flat-type coplanar gas sensor arrays to 100 ppm trichloroethylene in air was investigated. The adsorption and surface reactions of trichloroethylene were investigated at 100-200 °C by in-situ diffuse reflection Fourier transform infrared spectroscopy (DIRFTS) on SnO2 films. Molecularly adsorbed trichloroethylene, dichloroacetyl chloride (DCAC), phosgene, HCl, CO, H2O, CHCl3, Cl2 and CO2 surface species are formed during trichloroethylene adsorption at 100-200 °C. A possible mechanism of the reaction process is discussed.

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

Campos, Rafael G.; Tututi, Eduardo S.

We study the Schwinger model on a lattice constructed from zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the correct value of the mass in the asymptotic limit.

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.

Effect of temperature on the magnetic properties of nano-sized M-type barium hexagonal ferrites

NASA Astrophysics Data System (ADS)

Tchouank Tekou Carol, T.; Sharma, Jyoti; Mohammed, J.; Kumar, Sachin; Srivastava, A. K.

2017-07-01

The application of M-type hexagonal ferrites in electronic devices is increasing with technological advancement. This is due to the possibility of improving the physical and magnetic properties to suit the desired application. Enhanced magnetic properties make hexagonal ferrites suitable for hyper frequency and radar absorbing application. In this paper, we investigated the effect of heat-treatment temperature on the structural and magnetic properties of M-type barium hexagonal ferrites with chemical composition Ba1-xAlxFe12-yMnyO19 (x=0.6 and y=0.3) synthesized by sol-gel auto-combustion method and sintered at 750°C, 850°C, 950°C and 1050°C. Characterisations of the prepared samples were done using Fourier transform-infrared (FT-IR), and vibrating sample magnetometer (VSM). The formation of M-type hexaferrite has been confirmed from XRD. The presence of two prominent peaks between 400 cm-1 and 600 cm-1 in the spectra of Fourier transform-infrared spectroscopy (FT-IR) also shows the formation of ferrite phase. Saturation magnetisation (MS), remnant magnetisation (Mr), coercivity (Hc) and squareness ratio (SR) were calculated from the M-H loop obtained from vibrating sample magnetometer (VSM).

Morphology, Mechanical and Thermal Properties of Thermoplastic Polyurethane Containing Reduced Graphene Oxide and Graphene Nanoplatelets.

PubMed

Strankowski, Michał; Korzeniewski, Piotr; Strankowska, Justyna; A S, Anu; Thomas, Sabu

2018-01-06

Polyurethane/graphene nanocomposites were synthesized using commercial thermoplastic polyurethane (TPU, Apilon 52DE55), and two types of graphene derivatives: graphene nanoplatelets (GNP) and reduced graphene oxide (RGO). Fourier Transformation Infrared Spectroscopy Fourier Transformation Infrared Spectroscopy (FTIR) spectroscopy, TEM, and SEM microscopy and XRD techniques were used to chemically and structurally characterize GNP and RGO nanofillers. The properties of the new TPU nanocomposite materials were studied using thermal analysis techniques (Dynamical Mechanical Analysis (DMA), Differential Scanning Calorimetry (DSC), Thermogravimetric Analysis (TG)) to describe the influence of graphene nanofillers on polyurethane matrix. Our investigation describes the comparison of two types of graphene derivatives, commercial one (GNP) and synthesized (RGO) on thermoplastic polyurethanes. These nanofillers provides opportunities to achieve compatibility with the TPU matrix. The property enhancements are attributed commonly to high aspect ratio of graphene nanoplatelets and filler-polymer interactions at the interface. The obtained nanocomposites exhibit higher thermal and mechanical properties due to the good dispersion of both nanofillers into TPU matrix. It was found that the addition of 2 wt % of the nanofiller could lead to a significant reinforcement effect on the TPU matrix. Also, with high content of nanofiller (GNP and RGO), the Payne effect was observed.

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

PubMed

Gao, W; Wu, X

2017-11-01

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

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.

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.

Light scattering properties of kidney epithelial cells and nuclei

NASA Astrophysics Data System (ADS)

Vitol, Elina A.; Kurzweg, Timothy P.; Nabet, Bahram

2006-02-01

Enlargement of mammalian cells nuclei due to the cancerous inflammation can be detected early through noninvasive optical techniques. We report on the results of cellular experiments, aimed towards the development of a fiber optic endoscopic probe used for precancerous detection of Barrett's esophagus. We previously presented white light scattering results from tissue phantoms (polystyrene polybead microspheres). In this paper, we discuss light scattering properties of epithelial MDCK (Madine-Darby Canine Kidney) cells and cell nuclei suspensions. A bifurcated optical fiber is used for experimental illumination and signal detection. The resulting scattering spectra from the cells do not exhibit the predicted Mie theory oscillatory behavior inherent to ideally spherical scatterers, such as polystyrene microspheres. However, we are able to demonstrate that the Fourier transform spectra of the cell suspensions are well correlated with the Fourier transform spectra of cell nuclei, concluding that the dominate scatterer in the backscattering region is the nucleus. This correlation experimentally illustrates that in the backscattering region, the cell nuclei are the main scatterer in the cells of the incident light.

Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems

NASA Astrophysics Data System (ADS)

Leuschner, Matthias; Fritzen, Felix

2017-11-01

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

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.

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

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2009-02-01

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

Characterization of interaction between natural rubber and silica by FTIR

NASA Astrophysics Data System (ADS)

Jarnthong, Methakarn; Liao, Lusheng; Zhang, Fuquan; Wang, Yueqiong; Li, Puwang; Peng, Zheng; Malawet, Chutarat; Intharapat, Punyanich

2017-05-01

Blending of natural rubber (NR) and nanosilica (SiO2) was performed in latex state. The mechanical properties of NR/SiO2 nanocomposites at various filler contents were investigated. The interactions of unvulcanized natural rubber and nanosilica filler were characterized using Fourier Transform Infrared (FTIR)-Attenuated Total Reflectance (ATR) spectroscopy. The relationship between mechanical properties and rubber-filler interaction was discussed.

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

Modification of wheat gluten with citric acid to produce superabsorbent materials

USDA-ARS?s Scientific Manuscript database

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

Comparative properties of cellulose nano-crystals from native and mercerized cotton fibers

USDA-ARS?s Scientific Manuscript database

Stable aqueous suspensions of cellulose nano-crystals (CNCs) were fabricated from both native and mercerized cotton fibers by sulfuric acid hydrolysis, followed by high-pressure homogenization. Fourier Transform Infrared Spectrometry and Wide-angle X-Ray Diffraction data showed that the fibers had b...

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.

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

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

2011-01-01

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

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

The gamma irradiation effects on structural and optical properties of silk fibroin/HPMC blend films

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

Shetty, G. Rajesha; Rao, B. Lakshmeesha; Gowda, Mahadeva

In this paper the structural, chemical and optical properties of gamma irradiated silk fibroin/Hydroxypropyl methyl cellulose (SF-HPMC) blend films were studied using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and UV-visible spectroscopy. The results indicate that the gamma radiation did not affect significantly the primary structure of polypeptide arrangement in the blend films. But the optical properties of the blends changed with gamma irradiation dosage.

Synthesis and electrochemical properties of polyaniline nanofibers by interfacial polymerization.

PubMed

Manuel, James; Ahn, Jou-Hyeon; Kim, Dul-Sun; Ahn, Hyo-Jun; Kim, Ki-Won; Kim, Jae-Kwang; Jacobsson, Per

2012-04-01

Polyaniline nanofibers were prepared by interfacial polymerization with different organic solvents such as chloroform and carbon tetrachloride. Field emission scanning electron microscopy and transmission electron microscopy were used to study the morphological properties of polyaniline nanofibers. Chemical characterization was carried out using Fourier transform infrared spectroscopy, UV-Vis spectroscopy, and X-ray diffraction spectroscopy and surface area was measured using BET isotherm. Polyaniline nanofibers doped with lithium hexafluorophosphate were prepared and their electrochemical properties were evaluated.

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

Galant, David C.

1992-01-01

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

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.

Modification of vital wheat gluten with phosphoric acid to produce high free-solution capacity

USDA-ARS?s Scientific Manuscript database

Wheat gluten reacts with phosphoric acid to produce natural superabsorbent gels. The gel properties are defined by Fourier Transform Infra-red (FTIR) spectroscopy, 2-dimensional gel electrophoresis (2DE), and uptake of water, salt solutions, and aqueous ethanol. Temperatures above 120'C and dry cond...

Acoustic Analysis of Chinese Fricatives and Affricates.

ERIC Educational Resources Information Center

Svantesson, Jan-Olof

1986-01-01

Develops a method of analyzing and describing the acoustic properties of fricatives, which consists of making frequency spectra using the Fast Fourier Transform and then analyzing the spectra in terms of critical bands. The six fricatives of Chinese are analyzed by this method, and comparison with other languages is made. (SED)

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.

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.

Application of Multivariable Analysis and FTIR-ATR Spectroscopy to the Prediction of Properties in Campeche Honey

PubMed Central

Pat, Lucio; Ali, Bassam; Guerrero, Armando; Córdova, Atl V.; Garduza, José P.

2016-01-01

Attenuated total reflectance-Fourier transform infrared spectrometry and chemometrics model was used for determination of physicochemical properties (pH, redox potential, free acidity, electrical conductivity, moisture, total soluble solids (TSS), ash, and HMF) in honey samples. The reference values of 189 honey samples of different botanical origin were determined using Association Official Analytical Chemists, (AOAC), 1990; Codex Alimentarius, 2001, International Honey Commission, 2002, methods. Multivariate calibration models were built using partial least squares (PLS) for the measurands studied. The developed models were validated using cross-validation and external validation; several statistical parameters were obtained to determine the robustness of the calibration models: (PCs) optimum number of components principal, (SECV) standard error of cross-validation, (R 2 cal) coefficient of determination of cross-validation, (SEP) standard error of validation, and (R 2 val) coefficient of determination for external validation and coefficient of variation (CV). The prediction accuracy for pH, redox potential, electrical conductivity, moisture, TSS, and ash was good, while for free acidity and HMF it was poor. The results demonstrate that attenuated total reflectance-Fourier transform infrared spectrometry is a valuable, rapid, and nondestructive tool for the quantification of physicochemical properties of honey. PMID:28070445

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

Morphology, Mechanical and Thermal Properties of Thermoplastic Polyurethane Containing Reduced Graphene Oxide and Graphene Nanoplatelets

PubMed Central

Korzeniewski, Piotr; Strankowska, Justyna; A. S., Anu; Thomas, Sabu

2018-01-01

Polyurethane/graphene nanocomposites were synthesized using commercial thermoplastic polyurethane (TPU, Apilon 52DE55), and two types of graphene derivatives: graphene nanoplatelets (GNP) and reduced graphene oxide (RGO). Fourier Transformation Infrared Spectroscopy Fourier Transformation Infrared Spectroscopy (FTIR) spectroscopy, TEM, and SEM microscopy and XRD techniques were used to chemically and structurally characterize GNP and RGO nanofillers. The properties of the new TPU nanocomposite materials were studied using thermal analysis techniques (Dynamical Mechanical Analysis (DMA), Differential Scanning Calorimetry (DSC), Thermogravimetric Analysis (TG)) to describe the influence of graphene nanofillers on polyurethane matrix. Our investigation describes the comparison of two types of graphene derivatives, commercial one (GNP) and synthesized (RGO) on thermoplastic polyurethanes. These nanofillers provides opportunities to achieve compatibility with the TPU matrix. The property enhancements are attributed commonly to high aspect ratio of graphene nanoplatelets and filler–polymer interactions at the interface. The obtained nanocomposites exhibit higher thermal and mechanical properties due to the good dispersion of both nanofillers into TPU matrix. It was found that the addition of 2 wt % of the nanofiller could lead to a significant reinforcement effect on the TPU matrix. Also, with high content of nanofiller (GNP and RGO), the Payne effect was observed. PMID:29316638

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.

Spectral properties of the massless relativistic quartic oscillator

NASA Astrophysics Data System (ADS)

Durugo, Samuel O.; Lőrinczi, József

2018-03-01

An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

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

PubMed

Capus, Chris; Brown, Keith

2003-06-01

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

Attenuated Total Reflection Fourier Transform Infrared Spectroscopy (ATR FT-IR) Applied to Study the Distribution of Ink Components in Printed Newspapers.

