Orientations of nonlocal vibrational modes from combined experimental and theoretical sum frequency spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Chase, Hilary M.; Chen, Shunli; Fu, Li; Upshur, Mary Alice; Rudshteyn, Benjamin; Thomson, Regan J.; Wang, Hong-Fei; Batista, Victor S.; Geiger, Franz M.

2017-09-01

Inferring molecular orientations from vibrational sum frequency generation (SFG) spectra is challenging in polarization combinations that result in low signal intensities, or when the local point group symmetry approximation fails. While combining experiments with density functional theory (DFT) could overcome this problem, the scope of the combined method has yet to be established. Here, we assess its feasibility of determining the distributions of molecular orientations for one monobasic ester, two epoxides and three alcohols at the vapor/fused silica interface. We find that molecular orientations of nonlocal vibrational modes cannot be determined using polarization-resolved SFG measurements alone.

Electro-Optical Imaging Fourier-Transform Spectrometer

Science.gov (United States)

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.

Circularly polarized infrared and visible sum-frequency-generation spectroscopy: Vibrational optical activity measurement

International Nuclear Information System (INIS)

Cheon, Sangheon; Cho, Minhaeng

2005-01-01

Vibrational optical activity spectroscopies utilizing either circularly polarized ir or circularly polarized visible beams were theoretically investigated by considering the infrared and visible sum-frequency-generation (IV-SFG) schemes. In addition to the purely electric dipole-allowed chiral component of the IV-SFG susceptibility, the polarizability-electric quadrupole hyperpolarizability term also contributes to the vibrationally resonant IV-SFG susceptibility. The circular-intensity-difference signal is shown to be determined by the interferences between the all-electric dipole-allowed chiral component and the polarizability-electric-dipole or electric-dipole-electric-quadrupole Raman optical activity tensor components. The circularly polarized SFG methods are shown to be potentially useful coherent spectroscopic tools for determining absolute configurations of chiral molecules in condensed phases

Theoretical study of sum-frequency vibrational spectroscopy on limonene surface

International Nuclear Information System (INIS)

Zheng, Ren-Hui; Liu, Hao; Jing, Yuan-Yuan; Wang, Bo-Yang; Shi, Qiang; Wei, Wen-Mei

2014-01-01

By combining molecule dynamics (MD) simulation and quantum chemistry computation, we calculate the surface sum-frequency vibrational spectroscopy (SFVS) of R-limonene molecules at the gas-liquid interface for SSP, PPP, and SPS polarization combinations. The distributions of the Euler angles are obtained using MD simulation, the ψ-distribution is between isotropic and Gaussian. Instead of the MD distributions, different analytical distributions such as the δ-function, Gaussian and isotropic distributions are applied to simulate surface SFVS. We find that different distributions significantly affect the absolute SFVS intensity and also influence on relative SFVS intensity, and the δ-function distribution should be used with caution when the orientation distribution is broad. Furthermore, the reason that the SPS signal is weak in reflected arrangement is discussed

Theoretical study of sum-frequency vibrational spectroscopy on limonene surface

Energy Technology Data Exchange (ETDEWEB)

Zheng, Ren-Hui, E-mail: zrh@iccas.ac.cn; Liu, Hao; Jing, Yuan-Yuan; Wang, Bo-Yang; Shi, Qiang [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China); Wei, Wen-Mei [Department of Chemistry, College of Basic Medicine, Anhui Medical University, Hefei, Anhui 230032 (China)

2014-03-14

By combining molecule dynamics (MD) simulation and quantum chemistry computation, we calculate the surface sum-frequency vibrational spectroscopy (SFVS) of R-limonene molecules at the gas-liquid interface for SSP, PPP, and SPS polarization combinations. The distributions of the Euler angles are obtained using MD simulation, the ψ-distribution is between isotropic and Gaussian. Instead of the MD distributions, different analytical distributions such as the δ-function, Gaussian and isotropic distributions are applied to simulate surface SFVS. We find that different distributions significantly affect the absolute SFVS intensity and also influence on relative SFVS intensity, and the δ-function distribution should be used with caution when the orientation distribution is broad. Furthermore, the reason that the SPS signal is weak in reflected arrangement is discussed.

Vibrational analysis of Fourier transform spectrum of the A3Π0–X1Σ ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 73; Issue 5. Vibrational analysis of Fourier transform spectrum of the A 3 0 – X 1 ∑ + and B 3 1 – X 1 ∑ + transitions of indium monobromide. Renu Singh K N Uttam M D Saksena M N Deo. Volume 73 Issue 5 November 2009 pp 889-899 ...

Separate recording of rationally related vibration frequencies using digital stroboscopic holographic interferometry

International Nuclear Information System (INIS)

Alexeenko, Igor; Gusev, Michael; Gurevich, Vadim

2009-01-01

A method for separate recording of rationally related vibration frequencies is presented. To record and measure the mode shape of vibrations, a synchronized stroboscopic CCD camera is used. Synchronization and control of the camera acquisition for recording stroboscopic holographic sequence has been realized. The phase for different states of the object vibration is calculated using the Fourier-transform method. Experimental results are presented, and the advantages and disadvantages of the proposed method are discussed.

The fractional Fourier transform and applications

Science.gov (United States)

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.

Combined IR-Raman vs vibrational sum-frequency heterospectral correlation spectroscopy

Science.gov (United States)

Roy, Sandra; Beutier, Clémentine; Hore, Dennis K.

2018-06-01

Vibrational sum-frequency generation spectroscopy is a valuable probe of surface structure, particularly when the same molecules are present in one of the adjacent bulk solid or solution phases. As a result of the non-centrosymmetric requirement of SFG, the signal generated is a marker of the extent to which the molecules are ordered in an arrangement that breaks the up-down symmetry at the surface. In cases where the accompanying changes in the bulk are of interest in understanding and interpreting the surface structure, simultaneous analysis of the bulk IR absorption or bulk Raman scattering is helpful, and may be used in heterospectral surface-bulk two-dimensional correlation. We demonstrate that, in such cases, generating a new type of bulk spectrum that combines the IR and Raman amplitudes is a better candidate than the individual IR and Raman spectra for the purpose of correlation with the SFG signal.

Clifford Fourier transform on vector fields.

Science.gov (United States)

Ebling, Julia; Scheuermann, Gerik

2005-01-01

Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

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

Science.gov (United States)

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

2017-07-01

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

Building Modern Vibration Diagnostics Systems Based on the Frequency-Time Transformations of A Measured Signal

Directory of Open Access Journals (Sweden)

Yasoveev Vasikh

2016-01-01

Full Text Available Basic methods of analysis of vibration transducers signals were reviewed. Continuous wavelet transform, being a time-frequency transform, was found to be an advanced mathematical tool for analysis of vibration signals. Experimental studies revealed obvious changes in the continuous wavelet transform spectrum depending on the existing defects. A method for detection and identification of technological violations based on the analysis of CWT spectrum components and normalized correlation coefficient was suggested. In accordance with the suggested method software for vibration diagnostics was developed.

Applications of Fourier transforms to generalized functions

CERN Document Server

Rahman, M

2011-01-01

This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...

Coherent optical effect on time-resolved vibrational SFG spectrum of adsorbates

Science.gov (United States)

Ueba, H.; Sawabu, T.; Mii, T.

2002-04-01

We present a theory to study the influence of the coherent mixing between pump-infrared and probe-visible pulse on a time-resolved sum-frequency generation (TR-SFG) spectrum for vibrations at surfaces. The general formula of the time-dependent and its Fourier transform of the SFG polarization and its Fourier transform allows us to calculate the time-resolved vibrational SFG spectrum and the transient characteristics of the SFG intensity as a function of the delay time td between the pump-infrared and probe-visible pulse. It is found the coherent optical effect manifests itself in the broadening and narrowing of the SFG spectrum with the intrinsic width of T2 at negative and positive td, respectively, being in qualitative agreement with recent experimental results. The influence of the coherent mixing on the transient behavior of the SFG intensity is also discussed in conjunction to the T2 determination.

Sum frequency generation and catalytic reaction studies of the removal of the organic capping agents from Pt nanoparticles by UV-ozone treatment

Energy Technology Data Exchange (ETDEWEB)

Aliaga, Cesar; Park, Jeong Y.; Yamada, Yusuke; Lee, Hyun Sook; Tsung, Chia-Kuang; Yang, Peidong; Somorjai, Gabor A.

2009-12-10

We report the structure of the organic capping layers of platinum colloid nanoparticles and their removal by UV-ozone exposure. Sum frequency generation vibrational spectroscopy (SFGVS) studies identify the carbon-hydrogen stretching modes on poly(vinylpyrrolidone) (PVP) and tetradecyl tributylammonium bromide (TTAB)-capped platinum nanoparticles. We found that the UV-ozone treatment technique effectively removes the capping layer on the basis of several analytical measurements including SFGVS, X-ray photoelectron spectroscopy, and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). The overall shape of the nanoparticles was preserved after the removal of capping layers, as confirmed by transmission electron microscopy (TEM). SFGVS of ethylene hydrogenation on the clean platinum nanoparticles demonstrates the existence of ethylidyne and di-{sigma}-bonded species, indicating the similarity between single-crystal and nanoparticle systems.

Vector frequency-comb Fourier-transform spectroscopy for characterizing metamaterials

International Nuclear Information System (INIS)

Ganz, T; Brehm, M; Von Ribbeck, H G; Keilmann, F; Van der Weide, D W

2008-01-01

We determine infrared transmission amplitude and phase spectra of metamaterial samples at well-defined incidence and polarization with a vector ('asymmetric') frequency-comb Fourier-transform spectrometer (c-FTS) that uses no moving elements. The metamaterials are free-standing metallic hole arrays; we study their resonances in the 7-13 μm and 100-1000 μm wavelength regions due both to interaction with bulk waves (Wood anomaly) and with leaky surface plasmon polaritons (near-unity transmittance, coupling features and dispersion). Such complex-valued transmission and reflection spectra could be used to compute a metamaterial's complex dielectric function directly, as well as its magnetic and magneto-optical permeability functions.

Sum Frequency Generation Vibrational Spectroscopy and Kinetic Study of 2-Methylfuran and 2,5-Dimethylfuran Hydrogenation over 7 nm Platinum Cubic Nanoparticles

KAUST Repository

Aliaga, Cesar; Tsung, Chia-Kuang; Alayoglu, Selim; Komvopoulos, Kyriakos; Yang, Peidong; Somorjai, Gabor A.

2011-01-01

Sum frequency generation vibrational spectroscopy and kinetic measurements obtained from gas chromatography were used to study the adsorption and hydrogenation of 2-methylfuran (MF) and 2,5-dimethylfuran (DMF) over cubic Pt nanoparticles of 7 nm

Pattern recognition based on time-frequency analysis and convolutional neural networks for vibrational events in φ-OTDR

Science.gov (United States)

Xu, Chengjin; Guan, Junjun; Bao, Ming; Lu, Jiangang; Ye, Wei

2018-01-01

Based on vibration signals detected by a phase-sensitive optical time-domain reflectometer distributed optical fiber sensing system, this paper presents an implement of time-frequency analysis and convolutional neural network (CNN), used to classify different types of vibrational events. First, spectral subtraction and the short-time Fourier transform are used to enhance time-frequency features of vibration signals and transform different types of vibration signals into spectrograms, which are input to the CNN for automatic feature extraction and classification. Finally, by replacing the soft-max layer in the CNN with a multiclass support vector machine, the performance of the classifier is enhanced. Experiments show that after using this method to process 4000 vibration signal samples generated by four different vibration events, namely, digging, walking, vehicles passing, and damaging, the recognition rates of vibration events are over 90%. The experimental results prove that this method can automatically make an effective feature selection and greatly improve the classification accuracy of vibrational events in distributed optical fiber sensing systems.