PubMed

Gómez, Nuria; Molleda, Cristina; Quintana, Ester; Carbajo, José M; Rodríguez, Alejandro; Villar, Juan C

2016-09-01

A new method was developed to study how the oil and cyan pigments of cold-set ink are distributed in newspaper thickness. The methodology involved laboratory printing followed by delamination of the printed paper. The unprinted side, printed side, and resulting layers were analyzed using attenuated total reflection Fourier transform infrared spectroscopy (ATR FT-IR). Three commercial newspapers and black and cyan cold-set inks were chosen for the study. Attenuated total reflection Fourier transform infrared spectroscopy enabled the proportion of oil and cyan pigment on the printed surface and throughout the sheet thickness to be measured. Oil percentage was evaluated as the area increment of the region from 2800 cm(-1) to 3000 cm(-1) The relative amount of cyan pigment was determined as the area of the absorption band at 730 cm(-1) The ink oil was found mainly below half the paper thickness, whereas the pigment was detected at the layers closer to the printed surface, at a depth penetration of less than 15 µm (20% of thickness). Distribution of these two components in paper thickness depended on the type of cold-set ink, the amount of ink transferred, and the newspaper properties. © The Author(s) 2016.

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

Study of Lamb Waves for Non-Destructive Testing Behind Screens

NASA Astrophysics Data System (ADS)

Kauffmann, P.; Ploix, M.-A.; Chaix, J.-F.; Gueudré, C.; Corneloup, G.; Baqué, F. AF(; )

2018-01-01

The inspection and control of sodium-cooled fast reactors (SFR) is a major issue for the nuclear industry. Ultrasonic solutions are under study because of the opacity of liquid sodium. In this paper, the use of leaky Lamb waves is considered for non-destructive testing (NDT) on parallel and immersed structures assimilated as plates. The first phase of our approach involved studying the propagation properties of leaky Lamb waves. Equations that model the propagation of Lamb waves in an immersed plate were solved numerically. The phase velocity can be experimentally measured using a two dimensional Fourier transform. The group velocity can be experimentally measured using a short-time Fourier transform technique. Attenuation of leaky Lamb waves is mostly due to the re-emission of energy into the surrounding fluid, and it can be measured by these two techniques.

Non linear optical studies on semiorganic single crystal: L-arginine 4-nitrophenalate 4-nitrophenol dihydrate (LAPP)

NASA Astrophysics Data System (ADS)

Mahadevan, M.; Sankar, P. K.; Vinitha, G.; Arivanandhan, M.; Ramachandran, K.; Anandan, P.

2017-07-01

L-arginine 4-nitrophenalate 4-nitrophenol dihydrate (LAPP) has been synthesized and grown by solution growth at room temperature using deionized water as a solvent. The various functional groups of the sample were identified by Fourier transform infra-red and Fourier transforms - Raman spectroscopic analyses. The Laser damage threshold of LAPP has been studied. Refractive index of LAPP single crystal was measured using Metricon prism coupler Instrument. The etching studies were carried out to study the quality of the grown crystals. The third order nonlinear optical properties of LAPP sample was analyzed by the Z-scan technique using 532 nm diode pumped CW Nd: YAG laser. The LAPP material exhibits negative optical nonlinearity. The results show that LAPP sample has potential applications in nonlinear optics and it can be exploited for optical limiting or switching.

Synthesis, crystal structure, vibrational spectra and theoretical calculations of quantum chemistry of a potential antimicrobial Meldrum's acid derivative

NASA Astrophysics Data System (ADS)

Campelo, M. J. M.; Freire, P. T. C.; Mendes Filho, J.; de Toledo, T. A.; Teixeira, A. M. R.; da Silva, L. E.; Bento, R. R. F.; Faria, J. L. B.; Pizani, P. S.; Gusmão, G. O. M.; Coutinho, H. D. M.; Oliveira, M. T. A.

2017-10-01

A new derivative of Meldrum's acid 5-((5-chloropyridin-2-ylamino)methylene)-2,2-dimethyl-1,3-dioxane-4,6-dione (CYMM) of molecular formula C12H11ClN2O4 was synthesized and structurally characterized using single crystal X-ray diffraction technique. The vibrational properties of the crystal were studied by Fourier Transform infrared (FT-IR), Fourier Transform Raman (FT-Raman) techniques and theoretical calculations of quantum chemistry using Density functional theory (DFT) and Density functional perturbation theory (DFPT). A comparison with experimental spectra allowed the assignment of all the normal modes. The descriptions of the normal modes were carried by means of potential energy distribution (PED). Additionally, analysis of the antimicrobial activity and antibiotic resistance modulatory activity was carried out to evaluate the antibacterial potential of the CYMM.

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.

Loading of halloysite nanotubes with BSA, α-Lac and β-Lg: a Fourier transform infrared spectroscopic and thermogravimetric study

NASA Astrophysics Data System (ADS)

Duce, Celia; Della Porta, Valentina; Bramanti, Emilia; Campanella, Beatrice; Spepi, Alessio; Tiné, Maria Rosaria

2017-02-01

Halloysite nanotubes (HNTs) are considered as ideal materials for biotechnological and medical applications. An important feature of halloysite is that it has a different surface chemistry on the inner and outer sides of the tubes. This property means that negatively-charged molecules can be selectively loaded inside the halloysite nanoscale its lumen. Loaded HNTs can be used for the controlled or sustained release of proteins, drugs, bioactive molecules and other agents. We studied the interaction between HNTs and bovine serum albumin, α lactalbumin and β -lactoglobulin loaded into HTNs using Fourier transform infrared spectroscopy and thermogravimetry. These techniques enabled us to study the protein conformation and thermal stability, respectively, and to estimate the amount of protein loaded into the HNTs. TEM images confirmed the loading of proteins into HTNs.

Discrete cosine and sine transforms generalized to honeycomb lattice

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Motlochová, Lenka

2018-06-01

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The honeycomb point sets are constructed by subtracting the root lattice from the weight lattice points of the crystallographic root system A2. The two-variable orbit functions of the Weyl group of A2, discretized simultaneously on the weight and root lattices, induce a novel parametric family of extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Three types of discrete complex Fourier-Weyl transforms and real-valued Hartley-Weyl transforms are described. Unitary transform matrices and interpolating behavior of the discrete transforms are exemplified. Consequences of the developed discrete transforms for transversal eigenvibrations of the mechanical graphene model are discussed.

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.

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

PubMed

Kim, Jaehee

2011-01-01

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

Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

NASA Astrophysics Data System (ADS)

Kuhlman, K. L.; Neuman, S. P.

2006-12-01

Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow. LT-AEM applies the traditionally steady-state AEM to the Laplace transformed groundwater flow equation, and back-transforms the resulting solution to the time domain using a Fourier Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have extended the method so it can compute hydraulic head and flow velocity distributions due to any two-dimensional combination and arrangement of point, line, circular and elliptical area sinks and sources, nested circular or elliptical regions having different hydraulic properties, and areas of specified head, flux or initial condition. The strengths of all sinks and sources, and the specified head and flux values, can all vary in both space and time in an independent and arbitrary fashion. Initial conditions may vary from one area element to another. A solution is obtained by matching heads and normal fluxes along the boundary of each element. The effect which each element has on the total flow is expressed in terms of generalized Fourier series which converge rapidly (<20 terms) in most cases. As there are more matching points than unknown Fourier terms, the matching is accomplished in Laplace space using least-squares. The method is illustrated by calculating the resulting transient head and flow velocities due to an arrangement of elements in both finite and infinite domains. The 2D LT-AEM elements already developed and implemented are currently being extended to solve the 3D groundwater flow equation.

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.

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

USDA-ARS?s Scientific Manuscript database

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

Surface characterization of weathered wood-plastic composites produced from modified wood flour

Treesearch

James S. Fabiyi; Armando G. McDonald; Nicole M. Stark

2007-01-01

The effects of weathering on the surface properties of wood-plastic composites (WPC) were examined. High-density polyethylene (HDPE) based WPCs made from modified wood flour (untreated, extractives free, and holocellulose (delignified) fibers) were subjected to accelerated (xenon-arc) weathering. Colorimetry and Fourier-transform infrared spectroscopy were employed to...

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…

Infrared spectral properties of germ, pericarp, and endosperm sections of sound wheat kernels and those damaged by Fusarium graminearum

USDA-ARS?s Scientific Manuscript database

Mid-infrared attenuated total reflectance (MIR-ATR) spectra (4000-380 cm-1) of pericarp, germ, and endosperm sections from sound and Fusarium-damaged wheat kernels of cultivars Everest and Tomahawk were collected using a Fourier Transform Infrared (FTIR) spectrometer. The differences in infrared abs...

Modulation of anisotropy in electrospun tissue-engineering scaffolds: Analysis of fiber alignment by the fast Fourier transform

PubMed Central

Ayres, Chantal; Bowlin, Gary L.; Henderson, Scott C.; Taylor, Leander; Shultz, Jackie; Alexander, John; Telemeco, Todd A.; Simpson, David G.

2010-01-01

We describe the use of the fast Fourier transform (FFT) in the measurement of anisotropy in electrospun scaffolds of gelatin as a function of the starting conditions. In electrospinning, fiber alignment and overall scaffold anisotropy can be manipulated by controlling the motion of the collecting mandrel with respect to the source electrospinning solution. By using FFT to assign relative alignment values to an electrospun matrix it is possible to systematically evaluate how different processing variables impact the structure and material properties of a scaffold. Gelatin was suspended at varying concentrations (80, 100, 130, 150 mg/ml) and electrospun from 2,2,2 trifluoroethanol onto rotating mandrels (200–7000 RPM). At each starting concentration, fiber diameter remained constant over a wide range of mandrel RPM. Scaffold anisotropy developed as a function of fiber diameter and mandrel RPM. The induction of varying degrees of anisotropy imparted distinctive material properties to the electrospun scaffolds. The FFT is a rapid method for evaluating fiber alignment in tissue-engineering materials. PMID:16859744

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.

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.

Extracting oscillation frequencies from sparse spectra: Fourier analysis

NASA Astrophysics Data System (ADS)

Jerzykiewicz, M.

2008-12-01

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

Terahertz optical properties of nonlinear optical CdSe crystals

NASA Astrophysics Data System (ADS)

Yan, Dexian; Xu, Degang; Li, Jining; Wang, Yuye; Liang, Fei; Wang, Jian; Yan, Chao; Liu, Hongxiang; Shi, Jia; Tang, Longhuang; He, Yixin; Zhong, Kai; Lin, Zheshuai; Zhang, Yingwu; Cheng, Hongjuan; Shi, Wei; Yao, Jianquan; Wu, Yicheng

2018-04-01

We investigate the optical properties of cadmium selenide (CdSe) crystals in a wide terahertz (THz) range from 0.2 to 6 THz by THz time-domain spectroscopy (THz-TDS) and Fourier transform infrared spectroscopy (FTIR). The refractive index, absorption coefficient and transmittance are measured and analyzed. The properties are characterized by several absorption peaks which represent the relevant phonon vibrations modes. The experimental results are in agreement with the theoretical results. The dispersion and absorption properties of CdSe crystal are analyzed in THz range. These properties indicate a good potential for THz sources and THz modulated devices.

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.

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

DTIC Science & Technology

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

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

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

PubMed

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

2010-03-01

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

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...

Propagation of a general-type beam through a truncated fractional Fourier transform optical system.

PubMed

Zhao, Chengliang; Cai, Yangjian

2010-03-01

Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

Molecular structure, vibrational spectral assignments (FT-IR and FT-RAMAN), NMR, NBO, HOMO-LUMO and NLO properties of O-methoxybenzaldehyde based on DFT calculations

NASA Astrophysics Data System (ADS)

Vennila, P.; Govindaraju, M.; Venkatesh, G.; Kamal, C.

2016-05-01

Fourier transform - Infra red (FT-IR) and Fourier transform - Raman (FT-Raman) spectroscopic techniques have been carried out to analyze O-methoxy benzaldehyde (OMB) molecule. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT). The vibrational analysis of stable isomer of OMB has been carried out by FT-IR and FT-Raman in combination with theoretical method simultaneously. The first-order hyperpolarizability and the anisotropy polarizability invariant were computed by DFT method. The atomic charges, hardness, softness, ionization potential, electronegativity, HOMO-LUMO energies, and electrophilicity index have been calculated. The 13C and 1H Nuclear magnetic resonance (NMR) have also been obtained by GIAO method. Molecular electronic potential (MEP) has been calculated by the DFT calculation method. Electronic excitation energies, oscillator strength and excited states characteristics were computed by the closed-shell singlet calculation method.

Intra-pulse modulation recognition using short-time ramanujan Fourier transform spectrogram

NASA Astrophysics Data System (ADS)

Ma, Xiurong; Liu, Dan; Shan, Yunlong

2017-12-01

Intra-pulse modulation recognition under negative signal-to-noise ratio (SNR) environment is a research challenge. This article presents a robust algorithm for the recognition of 5 types of radar signals with large variation range in the signal parameters in low SNR using the combination of the Short-time Ramanujan Fourier transform (ST-RFT) and pseudo-Zernike moments invariant features. The ST-RFT provides the time-frequency distribution features for 5 modulations. The pseudo-Zernike moments provide invariance properties that are able to recognize different modulation schemes on different parameter variation conditions from the ST-RFT spectrograms. Simulation results demonstrate that the proposed algorithm achieves the probability of successful recognition (PSR) of over 90% when SNR is above -5 dB with large variation range in the signal parameters: carrier frequency (CF) for all considered signals, hop size (HS) for frequency shift keying (FSK) signals, and the time-bandwidth product for Linear Frequency Modulation (LFM) signals.

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Preliminary evidence of oxidation in standard oven drying of cotton: attenuated total reflectance/ Fourier transform spectroscopy, colorimetry, and particulate matter formation

USDA-ARS?s Scientific Manuscript database

Moisture is paramount to cotton fiber properties dictating harvesting, ginning, storage and spinning as well as others. Currently, oven drying in air is often utilized to generate the percentage of moisture in cotton fibers. Karl Fischer Titration another method for cotton moisture, has been compa...

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.

Complete fourier direct magnetic resonance imaging (CFD-MRI) for diffusion MRI

PubMed Central

Özcan, Alpay

2013-01-01

The foundation for an accurate and unifying Fourier-based theory of diffusion weighted magnetic resonance imaging (DW–MRI) is constructed by carefully re-examining the first principles of DW–MRI signal formation and deriving its mathematical model from scratch. The derivations are specifically obtained for DW–MRI signal by including all of its elements (e.g., imaging gradients) using complex values. Particle methods are utilized in contrast to conventional partial differential equations approach. The signal is shown to be the Fourier transform of the joint distribution of number of the magnetic moments (at a given location at the initial time) and magnetic moment displacement integrals. In effect, the k-space is augmented by three more dimensions, corresponding to the frequency variables dual to displacement integral vectors. The joint distribution function is recovered by applying the Fourier transform to the complete high-dimensional data set. In the process, to obtain a physically meaningful real valued distribution function, phase corrections are applied for the re-establishment of Hermitian symmetry in the signal. Consequently, the method is fully unconstrained and directly presents the distribution of displacement integrals without any assumptions such as symmetry or Markovian property. The joint distribution function is visualized with isosurfaces, which describe the displacement integrals, overlaid on the distribution map of the number of magnetic moments with low mobility. The model provides an accurate description of the molecular motion measurements via DW–MRI. The improvement of the characterization of tissue microstructure leads to a better localization, detection and assessment of biological properties such as white matter integrity. The results are demonstrated on the experimental data obtained from an ex vivo baboon brain. PMID:23596401

Structural and magnetic properties of multi-core nanoparticles analysed using a generalised numerical inversion method

PubMed Central

Bender, P.; Bogart, L. K.; Posth, O.; Szczerba, W.; Rogers, S. E.; Castro, A.; Nilsson, L.; Zeng, L. J.; Sugunan, A.; Sommertune, J.; Fornara, A.; González-Alonso, D.; Barquín, L. Fernández; Johansson, C.

2017-01-01

The structural and magnetic properties of magnetic multi-core particles were determined by numerical inversion of small angle scattering and isothermal magnetisation data. The investigated particles consist of iron oxide nanoparticle cores (9 nm) embedded in poly(styrene) spheres (160 nm). A thorough physical characterisation of the particles included transmission electron microscopy, X-ray diffraction and asymmetrical flow field-flow fractionation. Their structure was ultimately disclosed by an indirect Fourier transform of static light scattering, small angle X-ray scattering and small angle neutron scattering data of the colloidal dispersion. The extracted pair distance distribution functions clearly indicated that the cores were mostly accumulated in the outer surface layers of the poly(styrene) spheres. To investigate the magnetic properties, the isothermal magnetisation curves of the multi-core particles (immobilised and dispersed in water) were analysed. The study stands out by applying the same numerical approach to extract the apparent moment distributions of the particles as for the indirect Fourier transform. It could be shown that the main peak of the apparent moment distributions correlated to the expected intrinsic moment distribution of the cores. Additional peaks were observed which signaled deviations of the isothermal magnetisation behavior from the non-interacting case, indicating weak dipolar interactions. PMID:28397851

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.

On the asymptotic evolution of finite energy Airy wave functions.

PubMed

Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S

2015-06-15

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

The physicochemical properties of the low-temperature ionic liquid silver bromide-1-butyl-3-methylimidazolium bromide

NASA Astrophysics Data System (ADS)

Grishina, E. P.; Ramenskaya, L. M.; Pimenova, A. M.

2009-11-01

The physicochemical properties of the low-temperature ionic liquid based on 1-butyl-3-methylimidazolium bromide (BMImBr) and silver bromide were studied. Differential scanning calorimetry, Fourier transform IR spectroscopy, densimetry, viscometry, and conductometry measurements were performed to determine the dependences of the parameters under study on the concentration of AgBr. It was shown that the temperature and concentration behavior of the physicochemical properties of BMImBr-AgBr melts characterized the interaction between the system components with the formation of complex particles.

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.

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.

Structural evolution and electronic properties of n-type doped hydrogenated amorphous silicon thin films

NASA Astrophysics Data System (ADS)

He, Jian; Li, Wei; Xu, Rui; Qi, Kang-Cheng; Jiang, Ya-Dong

2011-12-01

The relationship between structure and electronic properties of n-type doped hydrogenated amorphous silicon (a-Si:H) thin films was investigated. Samples with different features were prepared by plasma enhanced chemical vapor deposition (PECVD) at various substrate temperatures. Raman spectroscopy and Fourier transform infrared (FTIR) spectroscopy were used to evaluate the structural evolution, meanwhile, electronic-spin resonance (ESR) and optical measurement were applied to explore the electronic properties of P-doped a-Si:H thin films. Results reveal that the changes in materials structure affect directly the electronic properties and the doping efficiency of dopant.

Monitoring light-induced structural changes of Channelrhodopsin-2 by UV-visible and Fourier transform infrared spectroscopy.

PubMed

Ritter, Eglof; Stehfest, Katja; Berndt, Andre; Hegemann, Peter; Bartl, Franz J

2008-12-12

Channelrhodopsin-2 (ChR2) is a microbial type rhodopsin and a light-gated cation channel that controls phototaxis in Chlamydomonas. We expressed ChR2 in COS-cells, purified it, and subsequently investigated this unusual photoreceptor by flash photolysis and UV-visible and Fourier transform infrared difference spectroscopy. Several transient photoproducts of the wild type ChR2 were identified, and their kinetics and molecular properties were compared with those of the ChR2 mutant E90Q. Based on the spectroscopic data we developed a model of the photocycle comprising six distinguishable intermediates. This photocycle shows similarities to the photocycle of the ChR2-related Channelrhodopsin of Volvox but also displays significant differences. We show that molecular changes include retinal isomerization, changes in hydrogen bonding of carboxylic acids, and large alterations of the protein backbone structure. These alterations are stronger than those observed in the photocycle of other microbial rhodopsins like bacteriorhodopsin and are related to those occurring in animal rhodopsins. UV-visible and Fourier transform infrared difference spectroscopy revealed two late intermediates with different time constants of tau = 6 and 40 s that exist during the recovery of the dark state. The carboxylic side chain of Glu(90) is involved in the slow transition. The molecular changes during the ChR2 photocycle are discussed with respect to other members of the rhodopsin family.

Monitoring Light-induced Structural Changes of Channelrhodopsin-2 by UV-visible and Fourier Transform Infrared Spectroscopy*

PubMed Central

Ritter, Eglof; Stehfest, Katja; Berndt, Andre; Hegemann, Peter; Bartl, Franz J.

2008-01-01

Channelrhodopsin-2 (ChR2) is a microbial type rhodopsin and a light-gated cation channel that controls phototaxis in Chlamydomonas. We expressed ChR2 in COS-cells, purified it, and subsequently investigated this unusual photoreceptor by flash photolysis and UV-visible and Fourier transform infrared difference spectroscopy. Several transient photoproducts of the wild type ChR2 were identified, and their kinetics and molecular properties were compared with those of the ChR2 mutant E90Q. Based on the spectroscopic data we developed a model of the photocycle comprising six distinguishable intermediates. This photocycle shows similarities to the photocycle of the ChR2-related Channelrhodopsin of Volvox but also displays significant differences. We show that molecular changes include retinal isomerization, changes in hydrogen bonding of carboxylic acids, and large alterations of the protein backbone structure. These alterations are stronger than those observed in the photocycle of other microbial rhodopsins like bacteriorhodopsin and are related to those occurring in animal rhodopsins. UV-visible and Fourier transform infrared difference spectroscopy revealed two late intermediates with different time constants of τ = 6 and 40 s that exist during the recovery of the dark state. The carboxylic side chain of Glu90 is involved in the slow transition. The molecular changes during the ChR2 photocycle are discussed with respect to other members of the rhodopsin family. PMID:18927082

Next generation techniques in the high resolution spectroscopy of biologically relevant molecules.

PubMed

Neill, Justin L; Douglass, Kevin O; Pate, Brooks H; Pratt, David W

2011-04-28

Recent advances in the technology of test and measurement equipment driven by the computer and telecommunications industries have made possible the development of a new broadband, Fourier-transform microwave spectrometer that operates on principles similar to FTNMR. This technique uses a high sample-rate arbitrary waveform generator to construct a phase-locked chirped microwave pulse that gives a linear frequency sweep over a wide frequency range in 1 μs. The chirped pulse efficiently polarizes the molecular sample at all frequencies lying within this band. The subsequent free induction decay of this polarization is measured with a high-speed digitizer and then fast Fourier-transformed to yield a broadband, frequency-resolved rotational spectrum, spanning up to 11.5 GHz and containing lines that are as narrow as 100 kHz. This new technique is called chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy. The technique offers the potential to determine the structural and dynamical properties of very large molecules solely from fully resolved pure rotational spectra. FTMW double resonance techniques employing a low-resolution UV laser facilitate an easy assignment of overlapping spectra produced by different conformers in the sample. Of particular interest are the energy landscapes of conformationally flexible molecules of biological importance, including studies of their interaction with solvent and/or other weakly bound molecules. An example is provided from the authors' work on p-methoxyphenethylamine, a neurotransmitter, and its complexes with water.

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.

Coherence Conversion for Optimized Resolution in Optical Measurements - Example of Femtosecond Time Resolution Using the Transverse Coherence of 100-Picosecond X-Rays

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

Adams, Bernhard W.

2015-01-01

A way is proposed to obtain a femtosecond time resolution over a picosecond range in x-ray spectroscopic measurements where the light source and the detector are much slower than that. It is based on the invariance of the modulus of the Fourier transform to object translations. The method geometrically correlates time in the sample with x-ray amplitudes over a spatial coordinate, and then takes the optical Fourier transform through far-field diffraction. Thus, explicitly time-invariant intensities that encode the time evolution of the sample can be measured with a slow detector. This corresponds to a phase-space transformation that converts the transversemore » coherence to become effective in the longitudinal direction. Because synchrotron-radiation sources have highly anisotropic coherence properties with about $10^5$ longitudinal electromagnetic-field modes at 1 eV bandwidth, but only tens to hundreds transverse modes, coherence conversion can drastically improve the time resolution. Reconstruction of the femtosecond time evolution in the sample from the Fourier intensities is subject to a phase ambiguity that is well-known in crystallography. However, a way is presented to resolve it that is not available in that discipline. Finally, data from a demonstration experiment are presented. The same concept can be used to obtain attosecond time resolution with an x-ray free-electron laser.« less

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.

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

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

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

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

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

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

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

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

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

PubMed

Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

2017-08-01

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

Fast Fourier Transform algorithm design and tradeoffs

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Multifractal surrogate-data generation algorithm that preserves pointwise Hölder regularity structure, with initial applications to turbulence

NASA Astrophysics Data System (ADS)

Keylock, C. J.