Fourier transform nuclear magnetic resonance

International Nuclear Information System (INIS)

Geick, R.

1981-01-01

This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)

Vibration mode and vibration shape under excitation of a three phase model transformer core

Science.gov (United States)

Okabe, Seiji; Ishigaki, Yusuke; Omura, Takeshi

2018-04-01

Structural vibration characteristics and vibration shapes under three-phase excitation of a archetype transformer core were investigated to consider their influences on transformer noise. Acoustic noise and vibration behavior were measured in a three-limb model transformer core. Experimental modal analysis by impact test was performed. The vibration shapes were measured by a laser scanning vibrometer at different exciting frequencies. Vibration amplitude of the core in out-of-plane direction were relatively larger than those in other two in-plane directions. It was consistent with the result that the frequency response function of the core in out-of-plane direction was larger by about 20 dB or more than those in in-plane directions. There were many vibration modes having bending deformation of limbs in out-of-plane direction. The vibration shapes of the core when excited at 50 Hz and 60 Hz were almost the same because the fundamental frequencies of the vibration were not close to the resonance frequencies. When excitation frequency was 69 Hz which was half of one of the resonance frequencies, the vibration shape changed to the one similar to the resonance vibration mode. Existence of many vibration modes in out-of-plane direction of the core was presumed to be a reason why frequency characteristics of magnetostriction and transformer noise do not coincide.

Quantitative Surface Chirality Detection with Sum Frequency Generation Vibrational Spectroscopy: Twin Polarization Angle Approach

International Nuclear Information System (INIS)

Wei, Feng; Xu, Yanyan; Guo, Yuan; Liu, Shi-lin; Wang, Hongfei

2009-01-01

Here we report a novel twin polarization angle (TPA) approach in the quantitative chirality detection with the surface sum-frequency generation vibrational spectroscopy (SFG-VS). Generally, the achiral contribution dominates the surface SFG-VS signal, and the pure chiral signal is usually two or three orders of magnitude smaller. Therefore, it has been difficult to make quantitative detection and analysis of the chiral contributions to the surface SFG-VS signal. In the TPA method, by varying together the polarization angles of the incoming visible light and the sum frequency signal at fixed s or p polarization of the incoming infrared beam, the polarization dependent SFG signal can give not only direct signature of the chiral contribution in the total SFG-VS signal, but also the accurate measurement of the chiral and achiral components in the surface SFG signal. The general description of the TPA method is presented and the experiment test of the TPA approach is also presented for the SFG-VS from the S- and R-limonene chiral liquid surfaces. The most accurate degree of chiral excess values thus obtained for the 2878 cm -1 spectral peak of the S- and R-limonene liquid surfaces are (23.7±0.4)% and (25.4±1.3)%, respectively.

Surface Fourier-transform lens using a metasurface

International Nuclear Information System (INIS)

Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun

2015-01-01

We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)

Selective detection of crystalline cellulose in plant cell walls with sum-frequency-generation (SFG) vibration spectroscopy.

Science.gov (United States)

Barnette, Anna L; Bradley, Laura C; Veres, Brandon D; Schreiner, Edward P; Park, Yong Bum; Park, Junyeong; Park, Sunkyu; Kim, Seong H

2011-07-11

The selective detection of crystalline cellulose in biomass was demonstrated with sum-frequency-generation (SFG) vibration spectroscopy. SFG is a second-order nonlinear optical response from a system where the optical centrosymmetry is broken. In secondary plant cell walls that contain mostly cellulose, hemicellulose, and lignin with varying concentrations, only certain vibration modes in the crystalline cellulose structure can meet the noninversion symmetry requirements. Thus, SFG can be used to detect and analyze crystalline cellulose selectively in lignocellulosic biomass without extraction of noncellulosic species from biomass or deconvolution of amorphous spectra. The selective detection of crystalline cellulose in lignocellulosic biomass is not readily achievable with other techniques such as XRD, solid-state NMR, IR, and Raman analyses. Therefore, the SFG analysis presents a unique opportunity to reveal the cellulose crystalline structure in lignocellulosic biomass.

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2001-01-01

The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution

Effects of cations and cholesterol with sphingomyelin membranes investigated by high-resolution broadband sum frequency vibrational spectroscopy

Science.gov (United States)

Zhang, Zhen; Feng, Rong-juan; Li, Yi-yi; Liu, Ming-hua; Guo, Yuan

2017-08-01

Sphingomyelin(SM) is specifically enriched in the plasma membrane of mammalian cells. Its molecular structure is compose by N-acyl-Derythro-sphingosylphosphorylcholine. The function of the SM related to membrane signaling and protein trafficking are relied on the interactions of the SM, cations, cholesterol and proteins. In this report, the interaction of three different nature SMs, cations and cholesterol at air/aqueous interfaces studied by high-resolution broadband sum frequency vibrational spectroscopy, respectively. Our results shed lights on understanding the relationship between SMs monolayer, cholesterol and Cations.

Intrinsic Chirality and Prochirality at Air/R-(+)- and S-(-)-Limonene Interfaces: Spectral Signatures with Interference Chiral Sum-Frequency Generation Vibrational Spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Fu, Li; Zhang, Yun; Wei, Zhehao; Wang, Hongfei

2014-06-04

We report in this work detailed measurements on the chiral and achiral sum-frequency vibrational spectra in the C-H stretching vibration region (2800-3050cm-1) of the air/liquid interfaces of R-limonene and S-limonene, using the recently developed high-resolution broadband sum-frequency generation vibrational spectroscopy (HR-BB-SFG-VS). The achiral SFG spectra of R-limonene and S-limonene, as well as the equal amount (50/50) racemic mixture show that the enantiomers are with the same interfacial orientations. The interference chiral SFG spectra of the limonene enantiomers exhibit spectral signature from chiral response of the Cα-H stretching mode, and spectral signature from prochiral response of the CH2 asymmetric stretching mode, respectively. The chiral spectral feature of the Cα-H stretching mode changes sign from R-limonene to S-limonene, and disappears for the 50/50 racemic mixture. While the prochiral spectral feature of the CH2 asymmetric stretching mode is the same for R-limonene and S-limonene, and also surprisingly remains the same for the 50/50 racemic mixture. These results provided detail information in understanding the structure and chirality of molecular interfaces, and demonstrated the sensitivity and potential of SFG-VS as unique spectroscopic tool for chirality characterization and chiral recognition at the molecular interface.

App. 1. Fourier series and Fourier transform

International Nuclear Information System (INIS)

Anon.

1977-01-01

Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

Sum-Frequency Generation from Chiral Media and Interfaces

Energy Technology Data Exchange (ETDEWEB)

Ji, Na [Univ. of California, Berkeley, CA (United States)

2006-02-13

Sum frequency generation (SFG), a second-order nonlinear optical process, is electric-dipole forbidden in systems with inversion symmetry. As a result, it has been used to study chiral media and interfaces, systems intrinsically lacking inversion symmetry. This thesis describes recent progresses in the applications of and new insights into SFG from chiral media and interfaces. SFG from solutions of chiral amino acids is investigated, and a theoretical model explaining the origin and the strength of the chiral signal in electronic-resonance SFG spectroscopy is discussed. An interference scheme that allows us to distinguish enantiomers by measuring both the magnitude and the phase of the chiral SFG response is described, as well as a chiral SFG microscope producing chirality-sensitive images with sub-micron resolution. Exploiting atomic and molecular parity nonconservation, the SFG process is also used to solve the Ozma problems. Sum frequency vibrational spectroscopy is used to obtain the adsorption behavior of leucine molecules at air-water interfaces. With poly(tetrafluoroethylene) as a model system, we extend the application of this surface-sensitive vibrational spectroscopy to fluorine-containing polymers.

Sum-Frequency Generation from Chiral Media and Interfaces

International Nuclear Information System (INIS)

Ji, Na

2006-01-01

Sum frequency generation (SFG), a second-order nonlinear optical process, is electric-dipole forbidden in systems with inversion symmetry. As a result, it has been used to study chiral media and interfaces, systems intrinsically lacking inversion symmetry. This thesis describes recent progresses in the applications of and new insights into SFG from chiral media and interfaces. SFG from solutions of chiral amino acids is investigated, and a theoretical model explaining the origin and the strength of the chiral signal in electronic-resonance SFG spectroscopy is discussed. An interference scheme that allows us to distinguish enantiomers by measuring both the magnitude and the phase of the chiral SFG response is described, as well as a chiral SFG microscope producing chirality-sensitive images with sub-micron resolution. Exploiting atomic and molecular parity nonconservation, the SFG process is also used to solve the Ozma problems. Sum frequency vibrational spectroscopy is used to obtain the adsorption behavior of leucine molecules at air-water interfaces. With poly(tetrafluoroethylene) as a model system, we extend the application of this surface-sensitive vibrational spectroscopy to fluorine-containing polymers

Method of local pointed function reduction of original shape in Fourier transformation

International Nuclear Information System (INIS)

Dosch, H.; Slavyanov, S.Yu.

2002-01-01

The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru

The PROSAIC Laplace and Fourier Transform

International Nuclear Information System (INIS)

Smith, G.A.

1994-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting

Vibration of machine

International Nuclear Information System (INIS)

Kwak, Mun Gyu; Na, Sung Su; Baek, Gwang Hyeon; Song, Chul Gi; Han, Sang Bo

2001-09-01

This book deals with vibration of machine which gives descriptions of free vibration using SDOF system, forced vibration using SDOF system, vibration of multi-degree of freedom system like introduction and normal form, distribution system such as introduction, free vibration of bar and practice problem, approximate solution like lumped approximations and Raleigh's quotient, engineering by intuition and experience, real problem and experimental method such as technology of signal, fourier transform analysis, frequency analysis and sensor and actuator.

Characterisation of the membrane affinity of an isoniazide peptide conjugate by tensiometry, atomic force microscopy and sum-frequency vibrational spectroscopy, using a phospholipid Langmuir monolayer model.

Science.gov (United States)

Hill, Katalin; Pénzes, Csanád Botond; Schnöller, Donát; Horváti, Kata; Bosze, Szilvia; Hudecz, Ferenc; Keszthelyi, Tamás; Kiss, Eva

2010-10-07

Tensiometry, sum-frequency vibrational spectroscopy, and atomic force microscopy were employed to assess the cell penetration ability of a peptide conjugate of the antituberculotic agent isoniazide. Isoniazide was conjugated to peptide (91)SEFAYGSFVRTVSLPV(106), a functional T-cell epitope of the immunodominant 16 kDa protein of Mycobacterium tuberculosis. As a simple but versatile model of the cell membrane a phospholipid Langmuir monolayer at the liquid/air interface was used. Changes induced in the structure of the phospholipid monolayer by injection of the peptide conjugate into the subphase were followed by tensiometry and sum-frequency vibrational spectroscopy. The drug penetrated lipid films were transferred to a solid support by the Langmuir-Blodgett technique, and their structures were characterized by atomic force microscopy. Peptide conjugation was found to strongly enhance the cell penetration ability of isoniazide.