2017-03-01

An algorithm is described that can generate random variants of a time series while preserving the probability distribution of original values and the pointwise Hölder regularity. Thus, it preserves the multifractal properties of the data. Our algorithm is similar in principle to well-known algorithms based on the preservation of the Fourier amplitude spectrum and original values of a time series. However, it is underpinned by a dual-tree complex wavelet transform rather than a Fourier transform. Our method, which we term the iterated amplitude adjusted wavelet transform can be used to generate bootstrapped versions of multifractal data, and because it preserves the pointwise Hölder regularity but not the local Hölder regularity, it can be used to test hypotheses concerning the presence of oscillating singularities in a time series, an important feature of turbulence and econophysics data. Because the locations of the data values are randomized with respect to the multifractal structure, hypotheses about their mutual coupling can be tested, which is important for the velocity-intermittency structure of turbulence and self-regulating processes.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« 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.

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory.

PubMed

Likos, Christos N; Mladek, Bianca M; Gottwald, Dieter; Kahl, Gerhard

2007-06-14

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

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...

Analysis of Coherent Phonon Signals by Sparsity-promoting Dynamic Mode Decomposition

NASA Astrophysics Data System (ADS)

Murata, Shin; Aihara, Shingo; Tokuda, Satoru; Iwamitsu, Kazunori; Mizoguchi, Kohji; Akai, Ichiro; Okada, Masato

2018-05-01

We propose a method to decompose normal modes in a coherent phonon (CP) signal by sparsity-promoting dynamic mode decomposition. While the CP signals can be modeled as the sum of finite number of damped oscillators, the conventional method such as Fourier transform adopts continuous bases in a frequency domain. Thus, the uncertainty of frequency appears and it is difficult to estimate the initial phase. Moreover, measurement artifacts are imposed on the CP signal and deforms the Fourier spectrum. In contrast, the proposed method can separate the signal from the artifact precisely and can successfully estimate physical properties of the normal modes.

Infrared spectra and physochemical properties of oils

NASA Astrophysics Data System (ADS)

Strelets, L. A.; Svarovskaya, L. I.; Manakov, A. Yu.

2017-12-01

The paper reports on a multiparametric study of West Siberian crude oils using Fourier transform infrared (FTIR) spectroscopy to establish a relationship between the physicochemical properties of the oils, their spectral coefficients, and biodegradation levels. It is found that the test oils are slightly biodegraded, feature a roughly linear dependence between the freezing temperature and the content of resin and asphaltene, and display a relation of their emulsifying ability and spectral coefficient C2, being the ratio of alkanes and substituted alkylbenzene compounds.

Structural and Luminescent property of Holmium doped Borate Glasses

NASA Astrophysics Data System (ADS)

Usharani, V. L.; Eraiah, B.

2018-02-01

Holmium doped Lithium Lead Borate glasses of different compositions were prepared by melt quenching technique. Fourier transform infrared investigations on lithium lead borate glasses have been made to study the local order and vibrations of atoms in the glass network and it contains mainly BO3 and BO4 structural units. Photoluminescence techniques were employed to investigate the luminescent property of these glasses excited at 451nm. Blue emission have been observed from the transition 495 (5F3 → 5I8).

Sol-gel synthesis and characterization of SiO{sub 2}/PEG hybrid materials containing quercetin as implants with antioxidant properties

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

Catauro, Michelina; Bollino, Flavia; Gloria, Antonio

2016-05-18

In the present work, Silica/Polyethylene glycol (PEG) hybrid nanocomposites containing an antioxidant agent, the quercetin, were synthesized via sol-gel to be used as implants with antioxidant properties. Fourier transform infrared (FT-IR) analysis proved that a modification of both polymer and quercetin occurs due to synthesis process. Scanning electron microscope (SEM) showed that the proposed materials were hybrid nanocomposites. The bioactivity was ascertained by soaking the samples in a simulated body fluid (SBF).

Cheating Heisenberg: Achieving certainty in wideband spectrography

NASA Astrophysics Data System (ADS)

Fulop, Sean

2003-10-01

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

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

Frictionless Contact of Multilayered Composite Half Planes Containing Layers With Complex Eigenvalues

NASA Technical Reports Server (NTRS)

Zhang, Wang; Binienda, Wieslaw K.; Pindera, Marek-Jerzy

1997-01-01

A previously developed local-global stiffness matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained using Fourier transforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a global stiffness matrix for the entire multilayered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transform of the contact pressure. The solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycomb, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

SMERFS: Stochastic Markov Evaluation of Random Fields on the Sphere

NASA Astrophysics Data System (ADS)

Creasey, Peter; Lang, Annika

2018-04-01

SMERFS (Stochastic Markov Evaluation of Random Fields on the Sphere) creates large realizations of random fields on the sphere. It uses a fast algorithm based on Markov properties and fast Fourier Transforms in 1d that generates samples on an n X n grid in O(n2 log n) and efficiently derives the necessary conditional covariance matrices.

Control analysis for autonomously oscillating biochemical networks.

PubMed Central

Reijenga, Karin A; Westerhoff, Hans V; Kholodenko, Boris N; Snoep, Jacky L

2002-01-01

It has hitherto not been possible to analyze the control of oscillatory dynamic cellular processes in other than qualitative ways. The control coefficients, used in metabolic control analyses of steady states, cannot be applied directly to dynamic systems. We here illustrate a way out of this limitation that uses Fourier transforms to convert the time domain into the stationary frequency domain, and then analyses the control of limit cycle oscillations. In addition to the already known summation theorems for frequency and amplitude, we reveal summation theorems that apply to the control of average value, waveform, and phase differences of the oscillations. The approach is made fully operational in an analysis of yeast glycolytic oscillations. It follows an experimental approach, sampling from the model output and using discrete Fourier transforms of this data set. It quantifies the control of various aspects of the oscillations by the external glucose concentration and by various internal molecular processes. We show that the control of various oscillatory properties is distributed over the system enzymes in ways that differ among those properties. The models that are described in this paper can be accessed on http://jjj.biochem.sun.ac.za. PMID:11751299

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.

Annealing improves tribological property of poly(octadecene- alt -maleic anhydride) self-assembled film

NASA Astrophysics Data System (ADS)

Song, Shiyong; Liu, Lei; Zhang, Junyan

2011-09-01

A poly(octadecene-alt-maleic anhydride) (POMA) film was covalently immobilized on N-[3-(trimethoxylsilyl)propyl]ethylenediamine self-assembled monolayer modified silicon surface. Attenuated total reflectance Fourier transform infrared spectra were used to confirm the chemical bonding. Water contact angles and ellipsometric thicknesses were measured before and after annealing treatment. Atomic force microscopy was applied for top morphology, surface adhesion force and friction force. Anti-wear properties of the films were also evaluated on a ball-on-plate tribometer. It was found that annealing treatment which would evoke a conformation transform thermodynamically, was a critical step in the preparation of anti-wear films, especially for polymer ones. The correlation between structure and tribological property was revealed, which has profound meaning in designing excellent anti-wear nano-coatings used in microelectronic mechanical systems (MEMS).

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.

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 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.

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).

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.

Digital signal processing techniques for pitch shifting and time scaling of audio signals

NASA Astrophysics Data System (ADS)

Buś, Szymon; Jedrzejewski, Konrad

2016-09-01

In this paper, we present the techniques used for modifying the spectral content (pitch shifting) and for changing the time duration (time scaling) of an audio signal. A short introduction gives a necessary background for understanding the discussed issues and contains explanations of the terms used in the paper. In subsequent sections we present three different techniques appropriate both for pitch shifting and for time scaling. These techniques use three different time-frequency representations of a signal, namely short-time Fourier transform (STFT), continuous wavelet transform (CWT) and constant-Q transform (CQT). The results of simulation studies devoted to comparison of the properties of these methods are presented and discussed in the paper.

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.

Synthesis and characterization of graphene quantum dots/cobalt ferrite nanocomposite

NASA Astrophysics Data System (ADS)

Ramachandran, Shilpa; Sathishkumar, M.; Kothurkar, Nikhil K.; Senthilkumar, R.

2018-02-01

A facile method has been developed for the synthesis of a graphene quantum dots/cobalt ferrite nanocomposite. Graphene quantum dots (GQDs) were synthesized by a simple bottom-up method using citric acid, followed by the co-precipitation of cobalt ferrite nanoparticles on the graphene quantum dots. The morphology, structural analysis, optical properties, magnetic properties were investigated using transmission electron microscopy (TEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), UV-vis absorption spectroscopy, fluorescence spectroscopy, vibrating sample magnetometry (VSM) measurements. The synthesized nanocomposite showed good fluorescence and superparamagnetic properties, which are important for biomedical applications.

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.

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)

Effect of SiO2, PVA and glycerol concentrations on chemical and mechanical properties of alginate-based films.

PubMed

Yang, Manli; Shi, Jinsheng; Xia, Yanzhi

2018-02-01

Sodium alginate (SA)/polyvinyl alcohol (PVA)/SiO 2 nanocomposite films were prepared by in situ polymerization through solution casting and solvent evaporation. The effect of different SA/PVA ratios, SiO 2 , and glycerol content on the mechanical properties, water content, water solubility, and water vapor permeability were studied. The nanocomposite films were characterized by Fourier transform infrared, X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and thermal stability (thermogravimetric analysis/differential thermogravimetry) analyses. The nanocomposites showed the highest values of mechanical properties, such as SA/PVA ratio, SiO 2 , and glycerol content was 7:3, 6wt.%, and 0.25g/g SA, respectively. The tensile strength and elongation at break (E%) of the nanocomposites increased by 525.7% and 90.7%, respectively, compared with those of the pure alginate film. The Fourier transform infrared spectra showed a new SiOC band formed in the SA/PVA/SiO 2 nanocomposite film. The scanning electron microscopy image revealed good adhesion between SiO 2 and SA/PVA matrix. After the incorporation of PVA and SiO 2 , the water resistance of the SA/PVA/SiO 2 nanocomposite film was markedly improved. Transparency decreased with increasing PVA content but was enhanced by adding SiO 2 . Copyright © 2017. Published by Elsevier B.V.

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.

[Application of Fourier transform infrared spectroscopy in identification of wine spoilage].

PubMed

Zhao, Xian-De; Dong, Da-Ming; Zheng, Wen-Gang; Jiao, Lei-Zi; Lang, Yun

2014-10-01

In the present work, fresh and spoiled wine samples from three wines produced by different companies were studied u- sing Fourier transform infrared (FTIR) spectroscopy. We analyzed the physicochemical property change in the process of spoil- age, and then, gave out the attribution of some main FTIR absorption peaks. A novel determination method was explored based on the comparisons of some absorbance ratios at different wavebands although the absorbance ratios in this method were relative. Through the compare of the wine spectra before and after spoiled, the authors found that they were informative at the bands of 3,020~2,790, 1,760~1,620 and 1,550~800 cm(-1). In order to find the relation between these informative spectral bands and the wine deterioration and achieve the discriminant analysis, chemometrics methods were introduced. Principal compounds analysis (PCA) and soft independent modeling of class analogy (SIMCA) were used for classifying different-quality wines. And partial least squares discriminant analysis (PLS-DA) was applied to identify spoiled wines and good wines. Results showed that FTIR technique combined with chemometrics methods could effectively distinguish spoiled wines from fresh samples. The effect of classification at the wave band of 1 550-800 cm(-1) was the best. The recognition rate of SIMCA and PLSDA were respectively 94% and 100%. This study demonstrates that Fourier transform infrared spectroscopy is an effective tool for monitoring red wine's spoilage and provides theoretical support for developing early-warning equipments.

Chemical and Physical Characterization of Comp A-3 Type II Prills

DTIC Science & Technology

2013-06-01

the composition and properties of the explosive for implementation into modeling and simulation tools as part of the Multi-scale Response of...emulsion were identified using desorption-gas chromatography/mass spectroscopy (D-GC- MS) and Fourier transform infrared ( FTIR ) spectroscopy. Quantitative...understanding the microstructure of the pressed explosive and provides critical information for the development of a high fidelity particle-based course-grain

Optical Properties of III-V Semiconductor Nanostructures and Quantum Wells

DTIC Science & Technology

2006-12-31

measurements were made using a BOMEM Fourier-transform infrared spectrometer in conjunction with a continuous flow cryostat. A low- noise current...infrared photodetector ( QWIP ). Quantum well infrared photodetectors are designed from wide bandgap (III-V) semiconductor materials in such a way where...quantum confinement is created. Unlike HgCdTe which utilizes electronic transitions across the fundamental bandgap, QWIPs relies on transitions between

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,...

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

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

1969-01-01

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

[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.

Holographic maps of quasiparticle interference

NASA Astrophysics Data System (ADS)

Dalla Torre, Emanuele G.; He, Yang; Demler, Eugene

2016-11-01

The analysis of Fourier-transformed scanning tunnelling microscopy images with subatomic resolution is a common tool for studying the properties of quasiparticle excitations in strongly correlated materials. Although Fourier amplitudes are generally complex valued, earlier analysis primarily focused on their absolute values. Their complex phases were often deemed random, and thus irrelevant, due to the unknown positions of the impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously unknown information about the electronic structures. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that d-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in scanning tunnelling microscopy.

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.

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

Deus, R.C.; Cortés, J.A., E-mail: leandrosrr89@gmail.com; Ramirez, M.A.

Highlights: • CeO{sub 2} nanoparticles were obtained by microwave-hydrothermal method. • Rietveld refinement reveals a cubic structure. • KOH mineralizer agent exhibit weak agglomeration at low temperature and shorter time. - Abstract: The structural and photoluminescent properties at room temperature of CeO{sub 2} and La-doped CeO{sub 2} particles were undertaken. The obtained particles were synthesized by a microwave-assisted hydrothermal method (MAH) under different lanthanum contents. X-ray diffraction (XRD), Fourier transform infrared (FT-IR), Fourier transform Raman (FT-Raman), Ultra-violet spectroscopy (UV–vis) and photoluminescence (PL) measurements were carried out. XRD revealed that the powders are free of secondary phases and crystallize in themore » cubic structure. Raman data show that increasing La doping content increase oxygen vacancies due to lattice expansion. The UV/vis absorption spectroscopy suggested the presence of intermediate energy levels in the band gap of structurally ordered powders. Lanthanum addition creates oxygen vacancies and shifts the photoluminescence in the low energy range leading to intense PL emission.« less

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

DOE PAGES

Vasudevan, Rama K.; Belianinov, Alex; Gianfrancesco, Anthony G.; ...

2015-03-03

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of themore » Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

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

Vasudevan, Rama K.; Belianinov, Alex; Gianfrancesco, Anthony G.

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of themore » Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

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.

1999-01-01

We have studied the spectroscopy and the cross sections of the simple molecules of atmospheric interest such as oxygen, nitric oxide, carbon dioxide, and water. We have made cross section measurements on an absolute base without the effects from the limited instrumental resolution. We have used the following different instruments- the grating spectrometer (6.65-m at CfA, 3-m at Photon Factory), VUV Fourier transform spectrometer at Imperial College, and then moved the same one to the Photon Factory. Selection of the instruments depend on the appearance of molecular bands, and their wavelength region. For example, the cross section measurements of Doppler limited bands can been done with the Fourier transform spectrometer at the very high resolution (0.025/ cm resolution). All of these spectroscopic measurements are needed for accurate calculations of the production of atomic oxygen penetration of solar radiation into the Earth's atmosphere, and photochemistry of minor molecules.

Classification of pumpkin seed oils according to their species and genetic variety by attenuated total reflection Fourier-transform infrared spectroscopy.

PubMed

Saucedo-Hernández, Yanelis; Lerma-García, María Jesús; Herrero-Martínez, José Manuel; Ramis-Ramos, Guillermo; Jorge-Rodríguez, Elisa; Simí-Alfonso, Ernesto F

2011-04-27

Attenuated total reflection Fourier-transform infrared spectroscopy (ATR-FTIR), followed by multivariate treatment of the spectral data, was used to classify seed oils of the genus Cucurbita (pumpkins) according to their species as C. maxima, C. pepo, and C. moschata. Also, C. moschata seed oils were classified according to their genetic variety as RG, Inivit C-88, and Inivit C-2000. Up to 23 wavelength regions were selected on the spectra, each region corresponding to a peak or shoulder. The normalized absorbance peak areas within these regions were used as predictors. Using linear discriminant analysis (LDA), an excellent resolution among all categories concerning both Cucurbita species and C. moschata varieties was achieved. The proposed method was straightforward and quick and can be easily implemented. Quality control of pumpkin seed oils is important because Cucurbita species and genetic variety are both related to the pharmaceutical properties of the oils.

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

NASA Astrophysics Data System (ADS)

Hobohm, Klaus

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

Novel preparation and characterization of human hair-based nanofibers using electrospinning process.

PubMed

Park, Mira; Shin, Hye Kyoung; Panthi, Gopal; Rabbani, Mohammad Mahbub; Alam, Al-Mahmnur; Choi, Jawun; Chung, Hea-Jong; Hong, Seong-Tshool; Kim, Hak-Yong

2015-05-01

Human hair-based biocomposite nanofibers (NFs) have been fabricated by an electrospinning technique. Aqueous keratin extracted from human hair was successfully blended with poly(vinyl alcohol) (PVA). The focus here is on transforming into keratin/PVA nanofibrous membranes and insoluble property of electrospun NFs. The resulting hair-based NFs were characterized using Fourier transform infrared (FT-IR) spectroscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD), differential scanning colorimetry (DSC), and thermogravimetric analysis (TGA). Toward the potential use of these NFs after cross-linking with various weight fractions of glyoxal, its physicochemical properties, such as morphology, mechanical strength, crystallinity, and chemical structure were investigated. Keratin/PVA ratio of 2/1 NFs with 6 wt%-glyoxal showed good uniformity in fiber morphology and suitable mechanical properties, and excellent antibacterial activity providing a potential application of hair-based NFs in biomedical field. Copyright © 2015 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.

The effect of benzalkonium chloride additions to AH Plus sealer. Antimicrobial, physical and chemical properties.

PubMed

Arias-Moliz, M T; Ruiz-Linares, M; Cassar, G; Ferrer-Luque, C M; Baca, P; Ordinola-Zapata, R; Camilleri, J

2015-07-01

The aim of this study was to determine the antimicrobial and antibiofilm activities and physicochemical properties of AH Plus sealer mixed with different concentrations of benzalkonium chloride (BC). AH Plus was tested alone and mixed with 1%, 2% and 3% of BC. The antimicrobial and antibiofilm activities of the sealers against Enterococcus faecalis were evaluated by the direct contact test (DCT) and by confocal laser scanning microscopy, respectively. Setting time, flow and solubility were assessed according to ANSI/ADA specifications. Microhardness and contact angle tests were also performed. The chemical changes of the sealers were evaluated by X-ray diffraction analysis, and both Fourier transform infrared spectroscopy (FT-IR) and attenuated total reflectance Fourier transform infrared (ATR FT-IR). AH Plus+3% BC was the only sealer to promote total elimination of E. faecalis and the biovolume in this group was significantly lower than in the rest of the sealers (p>0.05). The physical properties of the sealers were according to the ANSI/ADA specifications. The microhardness decreased significantly when BC was added and a significant reduction in contact angle was obtained when incorporating 2% and 3% BC (p<0.05). No phase changes were observed with the modified sealers. The addition of 2% or higher concentrations BC to AH Plus showed antimicrobial and antibiofilm activities without affecting the properties specified in ANSI/ADA standards. However, additives to the root canal sealer altered other physical and chemical properties that are not commonly found in the literature to evaluate filling materials. The present study highlights that the antimicrobial properties of AH Plus can be significantly improved with the addition of BC. Testing beyond what is specified in standards may be indicated. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Enhanced Photocatalytic Property of Cu Doped Sodium Niobate

DOE PAGES

Xu, Jianbin; Zhang, Feng; Sun, Bingyang; ...

2015-01-01

Here, we investigate the photocatalytic activity of Cu doped NaNbO 3 powder sample prepared by the modified polymer complex method. The photocatalytic activity of hydrogen evolution from methanol aqueous solution was improved by Cu 2.6 at% doping. The photocatalytic degradation of rhodamine B (RhB) under visible light irradiation was enhanced in comparison with pristine NaNbO 3. Cu introduction improved the adsorption property of NaNbO 3, judging from the Fourier transform infrared spectra. Moreover, the ultraviolet light excitation in Cu doped sample would accelerate the mineralized process.

Characterization of atmospheric pressure plasma treated wool/cashmere textiles: Treatment in nitrogen

NASA Astrophysics Data System (ADS)

Zanini, Stefano; Citterio, Attilio; Leonardi, Gabriella; Riccardi, Claudia

2018-01-01

We performed atmospheric pressure plasma treatments of wool/cashmere (15/85%) textiles with a dielectric barrier discharge (DBD) in nitrogen. The chemical properties of the plasma treated samples were investigated with attenuated total reflectance Fourier transform infrared (FTIR/ATR) spectroscopy, X-ray photoelectron microscopy (XPS), and fatty acid gas chromatographic analysis. Changes in mechanical properties and tactile performance of textiles after the plasma treatment were determined using the KES-F system. The analyses reveal significant surface modification of the treated fabrics, which enhances their surface wettability.

Synthesis and Properties of Ortho-Nitro-Fe Complex

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

Mishra, A.; Mishra, Niyati; Sharma, R.

2011-07-15

Ortho-Nitro-Fe complex (Transition metal complex) has synthesized by chemical route method and properties of made complex has characterized by X-Ray diffraction (XRD), Moessbauer spectroscopy, Fourier transformation infra-red spectroscopy (FTIR) and X-Ray photoelectron spectroscopy (XPS). XRD analysis shows that sample is crystalline in nature and having particle size in the range of few nano meters. Moessbauer spectroscopy at room temperature shows the oxidation state of Iron (central metal ion) after complaxasion. FTIR spectra of the complex confirms the coordination of metal ion with ligand.

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...

Gaussian beam profile shaping apparatus, method therefor and evaluation thereof

DOEpatents

Dickey, Fred M.; Holswade, Scott C.; Romero, Louis A.

1999-01-01

A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system.

Gaussian beam profile shaping apparatus, method therefore and evaluation thereof

DOEpatents

Dickey, F.M.; Holswade, S.C.; Romero, L.A.

1999-01-26

A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system. 27 figs.

Prediction and repeatability of milk coagulation properties and curd-firming modeling parameters of ovine milk using Fourier-transform infrared spectroscopy and Bayesian models.

PubMed

Ferragina, A; Cipolat-Gotet, C; Cecchinato, A; Pazzola, M; Dettori, M L; Vacca, G M; Bittante, G

2017-05-01

The aim of this study was to apply Bayesian models to the Fourier-transform infrared spectroscopy spectra of individual sheep milk samples to derive calibration equations to predict traditional and modeled milk coagulation properties (MCP), and to assess the repeatability of MCP measures and their predictions. Data consisted of 1,002 individual milk samples collected from Sarda ewes reared in 22 farms in the region of Sardinia (Italy) for which MCP and modeled curd-firming parameters were available. Two milk samples were taken from 87 ewes and analyzed with the aim of estimating repeatability, whereas a single sample was taken from the other 915 ewes. Therefore, a total of 1,089 analyses were performed. For each sample, 2 spectra in the infrared region 5,011 to 925 cm -1 were available and averaged before data analysis. BayesB models were used to calibrate equations for each of the traits. Prediction accuracy was estimated for each trait and model using 20 replicates of a training-testing validation procedure. The repeatability of MCP measures and their predictions were also compared. The correlations between measured and predicted traits, in the external validation, were always higher than 0.5 (0.88 for rennet coagulation time). We confirmed that the most important element for finding the prediction accuracy is the repeatability of the gold standard analyses used for building calibration equations. Repeatability measures of the predicted traits were generally high (≥95%), even for those traits with moderate analytical repeatability. Our results show that Bayesian models applied to Fourier-transform infrared spectra are powerful tools for cheap and rapid prediction of important traits in ovine milk and, compared with other methods, could help in the interpretation of results. Copyright © 2017 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

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.

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.

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

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions.

PubMed

Xia, Yan; Berger, Martin; Bauer, Sebastian; Hu, Shiyang; Aichert, Andre; Maier, Andreas

2017-01-01

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions

PubMed Central

Berger, Martin; Bauer, Sebastian; Hu, Shiyang; Aichert, Andre

2017-01-01

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method. PMID:28808441

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.

Quantum computation with classical light: Implementation of the Deutsch-Jozsa algorithm

NASA Astrophysics Data System (ADS)

Perez-Garcia, Benjamin; McLaren, Melanie; Goyal, Sandeep K.; Hernandez-Aranda, Raul I.; Forbes, Andrew; Konrad, Thomas

2016-05-01

We propose an optical implementation of the Deutsch-Jozsa Algorithm using classical light in a binary decision-tree scheme. Our approach uses a ring cavity and linear optical devices in order to efficiently query the oracle functional values. In addition, we take advantage of the intrinsic Fourier transforming properties of a lens to read out whether the function given by the oracle is balanced or constant.

Cotton fiber quality characterization with light scattering and fourier transform infrared techniques.