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

Science.gov (United States)

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.

[Research of dual-photoelastic-modulator-based beat frequency modulation and Fourier-Bessel transform imaging spectrometer].

Science.gov (United States)

Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang

2014-02-01

As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.

Characterization of polymer surface structure and surface mechanical behaviour by sum frequency generation surface vibrational spectroscopy and atomic force microscopy

International Nuclear Information System (INIS)

Opdahl, Aric; Koffas, Telly S; Amitay-Sadovsky, Ella; Kim, Joonyeong; Somorjai, Gabor A

2004-01-01

Sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM) have been used to study polymer surface structure and surface mechanical behaviour, specifically to study the relationships between the surface properties of polymers and their bulk compositions and the environment to which the polymer is exposed. The combination of SFG surface vibrational spectroscopy and AFM has been used to study surface segregation behaviour of polyolefin blends at the polymer/air and polymer/solid interfaces. SFG surface vibrational spectroscopy and AFM experiments have also been performed to characterize the properties of polymer/liquid and polymer/polymer interfaces, focusing on hydrogel materials. A method was developed to study the surface properties of hydrogel contact lens materials at various hydration conditions. Finally, the effect of mechanical stretching on the surface composition and surface mechanical behaviour of phase-separated polyurethanes, used in biomedical implant devices, has been studied by both SFG surface vibrational spectroscopy and AFM. (topical review)

Capturing inhomogeneous broadening of the -CN stretch vibration in a Langmuir monolayer with high-resolution spectra and ultrafast vibrational dynamics in sum-frequency generation vibrational spectroscopy (SFG-VS)

Science.gov (United States)

Velarde, Luis; Wang, Hong-fei

2013-08-01

While in principle the frequency-domain and time-domain spectroscopic measurements should generate identical information for a given molecular system, the inhomogeneous character of surface vibrations in sum-frequency generation vibrational spectroscopy (SFG-VS) studies has only been studied with time-domain SFG-VS by mapping the decay of the vibrational polarization using ultrafast lasers, this due to the lack of SFG vibrational spectra with high enough spectral resolution and accurate enough lineshape. Here, with the recently developed high-resolution broadband SFG-VS (HR-BB-SFG-VS) technique, we show that the inhomogeneous lineshape can be obtained in the frequency-domain for the anchoring CN stretch of the 4-n-octyl-4'-cyanobiphenyl (8CB) Langmuir monolayer at the air-water interface, and that an excellent agreement with the time-domain SFG free-induction-decay can be established. We found that the 8CB CN stretch spectrum consists of a single peak centered at 2234.00 ± 0.01 cm-1 with a total linewidth of 10.9 ± 0.3 cm-1 at half maximum. The Lorentzian contribution accounts only for 4.7 ± 0.4 cm-1 to this width and the Gaussian (inhomogeneous) broadening for as much as 8.1 ± 0.2 cm-1. Polarization analysis of the -CN spectra showed that the -CN group is tilted 57° ± 2° from the surface normal. The large heterogeneity in the -CN spectrum is tentatively attributed to the -CN group interactions with the interfacial water molecules penetrated/accommodated into the 8CB monolayer, a unique phenomenon for the nCB Langmuir monolayers reported previously.

The prosaic Laplace and Fourier transform

International Nuclear Information System (INIS)

Smith, G.A.

1995-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics

Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

Science.gov (United States)

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

2017-09-01

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

Fourier transform resampling: Theory and application

International Nuclear Information System (INIS)

Hawkins, W.G.

1996-01-01

One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

Salt Effects on Surface Structures of Polyelectrolyte Multilayers (PEMs) Investigated by Vibrational Sum Frequency Generation (SFG) Spectroscopy.

Science.gov (United States)

Ge, Aimin; Matsusaki, Michiya; Qiao, Lin; Akashi, Mitsuru; Ye, Shen

2016-04-26

Sum frequency generation (SFG) vibrational spectroscopy was employed to investigate the surface structures of polyelectrolyte multilayers (PEMs) constructed by sequentially alternating adsorption of poly(diallyldimethylammonium chloride) (PDDA) and poly(styrenesulfonate) (PSS). It was found that the surface structures and surface charge density of the as-deposited PEMs of PDDA/PSS significantly depend on the concentration of sodium chloride (NaCl) present in the polyelectrolyte solutions. Furthermore, it was found that the surface structure of the as-deposited PEMs is in a metastable state and will reach the equilibrium state by diffusion of the polyelectrolyte chain after an aging process, resulting in a polyelectrolyte mixture on the PEM surfaces.

Fourier transforms principles and applications

CERN Document Server

Hansen, Eric W

2014-01-01

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

A Novel Application of Fourier Transform Spectroscopy with HEMT Amplifiers at Microwave Frequencies

Science.gov (United States)

Wilkinson, David T.; Page, Lyman

1995-01-01

The goal was to develop cryogenic high-electron-mobility transistor (HEMT) based radiometers and use them to measure the anisotropy in the cosmic microwave background (CMB). In particular, a novel Fourier transform spectrometer (FTS) built entirely of waveguide components would be developed. A dual-polarization Ka-band HEMT radiometer and a similar Q-band radiometer were built. In a series of measurements spanning three years made from a ground-based site in Saskatoon, SK, the amplitude, frequency spectrum, and spatial frequency spectrum of the anisotropy were measured. A prototype Ka-band FTS was built and tested, and a simplified version is proposed for the MAP satellite mission. The 1/f characteristics of HEMT amplifiers were quantified using correlation techniques.

Two-dimensional fourier transform spectrometer

Science.gov (United States)

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

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

Science.gov (United States)

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.

Properties of the Simpson discrete fourier transform | Singh ...

African Journals Online (AJOL)

The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...

Fourier Transform Ion Cyclotron Resonance Mass Spectrometry at the Cyclotron Frequency.

Science.gov (United States)

Nagornov, Konstantin O; Kozhinov, Anton N; Tsybin, Yury O

2017-04-01

The phenomenon of ion cyclotron resonance allows for determining mass-to-charge ratio, m/z, of an ensemble of ions by means of measurements of their cyclotron frequency, ω c . In Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), the ω c quantity is usually unavailable for direct measurements: the resonant state is located close to the reduced cyclotron frequency (ω + ), whereas the ω c and the corresponding m/z values may be calculated via theoretical derivation from an experimental estimate of the ω + quantity. Here, we describe an experimental observation of a new resonant state, which is located close to the ω c frequency and is established because of azimuthally-dependent trapping electric fields of the recently developed ICR cells with narrow aperture detection electrodes. We show that in mass spectra, peaks close to ω + frequencies can be reduced to negligible levels relative to peaks close to ω c frequencies. Due to reduced errors with which the ω c quantity is obtained, the new resonance provides a means of cyclotron frequency measurements with precision greater than that achieved when ω + frequency peaks are employed. The described phenomenon may be considered for a development into an FT-ICR MS technology with increased mass accuracy for applications in basic research, life, and environmental sciences. Graphical Abstract ᅟ.

Fourier transforms in the complex domain

CERN Document Server

Wiener, N

1934-01-01

With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of Münz and Szász concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,

Reference Beam Pattern Design for Frequency Invariant Beamforming Based on Fast Fourier Transform

Directory of Open Access Journals (Sweden)

Wang Zhang

2016-09-01

Full Text Available In the field of fast Fourier transform (FFT-based frequency invariant beamforming (FIB, there is still an unsolved problem. That is the selection of the reference beam to make the designed wideband pattern frequency invariant (FI over a given frequency range. This problem is studied in this paper. The research shows that for a given array, the selection of the reference beam pattern is determined by the number of sensors and the ratio of the highest frequency to the lowest frequency of the signal (RHL. The length of the weight vector corresponding to a given reference beam pattern depends on the reference frequency. In addition, the upper bound of the weight length to ensure the FI property over the whole frequency band of interest is also given. When the constraints are added to the reference beam, it does not affect the FI property of the designed wideband beam as long as the symmetry of the reference beam is ensured. Based on this conclusion, a scheme for reference beam design is proposed.

Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....

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

Science.gov (United States)

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

2009-12-01

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

Time-frequency analysis of fusion plasma signals beyond the short-time Fourier transform paradigm: An overview

International Nuclear Information System (INIS)

Bizarro, Joao P.S.; Figueiredo, Antonio C.A.

2008-01-01

Performing a time-frequency (t-f) analysis on actual magnetic pick-up coil data from the JET tokamak, a comparison is presented between the spectrogram and the Wigner and Choi-Williams distributions. Whereas the former, which stems from the short-time Fourier transform and has been the work-horse for t-f signal processing, implies an unavoidable trade-off between time and frequency resolutions, the latter two belong to a later generation of distributions that yield better, if not optimal joint t-f localization. Topics addressed include signal representation in the t-f plane, frequency identification and evolution, instantaneous-frequency estimation, and amplitude tracking

Tunable fractional-order Fourier transformer

International Nuclear Information System (INIS)

Malyutin, A A

2006-01-01

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

On the moments of the Wigner distribution and the fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Veen, J.P.

2000-01-01

A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when

Sum Frequency Generation Vibrational Spectroscopy of 1,3-Butadiene Hydrogenation on 4 nm Pt@SiO 2 , Pd@SiO 2 , and Rh@SiO 2 Core–Shell Catalysts

KAUST Repository

Krier, James M.; Michalak, William D.; Cai, Xiaojun; Carl, Lindsay; Komvopoulos, Kyriakos; Somorjai, Gabor A.

2015-01-01

NPs (Stöber encapsulation) prepared by colloidal synthesis. Sum frequency generation (SFG) vibrational spectroscopy was performed to correlate surface intermediates observed in situ with reaction selectivity. It is shown that calcination is effective

Vibrational sum-frequency generation spectroscopy of lipid bilayers at repetition rates up to 100 kHz

Science.gov (United States)

Yesudas, Freeda; Mero, Mark; Kneipp, Janina; Heiner, Zsuzsanna

2018-03-01

Broadband vibrational sum-frequency generation (BB-VSFG) spectroscopy has become a well-established surface analytical tool capable of identifying the orientation and structure of molecular layers. A straightforward way to boost the sensitivity of the technique could be to increase the laser repetition rate beyond that of standard BB-VSFG spectrometers, which rely on Ti:sapphire lasers operating at repetition rates of 1-5 kHz. Nevertheless, possible thermally induced artifacts in the vibrational spectra due to higher laser average powers are unexplored. Here, we discuss laser power induced temperature accumulation effects that distort the BB-VSFG spectra of 1,2-diacyl-sn-glycero-3-phosphocholine at an interface between two transparent phases at repetition rates of 5, 10, 50, and 100 kHz at constant pulse energy. No heat-induced distortions were found in the spectra, suggesting that the increase in the laser repetition rate provides a feasible route to an improved signal-to-noise ratio or shorter data acquisition times in BB-VSFG spectroscopy for thin films on transparent substrates. The results have implications for future BB-VSFG spectrometers pushing the detection limit for molecular layers with low surface coverage.

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

Science.gov (United States)

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.

Fourier Transform Mass Spectrometry

Science.gov (United States)

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

Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

Science.gov (United States)

2017-08-01

Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array

Discrete Fourier transform in nanostructures using scattering

International Nuclear Information System (INIS)

Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.

2004-01-01

In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed

Fault detection of gearbox using time-frequency method

Science.gov (United States)

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

2017-04-01

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

Fourier transform infrared spectroscopy of peptides.