PubMed

Thomasson, J A; Manickavasagam, S; Mengüç, M P

2009-03-01

Fiber quality measurement is critical to assessing the value of a bale of cotton for various textile purposes. An instrument that could measure numerous cotton quality properties by optical means could be made simpler and faster than current fiber quality measurement instruments, and it might be more amenable to on-line measurement at processing facilities. To that end, a laser system was used to investigate cotton fiber samples with respect to electromagnetic scattering at various wavelengths, polarization angles, and scattering angles. A Fourier transform infrared (FT-IR) instrument was also used to investigate the transmission of electromagnetic energy at various mid-infrared wavelengths. Cotton samples were selected to represent a wide range of micronaire values. Varying the wavelength of the laser at a fixed polarization resulted in little variation in scattered light among the cotton samples. However, varying the polarization at a fixed wavelength produced notable variation, indicating that polarization might be used to differentiate among cotton samples with respect to certain fiber properties. The FT-IR data in the 12 to 22 microm range produced relatively large differences in the amount of scattered light among all samples, and FT-IR data at certain combinations of fixed wavelengths were highly linearly related to certain measures of cotton quality including micronaire.

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

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...

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.

XNBR-grafted halloysite nanotube core-shell as a potential compatibilizer for immiscible polymer systems

NASA Astrophysics Data System (ADS)

Paran, S. M. R.; Naderi, G.; Ghoreishy, M. H. R.

2016-09-01

Halloysite nanotubes (HNTs) grafted with carboxylated nitrile byutadiene rubber (XNBR) were synthesized via a sol-gel method. The HNTs as an inorganic cores were pre-treated with 3-Glycidoxypropyl trimethoxysilane, then successfully coated with the XNBR as an organic shell. The properties of XNBR-grafted HNTs were characterized by transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FTIR), attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The results suggested that the XNBR grafted to the surfaces of HNTs successfully. Then the TPE nanocomposites based on polyamide-6 (PA6) and nitrile butadiene rubber (NBR) containing various XNBR-grafted and pristine HNTs were prepared via a direct melt mixing method. The morphology, mechanical, dynamic mechanical and rheological properties of the prepared TPE nanocomposites were investigated. The results show that the XNBR-grafted HNTs can effectively improve the morphology and mechanical properties of the PA6/NBR TPEs. The morphology study of the prepared nanocomposites show that the effect of XNBR-grafted HNTs on the size reduction of NBR phase is markedly more effective than the pristine HNTs and rose by 50% in the same concentrations. Mechanical measurements show that the Young's modulus of the TPE nanocomposites rose by 60% in just 7 wt% of XNBR-grafted HNT loading. The results indicate that the introduction of HNT/XNBR core-shells into the PA6/NBR TPEs can enhances the interfacial interactions and provides a more fine rubber phase morphology and controlled mechanical properties in comparison with the accordingly TPE nanocomposites containing pristine HNTs.

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

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

Microwave processed NiMg ferrite: Studies on structural and magnetic properties

NASA Astrophysics Data System (ADS)

Chandra Babu Naidu, K.; Madhuri, W.

2016-12-01

Ferrites are magnetic semiconductors realizing an important role in electrical and electronic circuits where electrical and magnetic property coupling is required. Though ferrite materials are known for a long time, there is a large scope in the improvement of their properties (vice sintering and frequency dependence of electrical and magnetic properties) with the current technological trends. Forth coming technology is aimed at miniaturization and smart gadgets, electrical components like inductors and transformers cannot be included in integrated circuits. These components are incorporated into the circuit as surface mount devices whose fabrication involves low temperature co-firing of ceramics and microwave monolithic integrated circuits technologies. These technologies demand low temperature sinter-ability of ferrites. This article presents low temperature microwave sintered Ni-Mg ferrites of general chemical formula Ni1-xMgxFe2O4 (x=0, 0.2, 0.4, 0.5, 0.6, 0.8, 1) for potential applications as transformer core materials. The series of ferrites are characterized using X-ray diffractometer, scanning electron microscopy, Fourier transform infrared and vibrating sample magnetometer for investigating structural, morphological and magnetic properties respectively. The initial permeability is studied with magnesium content, temperature and frequency in the temperature range of 308 K-873 K and 42 Hz-5 MHz.

Mineral to matrix ratio determines biomaterial and biomechanical properties of rat femur--application of Fourier transform infrared spectroscopy.

PubMed

Takata, Shinjiro; Yonezu, Hiroshi; Shibata, Akira; Enishi, Tetsuya; Sato, Nori; Takahashi, Mitsuhiko; Nakao, Shigetaka; Komatsu, Koji; Yasui, Natsuo

2011-08-01

We studied the changes of biomaterial and biomechanical properties of the rat femur during development. Thirty male Wistar rats were allocated to 6 groups: aged 6 weeks (n=5), 9 weeks (n=5), 12 weeks (n=5), 15 weeks (n=5), 24 weeks (n=5), and 36 weeks (n=5). The mineral to matrix ratio (M/M ratio) of rat femur by Fourier transform infrared spectroscopy was 0.97 ± 0.10 at the age of 6 weeks, and reached the maximum of 1.52 ± 0.17 at the age of 36 weeks. Total bone mineral density (BMD) by peripheral quantitative computed tomography of the femoral shaft aged 6 weeks was 479.1 ± 58.7 mg/cm(3), and reached the maximum of 1022.2 ± 42.3 mg/cm(3) at the age of 36 weeks. The ultimate load to failure of the femur of the rat aged 6 weeks by the three-point bending test was 29.6 ± 6.1 N. At the age of 36 weeks, the ultimate load to failure of the rat femur increased to the maximum of 283.5 ± 14.7 N. The results showed that the M/M ratio increased with development as total BMD and bone strength increased. The results suggest that the M/M ratio is one of the determinants of the biomaterial and biomechanical properties of bone.

Structure comparison of PMN-PT and PMN-PZT nanocrystals prepared by gel-combustion method at optimized temperatures

NASA Astrophysics Data System (ADS)

Ghasemifard, M.; Hosseini, S. M.; Bagheri-Mohagheghi, M. M.; Shahtahmasbi, N.

2009-09-01

We have synthesized and were performed a comparison of structures and optical properties between relaxor ferroelectric PMN-PT and PMN-PZT nanopowders. A gel-combustion method has been used to synthesize PMN-PT and PMN-PZT nanocrystalline with the perovskite structure. The precursors employed in the gel-combustion process were lead nitrate, magnesium acetate, niobium ammonium oxalate and zirconium nitrate. The nanopowders were characterized using the X-ray diffraction (XRD) and transmission electron microscopy (TEM) observation. Fourier transform infrared (FTIR) spectroscopy was employed to monitor the transformation of precursor solutions during the thermal reactions leading to the formation of perovskite phase.

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

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

PubMed

Reed, George H; Poyner, Russell R

2015-01-01

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

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.

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.

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.

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

DTIC Science & Technology

1992-12-01

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

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.

Application of the Fractional Fourier Transform and S-Method in Doppler Radar Tomography

DTIC Science & Technology

2010-08-01

Distribution Series WVD - Wigner - Ville Distribution xi DSTO–RR–0357 xii DSTO–RR...for chirped signals include bilinear tech- niques such as the Wigner - Ville Distribution ( WVD ), the Cohen’s class, and the time- frequency distribution ...2which is also known as ”‘ Wigner - Ville Distribution ”’ 3Assuming the integration extent in (13) is from −∞ to +∞ and using the property of the Dirac

Proton transfer from imidazole to chloranil studied by FTIR spectroscopy

NASA Astrophysics Data System (ADS)

Sharma, Amit

2018-05-01

Imidazole is incorporated into many important biological molecules. The most obvious is the amino acid histidine, which has an imidazole side chain. Histidine is present in many proteins and enzymes and plays a vital part in the structure and binding functions of hemoglobin. Therefore it is important to study its proton transfer property. In the present work proton transfer from imidazole to chloranil is investigated by Fourier Transform Infra red Spectroscopy.

A new fractional operator of variable order: Application in the description of anomalous diffusion

NASA Astrophysics Data System (ADS)

Yang, Xiao-Jun; Machado, J. A. Tenreiro

2017-09-01

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Method and apparatus for analyzing particle-containing gaseous suspensions

DOEpatents

Solomon, Peter R.; Carangelo, Robert M.; Best, Philip E.

1987-01-01

The method and apparatus permit analyses, by optical means, of properties of gaseous suspensions of particles, by measuring radiation that is emitted, transmitted or scattered by the particles. Determinations of composition, size, temperature and spectral emittance can be performed either in-situ or by sampling, and Fourier-transform infrared spectrometric techniques are most effectively used. Apparatus specifically adapted for performing radiation scattering analyses, and for collecting radiation from different sources, are provided.

Method and apparatus for analyzing particle-containing gaseous suspensions

DOEpatents

Solomon, P.R.; Carangelo, R.M.; Best, P.E.

1987-03-24

The method and apparatus permit analyses, by optical means, of properties of gaseous suspensions of particles, by measuring radiation that is emitted, transmitted or scattered by the particles. Determinations of composition, size, temperature and spectral emittance can be performed either in-situ or by sampling, and Fourier-transform infrared spectrometric techniques are most effectively used. Apparatus specifically adapted for performing radiation scattering analyses, and for collecting radiation from different sources, are provided. 51 figs.

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.

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.

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.

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.

Effect of γ-irradiation on commercial polypropylene based mono and multi-layered retortable food packaging materials

NASA Astrophysics Data System (ADS)

George, Johnsy; Kumar, R.; Sajeevkumar, V. A.; Sabapathy, S. N.; Vaijapurkar, S. G.; Kumar, D.; Kchawahha, A.; Bawa, A. S.

2007-07-01

Irradiation processing of food in the prepackaged form may affect chemical and physical properties of the plastic packaging materials. The effect of γ-irradiation doses (2.5-10.0 kGy) on polypropylene (PP)-based retortable food packaging materials, were investigated using Fourier transform infrared (FTIR) spectroscopic analysis, which revealed the changes happening to these materials after irradiation. The mechanical properties decreased with irradiation while oxygen transmission rate (OTR) was not affected significantly. Colour measurement indicated that Nylon 6 containing multilayer films became yellowish after irradiation. Thermal characterization revealed the changes in percentage crystallinity.

Modification of Aspergillus niger by conducting polymer, Polypyrrole, and the evaluation of electrochemical properties of modified cells.

PubMed

Apetrei, Roxana-Mihaela; Carac, Geta; Bahrim, Gabriela; Ramanaviciene, Almira; Ramanavicius, Arunas

2018-06-01

The enhancement of bioelectrochemical properties of microorganism by in situ formation of conducting polymer within the cell structures (e.g. cell wall) was performed. The synthesis of polypyrrole (Ppy) within fungi (Aspergillus niger) cells was achieved. Two different Aspergillus niger strains were selected due to their ability to produce glucose oxidase, which initiated the Ppy formation through products of enzymatic reaction. The evolution of Ppy structural features was investigated by absorption spectroscopy, cyclic voltammetry and Fourier transform infrared spectroscopy. Copyright © 2018 Elsevier B.V. All rights reserved.

Thiolated poly(ɛ-caprolactone) macroligand with vacant coordination sites on gold substrate: Synthesis and surface characterization

NASA Astrophysics Data System (ADS)

Farah, Abdiaziz A.; Zheng, Susan H.; Morin, Sylvie; Bensebaa, Farid; Pietro, William J.

2007-04-01

Surface-confined telechelic poly(ɛ-caprolactone) macroligand with two distinct functional groups per polymeric chain has been synthesized and characterized. The molecular microstructure of the macroligand with regard to the properties of the end-capped functionalities and with those on surface substrate has been studied by solution and surface analytical methods (i.e., X-ray photoelectron spectroscopy (XPS), grazing angle reflectance-Fourier transform IR spectroscopy (GA-FTIR), water contact angle measurements, and atomic force microscopy (AFM)) to elucidate the structure and properties of such multifunctional polymer on gold (1 1 1) substrate.

Structural, optical and dielectric properties of graphene oxide

NASA Astrophysics Data System (ADS)

Bhargava, Richa; Khan, Shakeel

2018-05-01

The Modified Hummers method has been used to synthesize Graphene oxide nanoparticles. Microstructural analyses were carried out by X-ray diffraction and Fourier transform infrared spectroscopy. Optical properties were studied by UV-visible spectroscopy in the range of 200-700 nm. The energy band gap was calculated with the help of Tauc relation. The frequency dependence of dielectric constant and dielectric loss were studied over a range of the frequency 75Hz to 5MHz at room temperature. The dispersion in dielectric constant can be explained with the help of Maxwell-Wagner model in studied nanoparticles.

Evaluation of transport parameters for PVC based polyvinyl alcohol Ce(IV) phosphate composite membrane.

PubMed

Khan, Mohammad Mujahid Ali; Rafiuddin; Inamuddin

2013-05-01

The aim of this study was to investigate the preparation of novel membrane and the characterization of their properties. A new class of polyvinyl chloride (PVC) based polyvinyl alcohol Ce(IV) phosphate composite membrane was successfully prepared by solution casting method. The structural formation was confirmed by X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy and morphological studies. The thermal property was investigated by thermogravimetry analysis (TGA) method. The order of surface charge density for various electrolytes was found to be LiCl

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.

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

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

NASA Technical Reports Server (NTRS)

Sih, G. C.; Chen, E. P.

1979-01-01

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Applications of wavelets in interferometry and artificial vision

NASA Astrophysics Data System (ADS)

Escalona Z., Rafael A.

2001-08-01

In this paper we present a different point of view of phase measurements performed in interferometry, image processing and intelligent vision using Wavelet Transform. In standard and white-light interferometry, the phase function is retrieved by using phase-shifting, Fourier-Transform, cosinus-inversion and other known algorithms. Our novel technique presented here is faster, robust and shows excellent accuracy in phase determinations. Finally, in our second application, fringes are no more generate by some light interaction but result from the observation of adapted strip set patterns directly printed on the target of interest. The moving target is simply observed by a conventional vision system and usual phase computation algorithms are adapted to an image processing by wavelet transform, in order to sense target position and displacements with a high accuracy. In general, we have determined that wavelet transform presents properties of robustness, relative speed of calculus and very high accuracy in phase computations.

Synthesis, growth, structural characterization, Hirshfeld analysis and nonlinear optical studies of a methyl substituted chalcone

NASA Astrophysics Data System (ADS)

Prabhu, Shobha R.; Jayarama, A.; Chandrasekharan, K.; Upadhyaya, V.; Ng, Seik Weng

2017-05-01

A new chalcone compound (2E)-3-(3-methylphenyl)-1-(4-nitrophenyl)prop-2-en-1-one (3MPNP) with molecular formula C16H13NO3 has been synthesized and crystallized by slow solvent evaporation technique. The Fourier transform infrared, Fourier transform Raman and nuclear magnetic resonance techniques were used for structural characterization. UV-visible absorption studies were carried out to study the transparency of the crystal in the visible region. Differential scanning calorimetry study shows thermal stability of crystals up to temperature 122 °C. Single crystal X-ray diffraction and powder X-ray diffraction techniques were used to study crystal structure and cell parameters. The Hirshfeld surface and 2-D fingerprint analysis were performed to study the nature of interactions and their quantitative contributions towards the crystal packing. The third order non-linear optical properties have been studied using single beam Z-scan technique and the results show that the material is a potential candidate for optical device applications such as optical limiters and optical switches.

Synthesis and luminescent properties of the novel poly(ethylene-co-acrylic acid) films based on surface modification with lanthanide (Eu3+, Tb3+) complexes

NASA Astrophysics Data System (ADS)

Wu, Yuewen; Chu, Yang; Yu, Zhenjiang; Hao, Haixia; Wu, Qingyao; Xie, Hongde

2017-10-01

Two kinds of novel fluorescent films have been successfully synthesized by surface modification on the poly(ethylene-co-acrylic acid) films using the lanthanide (Eu3+, Tb3+) complexes. The process consists of three steps: conversion of carboxylic acid groups on the surface of the poly(ethylene-co-acrylic acid) films to acid chloride groups, synthesis of the lanthanide complexes bearing amino groups, and amidation to form the modified films. To characterize the modified films, Fourier transform infrared, thermogravimetric analysis, static water contact angle measurements and photoluminescence tests have been employed. Fourier transform infrared verifies the successful preparation of the lanthanide complexes and the modified poly(ethylene-co-acrylic acid) films. These films can emit strong characteristic red and green light under UV light excitation. In addition, the films both have short lifetime (1.14 ms and 1.21 ms), high thermal stability (Td = 408 °C and 411 °C) and, compared with unmodified ones, increased hydrophilicity. All these results suggest that the modified films have potential application as luminescent materials under high temperature.

Big data in reciprocal space: Sliding fast Fourier transforms for determining periodicity

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

Vasudevan, Rama K., E-mail: rvv@ornl.gov; Belianinov, Alex; Baddorf, Arthur P.

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La{sub 5/8}Ca{sub 3/8}MnO{sub 3} (LCMO) films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis and Independent Component Analysismore » of the Sliding FFT dataset reveal the distinct changes in crystallography, step edges, and boundaries between the multiple sub-lattices. The implications for the LCMO system are discussed. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Rotation invariant features for wear particle classification

NASA Astrophysics Data System (ADS)

Arof, Hamzah; Deravi, Farzin

1997-09-01

This paper investigates the ability of a set of rotation invariant features to classify images of wear particles found in used lubricating oil of machinery. The rotation invariant attribute of the features is derived from the property of the magnitudes of Fourier transform coefficients that do not change with spatial shift of the input elements. By analyzing individual circular neighborhoods centered at every pixel in an image, local and global texture characteristics of an image can be described. A number of input sequences are formed by the intensities of pixels on concentric rings of various radii measured from the center of each neighborhood. Fourier transforming the sequences would generate coefficients whose magnitudes are invariant to rotation. Rotation invariant features extracted from these coefficients were utilized to classify wear particle images that were obtained from a number of different particles captured at different orientations. In an experiment involving images of 6 classes, the circular neighborhood features obtained a 91% recognition rate which compares favorably to a 76% rate achieved by features of a 6 by 6 co-occurrence matrix.

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.

REPETITA: detection and discrimination of the periodicity of protein solenoid repeats by discrete Fourier transform

PubMed Central

Marsella, Luca; Sirocco, Francesco; Trovato, Antonio; Seno, Flavio; Tosatto, Silvio C.E.

2009-01-01

Motivation: Proteins with solenoid repeats evolve more quickly than non-repetitive ones and their periodicity may be rapidly hidden at sequence level, while still evident in structure. In order to identify these repeats, we propose here a novel method based on a metric characterizing amino-acid properties (polarity, secondary structure, molecular volume, codon diversity, electric charge) using five previously derived numerical functions. Results: The five spectra of the candidate sequences coding for structural repeats, obtained by Discrete Fourier Transform (DFT), show common features allowing determination of repeat periodicity with excellent results. Moreover it is possible to introduce a phase space parameterized by two quantities related to the Fourier spectra which allow for a clear distinction between a non-homologous set of globular proteins and proteins with solenoid repeats. The DFT method is shown to be competitive with other state of the art methods in the detection of solenoid structures, while improving its performance especially in the identification of periodicities, since it is able to recognize the actual repeat length in most cases. Moreover it highlights the relevance of local structural propensities in determining solenoid repeats. Availability: A web tool implementing the algorithm presented in the article (REPETITA) is available with additional details on the data sets at the URL: http://protein.bio.unipd.it/repetita/. Contact: silvio.tosatto@unipd.it PMID:19478001

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.

Crystal growth, structural, optical, mechanical and thermal properties of a new nonlinear optical single crystal: L-Ornithine monohydrochloride.

PubMed

Balakrishnan, T; Ramamurthi, K

2009-03-01

Amino acid family crystals exhibit excellent nonlinear optical and electro optical properties. l-Ornithine monohydrochloride single crystal, belongs to the amino acid group, was grown by the slow evaporation solution growth technique at room temperature. The grown crystals were characterized by single crystal and powder X-ray diffraction analysis, Fourier transform infrared (FTIR) spectroscopy, TGA, DTA and DSC analyses. UV-vis-NIR spectrum shows excellent transmission in the UV, visible and NIR region (300-1600nm). The mechanical properties of grown crystals were studied using Vickers microhardness tester. Its second harmonic generation efficiency was tested using Nd:YAG laser and is 1.25 times that of KDP.

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.

Computing the Power-Density Spectrum for an Engineering Model

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1982-01-01

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

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…

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)...

Propagation Characteristics Of Weakly Guiding Optical Fibers

NASA Technical Reports Server (NTRS)

Manshadi, Farzin

1992-01-01

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

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.

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 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.

Symmetry transition via tetravalent impurity and investigations on magnetic properties of Li0.5Fe2.5O4

NASA Astrophysics Data System (ADS)

Kounsalye, Jitendra S.; Kharat, Prashant B.; Chavan, Apparao R.; Humbe, Ashok V.; Borade, R. M.; Jadhav, K. M.

2018-04-01

The present study, deals with the phase symmetry transformation of lithium ferrite after introducing tetravalent (Ti4+) impurity. The sol-gel auto combustion technique was adopted for the synthesis of nanoparticle samples with generic chemical formula Li0.5Fe2.5O4 and Li0.55Ti0.10Fe2.35O4. The synthesized nanoparticles were characterized by X-ray diffraction (XRD) technique for structural analysis. The XRD patterns show the single phase cubic structure without any impurity phase but the P4332 to Fd-3m transformation was observed after introducing Ti4+ impurity. The Nano size of the synthesized particles was confirmed by crystallite size ( 20nm) calculated using Debye-Scherrer's formula. The Fourier transform infrared spectroscopy (FTIR) studies shows shifting of band frequencies which reflect the structural changes after tetravalent substitutional impurities. The magnetic properties were studied through pulse field hysteresis loop (M-H loop) technique at room temperature, the M-H loops showdecrease in magnetic properties afternonmagnetic Ti4+ ion substitution. This is attributed to transition of inverse spinel structure of lithium ferrite to random spinel structure.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Determination of glass transition temperature of reduced graphene oxide-poly(vinyl alcohol) composites using temperature dependent Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Mahendia, Suman; Heena; Kandhol, Geeta; Deshpande, Uday P.; Kumar, Shyam

2016-05-01

In the present work, structural properties of reduced graphene oxide (RGO) synthesized using modified Hummer's method and its composites with Poly(vinyl alcohol) (PVA) fabricated using solution-cast method have been studied. The structural properties of prepared samples have been systematically studied through UV-Visible absorption, Raman, Fourier Transform Infrared (FTIR) and Differential Scanning Calorimeter (DSC) spectroscopy. Infrared spectroscopy indicates the grafting of PVA chains with graphene layer through the formation of H-bonding linkage in the composites. Temperature-dependent FTIR spectra of PVA-RGO composite films were recorded to obtain the glass transition temperature (Tg) and to study its molecular origin. From these spectra the values of Tg were obtained using two-dimensional (2D) mapping of the first derivative of the absorbance intensity with respect to temperature (dA/dT), over the space of wavenumber and temperature. The value of Tg obtained for pure PVA increases from 78 °C to 92 °C after loading 0.5 wt.% of RGO in PVA and can be attributed to the strong H-bonding interaction between polymer chains and grafted solid surface of RGO. These results are in good agreement with those obtained from DSC analysis. This clearly indicates that the thermal behavior of PVA gets modified with loading of RGO.

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.

Crystalline structures, thermal properties and crystallizing mechanism of polyamide 6 nanotubes in confined space

NASA Astrophysics Data System (ADS)

Li, Xiaoru; Peng, Zhi; Yang, Chao; Han, Ping; Song, Guojun; Cong, Longliang

2016-09-01

The polyamide 6 (PA6) nanotubes were prepared by infiltrating the anodic aluminum oxide templates with polymer solution. Crystalline regions in the nanotube walls were detected by high-resolution transmission electron microscopy (HRTEM). X-ray diffraction (XRD), Fast Fourier Transform (FFT) and differential scanning calorimetry (DSC) techniques were employed to investigate crystallization, crystal faces and thermodynamics. It was found that the crystals were transformed from α-form in bulk to γ-form in nanotubes. It was made a detailed analysis in this article. Moreover, schematic diagram for the crystallizing mechanism of PA6 nanotubes was given to explain PA6 molecules how to crystallize in the nano-pores.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

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.

Study of nonlinear absorption properties of reduced graphene oxide by Z-scan technique

NASA Astrophysics Data System (ADS)

Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.

2017-05-01

Graphene has generated enormous research interest during the last decade due to its significant unique properties and wide applications in the field of optoelectronics and photonics. This research studied the structural and nonlinear absorption properties of reduced graphene oxide (rGO) synthesized by Modified Hummer's method. Structural and physiochemical properties of the rGO were explored with the help of Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy (Raman). Nonlinear absorption property in rGO, was investigated by open aperture Z-scan technique by using a continuous wave (CW) laser. The Z-scan results demonstrate saturable absorption property of rGO with a nonlinear absorption coefficient, β, of -2.62 × 10-4 cm/W, making it suitable for applications in Q switching, generation of ultra-fast high energy pulses in laser cavity and mode lockers.