Science.gov (United States)

Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell

2014-01-01

Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.

Quasi-static analysis of flexible pavements based on predicted frequencies using Fast Fourier Transform and Artificial Neural Network

Directory of Open Access Journals (Sweden)

Ali Reza Ghanizadeh

2018-01-01

Full Text Available New trend in design of flexible pavements is mechanistic-empirical approach. The first step for applying this method is analyzing the pavement structure for several times and computation of critical stresses and strains, which needs a fast analysis method with good accuracy. This paper aims to introduce a new rapid pavement analysis approach, which can consider the history of loading and rate effect. To this end, 1200 flexible pavement sections were analyzed, and equivalent frequencies (EF were calculated using Fast Fourier Transform (FFT method at various depths of asphalt layer. A nonlinear regression equation has been presented for determining EF at different depths of asphalt layer. For more accurate predicting of EF at low frequencies, a feed-forward Artificial Neural Network (ANN was employed, which allows accurate prediction of EF. The frequencies obtained by the proposed regression equation and ANN were compared with frequencies observed in Virginia Smart Road project, and it was found that there is a good agreement between observed and predicted frequencies. Comparison of quasi-static analysis of flexible pavements by frequencies obtained using FFT method and full dynamic analysis by 3D-Move program approves that the critical responses of pavement computed by proposed quasi-static analysis approach are comparable to critical responses computed using full dynamic analysis. Keywords: Equivalent frequency, Fast Fourier Transform (FFT, Pavement quasi-static analysis, Dynamic modulus, Artificial Neural Network (ANN

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

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

Science.gov (United States)

Debnath, Lokenath

2012-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

Intrinsic chirality and prochirality at Air/R-(+)- and S-(-)-limonene interfaces: spectral signatures with interference chiral sum-frequency generation vibrational spectroscopy.

Science.gov (United States)

Fu, Li; Zhang, Yun; Wei, Zhe-Hao; Wang, Hong-Fei

2014-09-01

We report in this work detailed measurements of the chiral and achiral sum-frequency vibrational spectra in the C-H stretching vibration region (2800-3050 cm(-1)) of the air/liquid interfaces of R-(+)-limonene and S-(-)-limonene, using the recently developed high-resolution broadband sum-frequency generation vibrational spectroscopy (HR-BB-SFG-VS). The achiral SFG spectra of R-limonene and S-limonene, as well as the RS racemic mixture (50/50 equal amount mixture), show that the corresponding molecular groups of the R and S enantiomers are with the same interfacial orientations. The interference chiral SFG spectra of the limonene enantiomers exhibit a spectral signature from the chiral response of the Cα-H stretching mode, and a spectral signature from the prochiral response of the CH(2) asymmetric stretching mode, respectively. The chiral spectral feature of the Cα-H stretching mode changes sign from R-(+)-limonene to S-(-)-limonene surfaces, and disappears for the RS racemic mixture surface. While the prochiral spectral feature of the CH(2) asymmetric stretching mode is the same for R-(+)-limonene and S-(-)-limonene surfaces, and also surprisingly remains the same for the RS racemic mixture surface. Therefore, the structures of the R-(+)-limonene and the S-(-)-limonene at the liquid interfaces are nevertheless not mirror images to each other, even though the corresponding groups have the same tilt angle from the interfacial normal, i.e., the R-(+)-limonene and the S-(-)-limonene at the surface are diastereomeric instead of enantiomeric. These results provide detailed information in understanding the structure and chirality of molecular interfaces and demonstrate the sensitivity and potential of SFG-VS as a unique spectroscopic tool for chirality characterization and chiral recognition at the molecular interface. © 2014 Wiley Periodicals, Inc.

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

Science.gov (United States)

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.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

Science.gov (United States)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

HIGH-RESOLUTION FOURIER-TRANSFORM MICROWAVE SPECTROSCOPY OF METHYL- AND DIMETHYLNAPTHALENES

Energy Technology Data Exchange (ETDEWEB)

Schnitzler, Elijah G.; Zenchyzen, Brandi L. M.; Jäger, Wolfgang, E-mail: wolfgang.jaeger@ualberta.ca [Department of Chemistry, University of Alberta, Edmonton, Alberta, T6G 2G2 (Canada)

2015-06-01

High-resolution pure rotational spectra of four alkylnaphthalenes were measured in the range of 6–15 GHz using a molecular-beam Fourier-transform microwave spectrometer. Both a- and b-type transitions were observed for 1-methylnaphthalene (1-MN), 1,2-dimethylnaphthalene (1,2-DMN), and 1,3-dimethylnaphthalene (1,3-DMN); only a-type transitions were observed for 2-methylnaphthalene (2-MN). Geometry optimization and vibrational analysis calculations at the B3LYP/6-311++G(d,p) level of theory aided in the assignments of the spectra and the characterization of the structures. Differences between the experimental and predicted rotational constants are small, and they can be attributed in part to low-lying out-of-plane vibrations, which distort the alkylnaphthalenes out of their equilibrium geometries. Splittings of rotational lines due to methyl internal rotation were observed in the spectra of 2-MN, 1,2-DMN, and 1,3-DMN, and allowed for the determination of the barriers to methyl internal rotation, which are compared to values from density functional theory calculations. All four species are moderately polar, so they are candidate species for detection by radio astronomy, by targeting the transition frequencies reported here.

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

Science.gov (United States)

Kumar, Gaurav; Kumar, Ashok

2017-11-01

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

Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

OpenAIRE

Kumar, Sanjay

2018-01-01

In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

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

Science.gov (United States)

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.

Transition dipole-moment of the ν1 +ν3 band of acetylene measured with dual-comb Fourier-transform spectroscopy

Science.gov (United States)

Okubo, Sho; Iwakuni, Kana; Yamada, Koichi M. T.; Inaba, Hajime; Onae, Atsushi; Hong, Feng-Lei; Sasada, Hiroyuki

2017-11-01

The ν1 +ν3 vibration band of acetylene (C2H2) in the near infrared region was recorded with a dual-comb Fourier-transform spectrometer. We observed 56 transitions from P (26) to R (29) at six different column densities. The integral line intensity was determined for each recorded absorption line by fitting the line profile to Lambert-Beer's law with a Voigt function. Thanks to the outstanding capability of dual-comb spectroscopy to cover a broad spectrum in a relatively short time with high resolution and high frequency precision, we determined the reliable line strength for each ro-vibrational transition as well as the transition dipole moment for this band.

Fourier transform inequalities for phylogenetic trees.

Science.gov (United States)

Matsen, Frederick A

2009-01-01

Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.

Fourier transformation for engineering and natural science

International Nuclear Information System (INIS)

Klingen, B.

2001-01-01

The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

Internal energy of HCl upon photolysis of 2-chloropropene at 193 nm investigated with time-resolved Fourier-transform spectroscopy and quasiclassical trajectories

International Nuclear Information System (INIS)

Chang, C.-M.; Huang, Y.-H.; Liu, S.-Y.; Lee, Y.-P.; Pombar-Perez, Marta; Martinez-Nunez, Emilio; Vazquez, Saulo A.

2008-01-01

Following photodissociation of 2-chloropropene (H 2 CCClCH 3 ) at 193 nm, vibration-rotationally resolved emission spectra of HCl (υ≤6) in the spectral region of 1900-2900 cm -1 were recorded with a step-scan time-resolved Fourier-transform spectrometer. All vibrational levels show a small low-J component corresponding to ∼400 K and a major high-J component corresponding to 7100-18 700 K with average rotational energy of 39± 3 11 kJ mol -1 . The vibrational population of HCl is inverted at υ=2, and the average vibrational energy is 86±5 kJ mol -1 . Two possible channels of molecular elimination producing HCl+propyne or HCl+allene cannot be distinguished positively based on the observed internal energy distribution of HCl. The observed rotational distributions fit qualitatively with the distributions of both channels obtained with quasiclassical trajectories (QCTs), but the QCT calculations predict negligible populations for states at small J. The observed vibrational distribution agrees satisfactorily with the total QCT distribution obtained as a weighted sum of contributions from both four-center elimination channels. Internal energy distributions of HCl from 2-chloropropene and vinyl chloride are compared.

Gas Measurement Using Static Fourier Transform Infrared Spectrometers.

Science.gov (United States)

Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W

2017-11-13

Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.

Iterative normalization technique for reference sequence generation for zero-tail discrete fourier transform spread orthogonal frequency division multiplexing

DEFF Research Database (Denmark)

2017-01-01

Systems, methods, apparatuses, and computer program products for generating sequences for zero-tail discrete fourier transform (DFT)-spread-orthogonal frequency division multiplexing (OFDM) (ZT DFT-s-OFDM) reference signals. One method includes adding a zero vector to an input sequence...... of each of the elements, converting the sequence to time domain, generating a zero-padded sequence by forcing a zero head and tail of the sequence, and repeating the steps until a final sequence with zero-tail and flat frequency response is obtained....

Chaos and dynamics on 0.5--300 ps time scales in vibrationally excited acetylene: Fourier transform of stimulated-emission pumping spectrum

International Nuclear Information System (INIS)

Pique, J.P.; Chen, Y.; Field, R.W.; Kinsey, J.L.

1987-01-01

A recently proposed technique based on the Fourier transform of the spectrum is applied to the stimulated-emission pumping spectrum of acetylene at --26 500 cm/sup -1/ above the vibrational ground state. Correlations on two different time scales (--3 and --45 ps) were found from analysis of low-resolution (0.3 cm/sup -1/) and high-resolution (0.05 cm/sup -1/) spectra, respectively. Additional structure produced dynamic information on a wider (0.5--300 ps) time scale. The results show that acetylene at 26 500 cm/sup -1/ is in the transition from the regular to the chaotic regime

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.

Science.gov (United States)

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…

Vibrational Spectral Studies of Gemfibrozil

Science.gov (United States)

Benitta, T. Asenath; Balendiran, G. K.; James, C.

2008-11-01

The Fourier Transform Raman and infrared spectra of the crystallized drug molecule 5-(2,5-Dimethylphenoxy)-2,2-dimethylpentanoic acid (Gemfibrozil) have been recorded and analyzed. Quantum chemical computational methods have been employed using Gaussian 03 software package based on Hartree Fock method for theoretically modeling the grown molecule. The optimized geometry and vibrational frequencies have been predicted. Observed vibrational modes have been assigned with the aid of normal coordinate analysis.

Comparative Study of Time-Frequency Decomposition Techniques for Fault Detection in Induction Motors Using Vibration Analysis during Startup Transient

Directory of Open Access Journals (Sweden)

Paulo Antonio Delgado-Arredondo

2015-01-01

Full Text Available Induction motors are critical components for most industries and the condition monitoring has become necessary to detect faults. There are several techniques for fault diagnosis of induction motors and analyzing the startup transient vibration signals is not as widely used as other techniques like motor current signature analysis. Vibration analysis gives a fault diagnosis focused on the location of spectral components associated with faults. Therefore, this paper presents a comparative study of different time-frequency analysis methodologies that can be used for detecting faults in induction motors analyzing vibration signals during the startup transient. The studied methodologies are the time-frequency distribution of Gabor (TFDG, the time-frequency Morlet scalogram (TFMS, multiple signal classification (MUSIC, and fast Fourier transform (FFT. The analyzed vibration signals are one broken rotor bar, two broken bars, unbalance, and bearing defects. The obtained results have shown the feasibility of detecting faults in induction motors using the time-frequency spectral analysis applied to vibration signals, and the proposed methodology is applicable when it does not have current signals and only has vibration signals. Also, the methodology has applications in motors that are not fed directly to the supply line, in such cases the analysis of current signals is not recommended due to poor current signal quality.

On the divergence of triangular and eccentric spherical sums of double Fourier series

Energy Technology Data Exchange (ETDEWEB)

Karagulyan, G A [Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan (Armenia)

2016-01-31

We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles.

On the divergence of triangular and eccentric spherical sums of double Fourier series

International Nuclear Information System (INIS)

Karagulyan, G A

2016-01-01

We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles

On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation

International Nuclear Information System (INIS)

Ardisasmita, M. Syamsa

1996-01-01

The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed

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

Science.gov (United States)

Neri, P.

2017-05-01

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

Sum frequency generation of CO on (III) and polycrystalline platinum electrode surfaces: Evidence for SFG invisible surface CO

Energy Technology Data Exchange (ETDEWEB)

Baldelli, S.; Markovic, N.; Ross, P.; Shen, Y.R.; Somorjai, G.

1999-10-21

The vibrational spectroscopy sum frequency generation (SFG) is used to investigate the adsorption of carbon monoxide on the single crystal (111) and polycrystalline platinum surfaces. By varying the frequency and polarization of the light beams, different surface species of CO species are probed. SFG signal intensities for different polarization indicate that adsorbed CO polarizability is significantly perturbed from the gas-phase molecule. The SFG signal of CO disappears well below the main oxidation potential of CO to CO{sub 2}. The disappearance of the CO signal is interpreted as a transformation in the CO layer to a state which is invisible to SFG. The invisible state is suggested to be CO with the bond axis nearly parallel to the platinum surface.

Sum Frequency Generation Vibrational Spectroscopy of Colloidal Platinum Nanoparticle Catalysts: Disordering versus Removal of Organic Capping

KAUST Repository

Krier, James M.

2012-08-23

Recent work with nanoparticle catalysts shows that size and shape control on the nanometer scale influences reaction rate and selectivity. Sum frequency generation (SFG) vibrational spectroscopy is a powerful tool for studying heterogeneous catalysis because it enables the observation of surface intermediates during catalytic reactions. To control the size and shape of catalytic nanoparticles, an organic ligand was used as a capping agent to stabilize nanoparticles during synthesis. However, the presence of an organic capping agent presents two major challenges in SFG and catalytic reaction studies: it blocks a significant fraction of active surface sites and produces a strong signal that prevents the detection of reaction intermediates with SFG. Two methods for cleaning Pt nanoparticles capped with poly (vinylpyrrolidone) (PVP) are examined in this study: solvent cleaning and UV cleaning. Solvent cleaning leaves more PVP intact and relies on disordering with hydrogen gas to reduce the SFG signal of PVP. In contrast, UV cleaning depends on nearly complete removal of PVP to reduce SFG signal. Both UV and solvent cleaning enable the detection of reaction intermediates by SFG. However, solvent cleaning also yields nanoparticles that are stable under reaction conditions, whereas UV cleaning results in aggregation during reaction. The results of this study indicate that solvent cleaning is more advantageous for studying the effects of nanoparticle size and shape on catalytic selectivity by SFG vibrational spectroscopy. © 2012 American Chemical Society.

A new twist to fourier transforms

CERN Document Server

Meikle, Hamish D

2004-01-01

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs

Fourier transform infrared emission spectra of MnH and MnD

Science.gov (United States)

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

2005-01-01

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

An optical Fourier transform coprocessor with direct phase determination.

Science.gov (United States)

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

2017-10-20

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

Fourier Transform Infrared Spectroscopy (FTIR) as a Tool for the Identification and Differentiation of Pathogenic Bacteria.

Science.gov (United States)

Zarnowiec, Paulina; Lechowicz, Łukasz; Czerwonka, Grzegorz; Kaca, Wiesław

2015-01-01

Methods of human bacterial pathogen identification need to be fast, reliable, inexpensive, and time efficient. These requirements may be met by vibrational spectroscopic techniques. The method that is most often used for bacterial detection and identification is Fourier transform infrared spectroscopy (FTIR). It enables biochemical scans of whole bacterial cells or parts thereof at infrared frequencies (4,000-600 cm(-1)). The recorded spectra must be subsequently transformed in order to minimize data variability and to amplify the chemically-based spectral differences in order to facilitate spectra interpretation and analysis. In the next step, the transformed spectra are analyzed by data reduction tools, regression techniques, and classification methods. Chemometric analysis of FTIR spectra is a basic technique for discriminating between bacteria at the genus, species, and clonal levels. Examples of bacterial pathogen identification and methods of differentiation up to the clonal level, based on infrared spectroscopy, are presented below.

Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

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

2016-01-01

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

Implementation of quantum and classical discrete fractional Fourier transforms.

Science.gov (United States)

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

2016-03-23

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

Vibration-based Fault Diagnostic of a Spur Gearbox

Directory of Open Access Journals (Sweden)

Hartono Dennis

2016-01-01

Full Text Available This paper presents comparative studies of Fast Fourier Transform (FFT, Short Time Fourier Transform (STFT and Continuous Wavelet Transform (CWT as several advanced time-frequency analysis methods for diagnosing an early stage of spur gear tooth failure. An incipient fault of a chipped tooth was investigated in this work using vibration measurements from a spur gearbox test rig. Time Synchronous Averaging was implemented for the analysis to enhance the clarity of fault feature from the gear of interest. Based on the experimental results and analysis, it was shown that FFT method could identify the location of the faulty gear with sufficient accuracy. On the other hand, Short Time Fourier Transform method could not provide the angular location information of the faulty gear. It was found that the Continuous Wavelet Transform method offered the best representation of angle-frequency representation. It was not only able to distinguish the difference between the normal and faulty gearboxes from the joint angle-frequency results but could also provide an accurate angular location of the faulty gear tooth in the gearbox.

Toward a simple molecular understanding of sum frequency generation at air-water interfaces

Energy Technology Data Exchange (ETDEWEB)

Noah-Vanhoucke, Joyce; Smith, Jared D.; Geissler, Phillip L.

2009-01-13

Second-order vibrational spectroscopies successfully isolate signals from interfaces, but they report on intermolecular structure in a complicated and indirect way. Here we adapt a perspective on vibrational response developed for bulk spectroscopies to explore the microscopic fluctuations to which sum frequency generation (SFG), a popular surface-specific measurement, is most sensitive. We focus exclusively on inhomogeneous broadening of spectral susceptibilities for OH stretching of HOD as a dilute solute in D{sub 2}O. Exploiting a simple connection between vibrational frequency shifts and an electric field variable, we identify several functions of molecular orientation whose averages govern SFG. The frequency-dependence of these quantities is well captured by a pair of averages, involving alignment of OH and OD bonds with the surface normal at corresponding values of the electric field. The approximate form we obtain for SFG susceptibility highlights a dramatic sensitivity to the way a simulated liquid slab is partitioned for calculating second-order response.

Alternating multivariate trigonometric functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2008-01-01

We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel

Properties of the distributional finite Fourier transform

OpenAIRE

Carmichael, Richard D.

2016-01-01

The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

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

Science.gov (United States)

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.

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Boashash, B.

2003-01-01

We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

The Fractional Fourier Transform and Its Application to Energy Localization Problems

Directory of Open Access Journals (Sweden)

ter Morsche Hennie G

2003-01-01

Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

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

Science.gov (United States)

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.

Digital Fourier analysis fundamentals

CERN Document Server

Kido, Ken'iti

2015-01-01

This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations.  These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...

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

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2015-12-15

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 Fourier transforms are the beams themselves.

Theoretical vibrational sum-frequency generation spectroscopy of water near lipid and surfactant monolayer interfaces

Energy Technology Data Exchange (ETDEWEB)

Roy, S.; Gruenbaum, S. M.; Skinner, J. L. [Theoretical Chemistry Institute and Department of Chemistry, 1101 University Ave., University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)

2014-11-14

Understanding the structure of water near cell membranes is crucial for characterizing water-mediated events such as molecular transport. To obtain structural information of water near a membrane, it is useful to have a surface-selective technique that can probe only interfacial water molecules. One such technique is vibrational sum-frequency generation (VSFG) spectroscopy. As model systems for studying membrane headgroup/water interactions, in this paper we consider lipid and surfactant monolayers on water. We adopt a theoretical approach combining molecular dynamics simulations and phase-sensitive VSFG to investigate water structure near these interfaces. Our simulated spectra are in qualitative agreement with experiments and reveal orientational ordering of interfacial water molecules near cationic, anionic, and zwitterionic interfaces. OH bonds of water molecules point toward an anionic interface leading to a positive VSFG peak, whereas the water hydrogen atoms point away from a cationic interface leading to a negative VSFG peak. Coexistence of these two interfacial water species is observed near interfaces between water and mixtures of cationic and anionic lipids, as indicated by the presence of both negative and positive peaks in their VSFG spectra. In the case of a zwitterionic interface, OH orientation is toward the interface on the average, resulting in a positive VSFG peak.

Rotor-System Log-Decrement Identification Using Short-Time Fourier-Transform Filter

OpenAIRE

Li, Qihang; Wang, Weimin; Chen, Lifang; Sun, Dan

2015-01-01

With the increase of the centrifugal compressor capability, such as large scale LNG and CO2 reinjection, the stability margin evaluation is crucial to assure the compressor work in the designed operating conditions in field. Improving the precision of parameter identification of stability is essential and necessary as well. Based on the time-varying characteristics of response vibration during the sine-swept process, a short-time Fourier transform (STFT) filter was introduced to increase the ...

Group-invariant finite Fourier transforms

International Nuclear Information System (INIS)

Shenefelt, M.H.

1988-01-01

The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

On the inverse windowed Fourier transform

OpenAIRE

Rebollo Neira, Laura; Fernández Rubio, Juan Antonio

1999-01-01

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed

The short time Fourier transform and local signals

Science.gov (United States)

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.

(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2007-01-01

We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

Sum Frequency Generation Vibrational Spectroscopy of Adsorbed Amino Acids, Peptides and Proteins of Hydrophilic and Hydrophobic Solid-Water Interfaces

Energy Technology Data Exchange (ETDEWEB)

Holinga IV, George Joseph [Univ. of California, Berkeley, CA (United States)

2010-09-01

Sum frequency generation (SFG) vibrational spectroscopy was used to investigate the interfacial properties of several amino acids, peptides, and proteins adsorbed at the hydrophilic polystyrene solid-liquid and the hydrophobic silica solid-liquid interfaces. The influence of experimental geometry on the sensitivity and resolution of the SFG vibrational spectroscopy technique was investigated both theoretically and experimentally. SFG was implemented to investigate the adsorption and organization of eight individual amino acids at model hydrophilic and hydrophobic surfaces under physiological conditions. Biointerface studies were conducted using a combination of SFG and quartz crystal microbalance (QCM) comparing the interfacial structure and concentration of two amino acids and their corresponding homopeptides at two model liquid-solid interfaces as a function of their concentration in aqueous solutions. The influence of temperature, concentration, equilibration time, and electrical bias on the extent of adsorption and interfacial structure of biomolecules were explored at the liquid-solid interface via QCM and SFG. QCM was utilized to quantify the biological activity of heparin functionalized surfaces. A novel optical parametric amplifier was developed and utilized in SFG experiments to investigate the secondary structure of an adsorbed model peptide at the solid-liquid interface.