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

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).

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.

Phase Transformation, Surface Morphology and Dielectric Property of P(VDF-HFP)/MgCl2·6H2O Nanocomposites

NASA Astrophysics Data System (ADS)

Yuennan, J.; Sukwisute, P.; Boripet, B.; Muensit, N.

2017-09-01

Nanocomposite piezoelectric films based on the blend of poly(vinylidenefluoride-hexafluoropropylene) (PVDF-HFP) and magnesium chloride hexahydrate (MgCl2•6H2O) have been investigated in this work. The films incorporated with 0.5 wt% MgCl2•6H2O were prepared using a solution casting technique and uniaxially stretched at various ratios from 2 to 6 times in order to characterize phase transformation, surface morphology and dielectric behaviour. The piezoelectric β phase transformation and crystallinity of the stretched films were identified by Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD). A scanning electron microscopy (SEM) was conducted to observe the surface microstructure and porosity. The frequency dependence of dielectric properties was also measured by LCR meter at room temperature. The stretched films show the larger the stretching ratio, the greater the microdefects appearance. This leads to a decrease of dielectric constant with stretching ratio. Nevertheless, the P(VDF-HFP) nanocomposites with stretching ratio of 4 times display a higher β phase fraction of 90% than the unstretched films. Thus, this result points out that the β phase transformation of the composite films can be enhanced by mechanically stretching process.

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.

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)

Processing study of a high temperature adhesive

NASA Technical Reports Server (NTRS)

Progar, D. J.

1984-01-01

An adhesive-bonding process cycle study was performed for a polyimidesulphone. The high molecular weight, linear aromatic system possesses properties which make it attractive as a processable, low-cost material for elevated temperature applications. The results of a study to better understand the parameters that affect the adhesive properties of the polymer for titanium alloy adherends are presented. These include the tape preparation, the use of a primer and press and simulated autoclave processing conditions. The polymer was characterized using Fourier transform infrared spectroscopy, glass transition temperature determination, flow measurements, and weight loss measurements. The lap shear strength of the adhesive was used to evaluate the effects of the bonding process variations.

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

Gantayat, S., E-mail: subhra-gantayat@rediffmail.com; Rout, D.; Swain, S. K.

The effect of the functionalization of multiwalled carbon nanotube on the structure and electrical properties of composites was investigated. Samples based on epoxy resin with different weight percentage of MWCNTs were prepared and characterized. The interaction between MWCNT & epoxy resin was noticed by Fourier transform infrared spectroscopy (FTIR). The structure of functionalized multiwalled carbon nanotube (f-MWCNT) reinforced epoxy composite was studied by field emission scanning electron microscope (FESEM). The dispersion of f-MWCNT in epoxy resin was evidenced by high resolution transmission electron microscope (HRTEM). Electrical properties of epoxy/f-MWCNT nanocomposites were measured & the result indicated that the conductivity increasedmore » with increasing concentration of f-MWCNTs.« less

Synthesis and mechanical properties of double cross-linked gelatin-graphene oxide hydrogels.

PubMed

Piao, Yongzhe; Chen, Biqiong

2017-08-01

Gelatin is an interesting biological macromolecule for biomedical applications. Here, double cross-linked gelatin nanocomposite hydrogels with incorporation of graphene oxide (GO) were synthesized in one pot using glutaraldehyde (GTA) and GTA-grafted GO as double chemical cross-linkers. The nanocomposite hydrogels, in contrast to the neat gelatin hydrogel, exhibited significant increases in mechanical properties by up to 288% in compressive strength, 195% in compressive modulus, 267% in compressive fracture energy and 160% shear storage modulus with the optimal GO concentration. Fourier transform infrared spectroscopy, scanning electron microscopy and swelling tests were implemented to characterize the nanocomposite hydrogels. Copyright © 2017 Elsevier B.V. All rights reserved.

Microwave assisted combustion synthesis of nanocrystalline CoFe2O4 for LPG sensing

NASA Astrophysics Data System (ADS)

Chaudhari, Prashant; Acharya, S. A.; Darunkar, S. S.; Gaikwad, V. M.

2015-08-01

A microwave-assisted citrate precursor method has been utilized for synthesis of nanocrystalline powders of CoFe2O4. The process takes only a few minutes to obtain as-synthesized CoFe2O4. Structural properties of the synthesized material were investigated by X-ray diffraction; scanning electron microscopy, Thermogravimetric analysis (TGA) and Fourier transform infrared spectroscopy. The gas sensing properties of thick film of CoFe2O4 prepared by screen printing towards Liquid Petroleum Gas (LPG) revealed that CoFe2O4 thick films are sensitive and shows maximum sensitivity at 350°C for 2500 ppm of LPG.

Properties of Unrelaxed InAs1-XSbX Alloys Grown on Compositionally Graded Buffers

DTIC Science & Technology

2011-10-07

beam epitaxy (MBE) as an alternative to HgCdTe for the fabrication of infrared (IR) photodetectors. These photodetector structures require the...FTIR) spectrometer equipped with a liquid-nitrogen cooled HgCdTe detector with a cut-off wavelength of 12 lm. The PL was excited by a 970 nm laser...characterized by surface roughness up to 10 nm for InAs0.56Sb0.44 samples. The PL and absorption spectra were measured with a Fourier-transform infrared

To study the effect of doping concentration of silver on structural and optical properties of cadmium oxide (CdO) nanostructure

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

Kumar, Rajesh, E-mail: rkkaushik06@gmail.com; Dept. of Physics, Vaish College of Engineering, Rohtak-124001, Haryana; Sharma, Ashwani

The present work deals with study of structural and optical properties of Silver (Ag) doped Cadmium oxide (CdO) nanostructured synthesized by Chemical Co-precipitation Techniques followed by calcinations at small temperature. The doping concentrations were changing from 0.1 to 10 at% respectively. Structural analysis study of these calcined materials is carried out by X-ray diffraction (XRD), Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). The optical properties of calcined samples were investigating by Fourier transformation infrared (FTIR)spectroscopy, UV-Visible Spectroscopy (UV-Vis). The structural properties analysis results revels that crystallite size are in the range of nano region and TEM results aremore » quite in accordance with XRD results.« less

Optical properties of Dy3+ doped YBO3 phosphor

NASA Astrophysics Data System (ADS)

Nair, Ramya G.; Nigam, Sandeep; Sudarsan, V.; Vatsa, R. K.

2018-04-01

Dysprosium doped YBO3 luminescent particleis synthesized via poly-ol method and by subsequent annealing at 800°C. The synthesized material has been characterized for structure properties using powder X-ray diffraction (XRD) and Fourier transform infrared (FTIR)spectroscopy. Photoluminescence properties of these samples are studiedby means of steady state measurements and decay curve. The phosphor shows characteristic transitions of Dy3+ in the excitation and emission spectra. Colour purity is determined in terms of yellow/blue ratio, which is found to be 1.8. The higher ratio of yellow/blue indicates that Dy3+ preferentially occupies the asymmetric site in host lattice. The average lifetime is found to be 1.1ms. The chromatic properties of the phosphor have been found to have chromaticity coordinates x = 0.245, y = 0.274.

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...

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.

Cryo-Infrared Optical Characterization at NASA GSFC

NASA Technical Reports Server (NTRS)

Boucarut, Ray; Quijada, Manuel A.; Henry, Ross M.

2004-01-01

The development of large space infrared optical systems, such as the Next Generation Space Telescope (NGST), has increased requirements for measurement accuracy in the optical properties of materials. Many materials used as optical components in infrared optical systems, have strong temperature dependence in their optical properties. Unfortunately, data on the temperature dependence of most of these materials is sparse. In this paper, we provide a description of the capabilities existing in the Optics Branch at the Goddard Space Flight Center that enable the characterization of the refractive index and absorption coefficient changes and other optical properties in infrared materials at cryogenic temperatures. Details of the experimental apparatus, which include continuous flow liquid helium optical cryostat, and a Fourier Transform Infrared (FTIR) spectrometer are discussed.

Preparation and Characterization of Extruded Composites Based on Polypropylene and Chitosan Compatibilized with Polypropylene-Graft-Maleic Anhydride.

PubMed

Carrasco-Guigón, Fernando Javier; Rodríguez-Félix, Dora Evelia; Castillo-Ortega, María Mónica; Santacruz-Ortega, Hisila C; Burruel-Ibarra, Silvia E; Encinas-Encinas, Jose Carmelo; Plascencia-Jatomea, Maribel; Herrera-Franco, Pedro Jesus; Madera-Santana, Tomas Jesus

2017-01-25

The preparation of composites of synthetic and natural polymers represent an interesting option to combine properties; in this manner, polypropylene and chitosan extruded films using a different proportion of components and polypropylene-graft-maleic anhydride (PPgMA) as compatibilizer were prepared. The effect of the content of the biopolymer in the polypropylene (PP) matrix, the addition of compatibilizer, and the particle size on the properties of the composites was analyzed using characterization by fourier transform-infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), tensile strength, and contact angle, finding that in general, the addition of the compatibilizer and reducing the particle size of the chitosan, favored the physicochemical and morphological properties of the films.

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.

Fourier Phase Domain Steganography: Phase Bin Encoding Via Interpolation

NASA Astrophysics Data System (ADS)

Rivas, Edward

2007-04-01

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

Spectral analysis for GNSS coordinate time series using chirp Fourier transform

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

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.

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.

Phase in Optical Image Processing

NASA Astrophysics Data System (ADS)

Naughton, Thomas J.

2010-04-01

The use of phase has a long standing history in optical image processing, with early milestones being in the field of pattern recognition, such as VanderLugt's practical construction technique for matched filters, and (implicitly) Goodman's joint Fourier transform correlator. In recent years, the flexibility afforded by phase-only spatial light modulators and digital holography, for example, has enabled many processing techniques based on the explicit encoding and decoding of phase. One application area concerns efficient numerical computations. Pushing phase measurement to its physical limits, designs employing the physical properties of phase have ranged from the sensible to the wonderful, in some cases making computationally easy problems easier to solve and in other cases addressing mathematics' most challenging computationally hard problems. Another application area is optical image encryption, in which, typically, a phase mask modulates the fractional Fourier transformed coefficients of a perturbed input image, and the phase of the inverse transform is then sensed as the encrypted image. The inherent linearity that makes the system so elegant mitigates against its use as an effective encryption technique, but we show how a combination of optical and digital techniques can restore confidence in that security. We conclude with the concept of digital hologram image processing, and applications of same that are uniquely suited to optical implementation, where the processing, recognition, or encryption step operates on full field information, such as that emanating from a coherently illuminated real-world three-dimensional object.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

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.

Comparative study of modified bitumen binder properties collected from mixing plant and quarry.

NASA Astrophysics Data System (ADS)

Mustafa Kamal, M.; Abu Bakar, R.; Hadithon, K. A.

2017-11-01

Quality control and assurance are essential in pavement construction. In general, the properties of bitumen change as it ages in bulk storage, transport, and storage on site. The minimization of bituminous hardening during storing, transportation and mixing depends on careful control of binder temperature. Hence therefore, bitumen should always be stored and handled at the lowest temperature possible, consistent with efficient use. The objective of the work is to monitor the quality of bitumen samples collected from mixing plant and quarry. Results showed that, samples modified bitumen which collected from quarry showed some adverse effects on rheological properties and physical properties after subjecting to high temperature storage within a period of time. The dynamic stiffness, elastic properties and other common binder properties were deteriorated too. The chemical changes that occurred during storage were analysed using Fourier transform infra-red spectroscopy (FTIR). Thus studies developed an understanding of bitumen ageing in storage.

The alterations in high density polyethylene properties with gamma irradiation

NASA Astrophysics Data System (ADS)

Zaki, M. F.; Elshaer, Y. H.; Taha, Doaa. H.

2017-10-01

In the present investigation, high density polyethylene (HDPE) polymer has been used to study the alterations in its properties under gamma-irradiation. Physico-chemical properties have been investigated with different spectroscopy techniques, Fourier Transform Infrared spectroscopy (FTIR), X-ray diffraction (XRD), biocompatibility properties, as well as, mechanical properties change. The FT-IR analysis shows the formation of new band at 1716 cm-1 that is attributed to the oxidation of irradiated polymer chains, which is due to the formation of carbonyl groups (C˭O). XRD patterns show that a decrease in the crystallite size and increase in the Full Width at Half Maximum (FWHM). This means that the crystallinity of irradiated samples is decreased with increase in gamma dose. The contact angle measurements show an increase in the surface free energy as the gamma irradiation increases. The measurements of mechanical properties of irradiated HDPE samples were discussed.

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.