Fourier Transform Spectroscopy of Carbonyl Sulfide from 3700 to 4800 cm -1and Selection of a Line-Pointing Program

Science.gov (United States)

Naı̈m, S.; Fayt, A.; Bredohl, H.; Blavier, J.-F.; Dubois, I.

1998-11-01

We have measured the Fourier transform spectrum of natural OCS from 3700 to 4800 cm-1with a near Doppler resolution and a line-position accuracy between 4 and 8 × 10-5cm-1. For the normal isotopic species, 37 vibrational transitions have been analyzed for both frequencies and intensities. We also report 15 bands of OC34S, eight bands of O13CS, nine bands of OC33S, and two bands of18OCS. Important effective Herman-Wallis terms are explained on the basis of eigenvectors. A comparison of different line-pointing programs is also presented.

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

Science.gov (United States)

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.

Rotor-System Log-Decrement Identification Using Short-Time Fourier-Transform Filter

Directory of Open Access Journals (Sweden)

Qihang Li

2015-01-01

Full Text Available With the increase of the centrifugal compressor capability, such as large scale LNG and CO2 reinjection, the stability margin evaluation is crucial to assure the compressor work in the designed operating conditions in field. Improving the precision of parameter identification of stability is essential and necessary as well. Based on the time-varying characteristics of response vibration during the sine-swept process, a short-time Fourier transform (STFT filter was introduced to increase the signal-noise ratio and improve the accuracy of the estimated stability parameters. A finite element model was established to simulate the sine-swept process, and the simulated vibration signals were used to study the filtering effect and demonstrate the feasibility to identify the stability parameters by using Multiple-Input and Multiple-Output system identification method that combines the prediction error method and instrumental variable method. Simulation results show that the identification method with STFT filter improves the estimated accuracy much well and makes the curves of frequency response function clearer. Experiment was carried out on a test rig as well, which indicates the identification method is feasible in stability identification, and the results of experiment indicate that STFT filter works very well.

Bevel Gearbox Fault Diagnosis using Vibration Measurements

Directory of Open Access Journals (Sweden)

Hartono Dennis

2016-01-01

Full Text Available The use of vibration measurementanalysis has been proven to be effective for gearbox fault diagnosis. However, the complexity of vibration signals observed from a gearbox makes it difficult to accurately detectfaults in the gearbox. This work is based on a comparative studyof several time-frequency signal processing methods that can be used to extract information from transient vibration signals containing useful diagnostic information. Experiments were performed on a bevel gearbox test rig using vibration measurements obtained from accelerometers. Initially, thediscrete wavelet transform was implementedfor vibration signal analysis to extract the frequency content of signal from the relevant frequency region. Several time-frequency signal processing methods werethen incorporated to extract the fault features of vibration signals and their diagnostic performances were compared. It was shown thatthe Short Time Fourier Transform (STFT could not offer a good time resolution to detect the periodicity of the faulty gear tooth due the difficulty in choosing an appropriate window length to capture the impulse signal. The Continuous Wavelet Transform (CWT, on the other hand, was suitable to detection of vibration transients generated by localized fault from a gearbox due to its multi-scale property. However, both methods still require a thorough visual inspection. In contrast, it was shown from the experiments that the diagnostic method using the Cepstrumanalysis could provide a direct indication of the faulty tooth without the need of a thorough visual inspection as required by CWT and STFT.

On the windowed Fourier transform as an interpolation of the Gabor transform

NARCIS (Netherlands)

Bastiaans, M.J.; Prochßzka, A.; Uhlør, J.; Sovka, P.

1997-01-01

The windowed Fourier transform and its sampled version - the Gabor transform - are introduced. With the help of Gabor's signal expansion, an interpolation function is derived with which the windowed Fourier transform can be constructed from the Gabor transform. Using the Zak transform, it is shown

Vibrational spectra and normal co-ordinate analysis of 2-aminopyridine and 2-amino picoline.

Science.gov (United States)

Jose, Sujin P; Mohan, S

2006-05-01

The Fourier transform infrared (FT-IR) and Raman (FT-R) spectra of 2-aminopyridine and 2-amino picoline were recorded and the observed frequencies were assigned to various modes of vibration in terms of fundamentals by assuming Cs point group symmetry. A normal co-ordinate analysis was also carried out for the proper assignment of the vibrational frequencies using simple valence force field. A complete vibrational analysis is presented here for the molecules and the results are briefly discussed.

Adaptive synchrosqueezing based on a quilted short-time Fourier transform

Science.gov (United States)

Berrian, Alexander; Saito, Naoki

2017-08-01

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

Fourier transform infrared spectroscopic study of gamma irradiated SiO2 nanoparticles

Science.gov (United States)

Huseynov, Elchin; Garibov, Adil; Mehdiyeva, Ravan; Huseynova, Efsane

2018-03-01

In the present work, nano SiO2 particles are investigated before and after gamma irradiation (25, 50, 75, 100 and 200 kGy) using Fourier transform infrared (FTIR) spectroscopy method for the wavenumber between 400-4000 cm-1. It is found that as a result of spectroscopic analysis, five new peaks have appeared after gamma radiation. Two of new obtained peaks (which are located at 687 cm-1 and 2357 cm-1 of wavenumber) were formed as a result of gamma radiation interaction with Si-O bonds. Another three new peaks (peaks appropriate to 941, 2052 and 2357 cm-1 values of wavenumber) appear as a result of interaction of water with nano SiO2 particles after gamma irradiation. It has been defined as asymmetrical bending vibration, symmetrical bending vibration, symmetrical stretching vibration and asymmetrical stretching vibration of Si-O bonds appropriate to peaks.

Dual resonant structure for energy harvesting from random vibration sources at low frequency

Directory of Open Access Journals (Sweden)

Shanshan Li

2016-01-01

Full Text Available We introduce a design with dual resonant structure which can harvest energy from random vibration sources at low frequency range. The dual resonant structure consists of two spring-mass subsystems with different frequency responses, which exhibit strong coupling and broad bandwidth when the two masses collide with each other. Experiments with piezoelectric elements show that the energy harvesting device with dual resonant structure can generate higher power output than the sum of the two separate devices from random vibration sources.

Vibrational sum frequency generation (SFG) spectroscopic study of crystalline cellulose in biomass

Science.gov (United States)

Kim, Seong H.; Lee, Christopher M.; Kafle, Kabindra; Park, Yong Bum; Xi, Xiaoning

2013-09-01

The noncentrosymmetry requirement of sum frequency generation (SFG) spectroscopy allows selective detection of crystalline cellulose in plant cell walls and lignocellulose biomass without spectral interferences from hemicelluloses and lignin. In addition, the phase synchronization requirement of the SFG process allows noninvasive investigation of spatial arrangement of crystalline cellulose microfibrils in the sample. This paper reviews how these principles are applied to reveal structural information of crystalline cellulose in plant cell walls and biomass.

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

Science.gov (United States)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

Application of Choi—Williams Reduced Interference Time Frequency Distribution to Machinery Diagnostics

Directory of Open Access Journals (Sweden)

Howard A. Gaberson

1995-01-01

Full Text Available This article discusses time frequency analysis of machinery diagnostic vibration signals. The short time Fourier transform, the Wigner, and the Choi–Williams distributions are explained and illustrated with test cases. Examples of Choi—Williams analyses of machinery vibration signals are presented. The analyses detect discontinuities in the signals and their timing, amplitude and frequency modulation, and the presence of different components in a vibration signal.

Facet-specific interaction between methanol and TiO2 probed by sum-frequency vibrational spectroscopy.

Science.gov (United States)

Yang, Deheng; Li, Yadong; Liu, Xinyi; Cao, Yue; Gao, Yi; Shen, Y Ron; Liu, Wei-Tao

2018-04-24

The facet-specific interaction between molecules and crystalline catalysts, such as titanium dioxides (TiO 2 ), has attracted much attention due to possible facet-dependent reactivity. Using surface-sensitive sum-frequency vibrational spectroscopy, we have studied how methanol interacts with different common facets of crystalline TiO 2 , including rutile(110), (001), (100), and anatase(101), under ambient temperature and pressure. We found that methanol adsorbs predominantly in the molecular form on all of the four surfaces, while spontaneous dissociation into methoxy occurs preferentially when these surfaces become defective. Extraction of Fermi resonance coupling between stretch and bending modes of the methyl group in analyzing adsorbed methanol spectra allows determination of the methanol adsorption isotherm. The isotherms obtained for the four surfaces are nearly the same, yielding two adsorbed Gibbs free energies associated with two different adsorption configurations singled out by ab initio calculations. They are ( i ) ∼-20 kJ/mol for methanol with its oxygen attached to a low-coordinated surface titanium, and ( ii ) ∼-5 kJ/mol for methanol hydrogen-bonded to a surface oxygen and a neighboring methanol molecule. Despite similar adsorption energetics, the Fermi resonance coupling strength for adsorbed methanol appears to depend sensitively on the surface facet and coverage.

Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

CERN Document Server

Goodman, Roe W

2016-01-01

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Time Lens based Optical Fourier Transformation for All-Optical Signal Processing of Spectrally-Efficient Data

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads

2017-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......, such as orthogonal frequency division multiplexing (OFDM), Nyquist wavelength-division multiplexing (Nyquist-WDM) and Nyquist optical time division multiplexing (Nyquist-OTDM) signals....

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

Science.gov (United States)

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.

Fourier transforms in radar and signal processing

CERN Document Server

Brandwood, David

2011-01-01

Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit

Quantum arithmetic with the Quantum Fourier Transform

OpenAIRE

Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

2014-01-01

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

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

Science.gov (United States)

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.

q-Generalization of the inverse Fourier transform

International Nuclear Information System (INIS)

Jauregui, M.; Tsallis, C.

2011-01-01

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.

Matrix-Vector Based Fast Fourier Transformations on SDR Architectures

Directory of Open Access Journals (Sweden)

Y. He

2008-05-01

Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.

Spectrums Transform Operators in Bases of Fourier and Walsh Functions

Directory of Open Access Journals (Sweden)

V. V. Syuzev

2017-01-01

components, allowed us to combine the nonzero coefficients in independent groups in each of the three cases of transformations. The original rules for group formation are formulated both for particular value of N, and in general terms.The formation rules of groups, group-by-group and common Parseval equalities were used to obtain descriptions of algorithms for mutual transformation of trigonometric Fourier spectrum into Hadamard, Paley and Hartmut spectra. An analytical record of these algorithms enables speaking of the Fourier kernels as of the new operators of spectra transformation. The computational complexity evaluation of operators showed the effectiveness of their use owing to more than three times reduction of the number of arithmetic operations as compared to the conventional method, i.e. direct calculation of the Walsh spectra. Because of this property the proposed operators become useful when solving the tasks of real-time discrete systems modeling.In the long run, there is a plan to solve a similar task for the mutual transformation of Walsh and Hartley spectra: both a Hartley basis system and a trigonometric system reflect the frequency structure of the signal that serves a useful purpose in terms of theory and practice.

On the Evaluation Overlap Integrals with the Same and Different Screening Parameters Over Slater Type Orbitals via the Fourier-Transform Method

International Nuclear Information System (INIS)

Yavuz, M.; Yuekcue, N.; Oeztekin, E.; Yilmaz, H.; Doenduer, S.

2005-01-01

In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.

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

Science.gov (United States)

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.

Calibration of the Herschel SPIRE Fourier Transform Spectrometer

OpenAIRE

Swinyard, Bruce; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.- P.; Bendo, G. J.; Ferlet, M.; Griffin, Matthew Jason; Lim, T. L.; Makiwa, G.

2014-01-01

The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of ∼450–1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a sp...

Vibration Finite Element Analysis of SC10 Dry-type Transformer Core

Directory of Open Access Journals (Sweden)

Gao Sheng Wei

2014-06-01

Full Text Available As the popularization and application of dry-type power transformer, its work when the vibration noise problem widely concerned, on the basis of time-varying electromagnetic field and structural mechanics equation, this paper established a finite element analysis model of dry-type transformer, through the electromagnetic field – Structural mechanics field – sound field more than physical field coupling calculation analysis, obtained in no load and the vibration modes of the core under different load and frequency. According to the transformer vibration mechanism, compared with the experimental data, verified the accuracy of the calculation results, as the core of how to provide the theory foundation and to reduce the noise of the experiment.

Rainbow Fourier Transform

Science.gov (United States)

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).

Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

Serov, Valery

2017-01-01

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...

Fourier transform and its application to 1D and 2D NMR

International Nuclear Information System (INIS)

Canet, D.

1988-01-01

In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr

Nonlinear optical response of a gold surface in the visible range: A study by two-color sum-frequency generation spectroscopy. I. Experimental determination.

Science.gov (United States)

Dalstein, L; Revel, A; Humbert, C; Busson, B

2018-04-07

We experimentally determine the effective nonlinear second-order susceptibility of gold over the visible spectral range. To reach that goal, we probe by vibrational two-color sum-frequency generation spectroscopy the methyl stretching region of a dodecanethiol self-assembled monolayer adsorbed on a gold film. The sum-frequency generation spectra show a remarkable shape reversal when the visible probe wavelength is tuned from 435 to 705 nm. After correcting from Fresnel effects, the methyl stretching vibrations serve as an internal reference, allowing to extract the dispersion of the absolute phase and relative amplitude of the effective nonlinear optical response of gold in the visible range.

Replica Fourier Transform: Properties and applications

International Nuclear Information System (INIS)

Crisanti, A.; De Dominicis, C.

2015-01-01

The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically

Unidirectional ring-laser operation using sum-frequency mixing

DEFF Research Database (Denmark)

Tidemand-Lichtenberg, Peter; Cheng, Haynes Pak Hay; Pedersen, Christian

2010-01-01

A technique enforcing unidirectional operation of ring lasers is proposed and demonstrated. The approach relies on sum-frequency mixing between a single-pass laser and one of the two counterpropagating intracavity fields of the ring laser. Sum-frequency mixing introduces a parametric loss for the...... where lossless second-order nonlinear materials are available. Numerical modeling and experimental demonstration of parametric-induced unidirectional operation of a diode-pumped solid-state 1342 nm cw ring laser are presented.......A technique enforcing unidirectional operation of ring lasers is proposed and demonstrated. The approach relies on sum-frequency mixing between a single-pass laser and one of the two counterpropagating intracavity fields of the ring laser. Sum-frequency mixing introduces a parametric loss...

FFT-BM, Code Accuracy Evaluations with the 1D Fast Fourier Transform (FFT) Methodology

International Nuclear Information System (INIS)

D'Auria, F.

2004-01-01

1 - Description of program or function: FFT-BM is an integrated version of the programs package performing code accuracy evaluations with the 1D Fast Fourier Transform (FFT) methodology. It contains two programs: - CASEM: Takes care of the complete manipulation of data in order to evaluate the quantities through which the FFT method quantifies the code accuracy. - AAWFTO completes the evaluation of the average accuracy (AA) and related weighted frequency (WF) values in order to obtain the AAtot and WFtot values characterising the global calculation performance. 2 - Methods: The Fast Fourier Transform, or FFT, which is based on the Fourier analysis method is an optimised method for calculating the amplitude Vs frequency, of functions or experimental or computed data. In order to apply this methodology, after selecting the parameters to be analyzed, it is necessary to choose the following parameters: - number of curves (exp + calc) to be analyzed; - number of time windows to be analyzed; - sampling frequency; - cut frequency; - time begin and time end of each time window. 3 - Restrictions on the complexity of the problem: Up to 30 curves (exp + calc) and 5 time windows may be analyzed

Non-stationary signal analysis based on general parameterized time-frequency transform and its application in the feature extraction of a rotary machine

Science.gov (United States)

Zhou, Peng; Peng, Zhike; Chen, Shiqian; Yang, Yang; Zhang, Wenming

2018-06-01

With the development of large rotary machines for faster and more integrated performance, the condition monitoring and fault diagnosis for them are becoming more challenging. Since the time-frequency (TF) pattern of the vibration signal from the rotary machine often contains condition information and fault feature, the methods based on TF analysis have been widely-used to solve these two problems in the industrial community. This article introduces an effective non-stationary signal analysis method based on the general parameterized time-frequency transform (GPTFT). The GPTFT is achieved by inserting a rotation operator and a shift operator in the short-time Fourier transform. This method can produce a high-concentrated TF pattern with a general kernel. A multi-component instantaneous frequency (IF) extraction method is proposed based on it. The estimation for the IF of every component is accomplished by defining a spectrum concentration index (SCI). Moreover, such an IF estimation process is iteratively operated until all the components are extracted. The tests on three simulation examples and a real vibration signal demonstrate the effectiveness and superiority of our method.

Determining In Situ Protein Conformation and Orientation from the Amide-I Sum-Frequency Generation Spectrum: Theory and Experiment

NARCIS (Netherlands)

Roeters, S.J.; van Dijk, C.N.; Torres Knoop, A.; Backus, E.H.G.; Campen, R.K.; Bonn, M.; Woutersen, S.

2013-01-01

Vibrational sum-frequency generation (VSFG) spectra of the amide-I band of proteins can give detailed insight into biomolecular processes near membranes. However, interpreting these spectra in terms of the conformation and orientation of a protein can be difficult, especially in the case of complex

Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS)

Science.gov (United States)

Wang, Hong-Fei; Gan, Wei; Lu, Rong; Rao, Yi; Wu, Bao-Hua

Sum frequency generation vibrational spectroscopy (SFG-VS) has been proven to be a uniquely effective spectroscopic technique in the investigation of molecular structure and conformations, as well as the dynamics of molecular interfaces. However, the ability to apply SFG-VS to complex molecular interfaces has been limited by the ability to abstract quantitative information from SFG-VS experiments. In this review, we try to make assessments of the limitations, issues and techniques as well as methodologies in quantitative orientational and spectral analysis with SFG-VS. Based on these assessments, we also try to summarize recent developments in methodologies on quantitative orientational and spectral analysis in SFG-VS, and their applications to detailed analysis of SFG-VS data of various vapour/neat liquid interfaces. A rigorous formulation of the polarization null angle (PNA) method is given for accurate determination of the orientational parameter D = /, and comparison between the PNA method with the commonly used polarization intensity ratio (PIR) method is discussed. The polarization and incident angle dependencies of the SFG-VS intensity are also reviewed, in the light of how experimental arrangements can be optimized to effectively abstract crucial information from the SFG-VS experiments. The values and models of the local field factors in the molecular layers are discussed. In order to examine the validity and limitations of the bond polarizability derivative model, the general expressions for molecular hyperpolarizability tensors and their expression with the bond polarizability derivative model for C3v, C2v and C∞v molecular groups are given in the two appendixes. We show that the bond polarizability derivative model can quantitatively describe many aspects of the intensities observed in the SFG-VS spectrum of the vapour/neat liquid interfaces in different polarizations. Using the polarization analysis in SFG-VS, polarization selection rules or

The morphing of geographical features by Fourier transformation.

Science.gov (United States)

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.

2D heterodyne-detected sum frequency generation study on the ultrafast vibrational dynamics of H{sub 2}O and HOD water at charged interfaces

Energy Technology Data Exchange (ETDEWEB)

Inoue, Ken-ichi; Singh, Prashant C. [Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Nihonyanagi, Satoshi; Tahara, Tahei, E-mail: tahei@riken.jp [Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Ultrafast Spectroscopy Research Team, RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Yamaguchi, Shoichi [Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Department of Applied Chemistry, Saitama University, 255 Shimo-Okubo, Saitama 338-8570 (Japan)

2015-06-07

Two-dimensional heterodyne-detected vibrational sum-frequency generation (2D HD-VSFG) spectroscopy is applied to study the ultrafast vibrational dynamics of water at positively charged aqueous interfaces, and 2D HD-VSFG spectra of cetyltrimethylammonium bromide (CTAB)/water interfaces in the whole hydrogen-bonded OH stretch region (3000 cm{sup −1} ≤ ω{sub pump} ≤ 3600 cm{sup −1}) are measured. 2D HD-VSFG spectrum of the CTAB/isotopically diluted water (HOD-D{sub 2}O) interface exhibits a diagonally elongated bleaching lobe immediately after excitation, which becomes round with a time constant of ∼0.3 ps due to spectral diffusion. In contrast, 2D HD-VSFG spectrum of the CTAB/H{sub 2}O interface at 0.0 ps clearly shows two diagonal peaks and their cross peaks in the bleaching region, corresponding to the double peaks observed at 3230 cm{sup −1} and 3420 cm{sup −1} in the steady-state HD-VSFG spectrum. Horizontal slices of the 2D spectrum show that the relative intensity of the two peaks of the bleaching at the CTAB/H{sub 2}O interface gradually change with the change of the pump frequency. We simulate the pump-frequency dependence of the bleaching feature using a model that takes account of the Fermi resonance and inhomogeneity of the OH stretch vibration, and the simulated spectra reproduce the essential features of the 2D HD-VSFG spectra of the CTAB/H{sub 2}O interface. The present study demonstrates that heterodyne detection of the time-resolved VSFG is critically important for studying the ultrafast dynamics of water interfaces and for unveiling the underlying mechanism.

Fast inverse nonlinear Fourier transformation using exponential one-step methods : Darboux transformation

NARCIS (Netherlands)

Vaibhav, V.K.

2017-01-01

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the

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

Science.gov (United States)

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…

Polymorph characterization of active pharmaceutical ingredients (APIs) using low-frequency Raman spectroscopy.

Science.gov (United States)

Larkin, Peter J; Dabros, Marta; Sarsfield, Beth; Chan, Eric; Carriere, James T; Smith, Brian C

2014-01-01

Polymorph detection, identification, and quantitation in crystalline materials are of great importance to the pharmaceutical industry. Vibrational spectroscopic techniques used for this purpose include Fourier transform mid-infrared (FT-MIR) spectroscopy, Fourier transform near-infrared (FT-NIR) spectroscopy, Raman spectroscopy, and terahertz (THz) and far-infrared (FIR) spectroscopy. Typically, the fundamental molecular vibrations accessed using high-frequency Raman and MIR spectroscopy or the overtone and combination of bands in the NIR spectra are used to monitor the solid-state forms of active pharmaceutical ingredients (APIs). The local environmental sensitivity of the fundamental molecular vibrations provides an indirect probe of the long-range order in molecular crystals. However, low-frequency vibrational spectroscopy provides access to the lattice vibrations of molecular crystals and, hence, has the potential to more directly probe intermolecular interactions in the solid state. Recent advances in filter technology enable high-quality, low-frequency Raman spectra to be acquired using a single-stage spectrograph. This innovation enables the cost-effective collection of high-quality Raman spectra in the 200-10 cm(-1) region. In this study, we demonstrate the potential of low-frequency Raman spectroscopy for the polymorphic characterization of APIs. This approach provides several benefits over existing techniques, including ease of sampling and more intense, information-rich band structures that can potentially discriminate among crystalline forms. An improved understanding of the relationship between the crystalline structure and the low-frequency vibrational spectrum is needed for the more widespread use of the technique.

Some Applications of Fourier's Great Discovery for Beginners

Science.gov (United States)

Kraftmakher, Yaakov

2012-01-01

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

Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods

Science.gov (United States)

Schröder, Markus; Meyer, Hans-Dieter

2017-08-01

We propose a Monte Carlo method, "Monte Carlo Potfit," for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.

Bi-resonant structure with piezoelectric PVDF films for energy harvesting from random vibration sources at low frequency

DEFF Research Database (Denmark)

Liang, Shanshan; Crovetto, Andrea; Peng, Zhuoteng

2016-01-01

and experiments with piezoelectric elements show that the energy harvesting device with the bi-resonant structure can generate higher power output than that of the sum of the two separate devices from random vibration sources at low frequency, and hence significantly improves the vibration-to- electricity......This paper reports on a bi-resonant structure of piezoelectric PVDF films energy harvester (PPEH), which consists of two cantilevers with resonant frequencies of 15 Hz and 22 Hz. With increased acceleration, the vibration amplitudes of the two cantilever-mass structures are increased and collision...

The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

International Nuclear Information System (INIS)

Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Wu, Lifu; Liu, Zhanwei

2014-01-01

The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method. (paper)

Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

Directory of Open Access Journals (Sweden)

WANG Minhao

2017-08-01

Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

High frequency vibration analysis by the complex envelope vectorization.

Science.gov (United States)

Giannini, O; Carcaterra, A; Sestieri, A

2007-06-01

The complex envelope displacement analysis (CEDA) is a procedure to solve high frequency vibration and vibro-acoustic problems, providing the envelope of the physical solution. CEDA is based on a variable transformation mapping the high frequency oscillations into signals of low frequency content and has been successfully applied to one-dimensional systems. However, the extension to plates and vibro-acoustic fields met serious difficulties so that a general revision of the theory was carried out, leading finally to a new method, the complex envelope vectorization (CEV). In this paper the CEV method is described, underlying merits and limits of the procedure, and a set of applications to vibration and vibro-acoustic problems of increasing complexity are presented.

Catalyzed hydrogenation of nitrogen and ethylene on metal (Fe, Pt) single crystal surfaces and effects of coadsorption: A sum frequency generation vibrational spectroscopy study

Energy Technology Data Exchange (ETDEWEB)

Westerberg, Staffan Per Gustav [Univ. of California, Berkeley, CA (United States)

2004-01-01

High-pressure catalytic reactions and associated processes, such as adsorption have been studied on a molecular level on single crystal surfaces. Sum Frequency Generation (SFG) vibrational spectroscopy together with Auger Electron Spectroscopy (AES), Temperature Programmed Desorption (TPD) and Gas Chromatography (GC) were used to investigate the nature of species on catalytic surfaces and to measure the catalytic reaction rates. Special attention has been directed at studying high-pressure reactions and in particular, ammonia synthesis in order to identify reaction intermediates and the influence of adsorbates on the surface during reaction conditions. The adsorption of gases N₂, H₂, O₂ and NH₃ that play a role in ammonia synthesis have been studied on the Fe(111) crystal surface by sum frequency generation vibrational spectroscopy using an integrated Ultra-High Vacuum (UHV)/high-pressure system. SFG spectra are presented for the dissociation intermediates, NH₂ (~3325 cm^-1) and NH (~3235 cm^-1) under high pressure of ammonia (200 Torr) on the clean Fe(111) surface. Addition of 0.5 Torr of oxygen to 200 Torr of ammonia does not significantly change the bonding of dissociation intermediates to the surface. However, it leads to a phase change of nearly 180° between the resonant and non-resonant second order non-linear susceptibility of the surface, demonstrated by the reversal of the SFG spectral features. Heating the surface in the presence of 200 Torr ammonia and 0.5 Torr oxygen reduces the oxygen coverage, which can be seen from the SFG spectra as another relative phase change of 180°. The reduction of the oxide is also supported by Auger electron spectroscopy. The result suggests that the phase change of the spectral features could serve as a sensitive indicator of the chemical environment of the adsorbates.

Sum Frequency Generation Vibrational Spectroscopy and Kinetic Study of 2-Methylfuran and 2,5-Dimethylfuran Hydrogenation over 7 nm Platinum Cubic Nanoparticles

KAUST Repository

Aliaga, Cesar

2011-04-28

Sum frequency generation vibrational spectroscopy and kinetic measurements obtained from gas chromatography were used to study the adsorption and hydrogenation of 2-methylfuran (MF) and 2,5-dimethylfuran (DMF) over cubic Pt nanoparticles of 7 nm average size, synthesized by colloidal methods and cleaned by ultraviolet light and ozone treatment. Reactions carried out at atmospheric pressure in the temperature range of 20-120 °C produced dihydro and tetrahydro species, as well as ring-opening products (alcohols) and ring-cracking products, showing high selectivity toward ring opening throughout the entire temperature range. The aromatic rings (MF and DMF) adsorbed parallel to the nanoparticle surface. Results yield insight into various surface reaction intermediates and the reason for the significantly lower selectivity for ring cracking in DMF hydrogenation compared to MF hydrogenation. © 2011 American Chemical Society.

Frequency identification of vibration signals using video camera image data.

Science.gov (United States)

Jeng, Yih-Nen; Wu, Chia-Hung

2012-10-16

This study showed that an image data acquisition system connecting a high-speed camera or webcam to a notebook or personal computer (PC) can precisely capture most dominant modes of vibration signal, but may involve the non-physical modes induced by the insufficient frame rates. Using a simple model, frequencies of these modes are properly predicted and excluded. Two experimental designs, which involve using an LED light source and a vibration exciter, are proposed to demonstrate the performance. First, the original gray-level resolution of a video camera from, for instance, 0 to 256 levels, was enhanced by summing gray-level data of all pixels in a small region around the point of interest. The image signal was further enhanced by attaching a white paper sheet marked with a black line on the surface of the vibration system in operation to increase the gray-level resolution. Experimental results showed that the Prosilica CV640C CMOS high-speed camera has the critical frequency of inducing the false mode at 60 Hz, whereas that of the webcam is 7.8 Hz. Several factors were proven to have the effect of partially suppressing the non-physical modes, but they cannot eliminate them completely. Two examples, the prominent vibration modes of which are less than the associated critical frequencies, are examined to demonstrate the performances of the proposed systems. In general, the experimental data show that the non-contact type image data acquisition systems are potential tools for collecting the low-frequency vibration signal of a system.

Frequency Identification of Vibration Signals Using Video Camera Image Data

Directory of Open Access Journals (Sweden)

Chia-Hung Wu

2012-10-01

Full Text Available This study showed that an image data acquisition system connecting a high-speed camera or webcam to a notebook or personal computer (PC can precisely capture most dominant modes of vibration signal, but may involve the non-physical modes induced by the insufficient frame rates. Using a simple model, frequencies of these modes are properly predicted and excluded. Two experimental designs, which involve using an LED light source and a vibration exciter, are proposed to demonstrate the performance. First, the original gray-level resolution of a video camera from, for instance, 0 to 256 levels, was enhanced by summing gray-level data of all pixels in a small region around the point of interest. The image signal was further enhanced by attaching a white paper sheet marked with a black line on the surface of the vibration system in operation to increase the gray-level resolution. Experimental results showed that the Prosilica CV640C CMOS high-speed camera has the critical frequency of inducing the false mode at 60 Hz, whereas that of the webcam is 7.8 Hz. Several factors were proven to have the effect of partially suppressing the non-physical modes, but they cannot eliminate them completely. Two examples, the prominent vibration modes of which are less than the associated critical frequencies, are examined to demonstrate the performances of the proposed systems. In general, the experimental data show that the non-contact type image data acquisition systems are potential tools for collecting the low-frequency vibration signal of a system.

Wetting effect on optical sum frequency generation (SFG) spectra of D-glucose, D-fructose, and sucrose

Science.gov (United States)

Hieu, Hoang Chi; Li, Hongyan; Miyauchi, Yoshihiro; Mizutani, Goro; Fujita, Naoko; Nakamura, Yasunori

2015-03-01

We report a sum frequency generation (SFG) spectroscopy study of D-glucose, D-fructose and sucrose in the Csbnd H stretching vibration regime. Wetting effect on the SFG spectra was investigated. The SFG spectrum of D-glucose changed from that of α-D-glucose into those of α-D-glucose monohydrate by wetting. The SFG spectra showed evidence of a small change of β-D-fructopyranose into other anomers by wetting. SFG spectra of sucrose did not change by wetting. Assignments of the vibrational peaks in the SFG spectra of the three sugars in the dry and wet states were performed in the Csbnd H stretching vibration region near 3000 cm-1.

Image reconstruction from pairs of Fourier-transform magnitude

International Nuclear Information System (INIS)

Hunt, B.R.; Overman, T.L.; Gough, P.

1998-01-01

The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America

The smoothing and fast Fourier transformation of experimental X-ray and neutron data from amorphous materials

International Nuclear Information System (INIS)

Dixon, M.; Wright, A.C.; Hutchinson, P.

1977-01-01

The application of fast Fourier transformation techniques to the analysis of experimental X-ray and neutron diffraction patterns from amorphous materials is discussed and compared with conventional techniques using Filon's quadrature. The fast Fourier transform package described also includes cubic spline smoothing and has been extensively tested, using model data to which statistical errors have been added by means of a pseudo-random number generator with Gaussian shaper. Neither cubic spline nor hand smoothing has much effect on the resulting transform since the noise removed is of too high a frequency. (Auth.)

Fourier Transform Mass Spectrometry.

Science.gov (United States)

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)

Utilização de filtro de transformada de fourier para a minimização de ruídos em sinais analíticos Utilization of fourier transform filter for noise minimization in analytical signals

Directory of Open Access Journals (Sweden)

Eduardo O. Cerqueira

2000-10-01

Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices

Quantitation of pulmonary nodule's border structure by means of Fourier transform by using chest X-ray CT images

International Nuclear Information System (INIS)

Shikata, Hidenori; Masuyama, Hiroshi; Kido, Shoji

1998-01-01

In order to evaluate quantitatively the border structure of pulmonary nodules by using chest X-ray CT images, we investigated whether the sum of high-frequency elements of the power spectrum in a Fourier-transformed nodule's contour line becomes a valuable measure of the border structure of pulmonary nodules. We expect that this measure clearly reflects the radiologic characteristics of a nodule, that is, the contour line is clear or unclear in benign or malignant nodules, respectively. We evaluated and analyzed images statistically for 31 patients (15 benign, 16 malignant), and we were able to recognize a measurable difference between the benign and malignant cases. We conclude that we can evaluate the border structure of a nodule by our proposed measure, and that this measure is valuable for quantitative differential diagnosis. (author)

Quantification of crystalline cellulose in lignocellulosic biomass using sum frequency generation (SFG) vibration spectroscopy and comparison with other analytical methods.

Science.gov (United States)

Barnette, Anna L; Lee, Christopher; Bradley, Laura C; Schreiner, Edward P; Park, Yong Bum; Shin, Heenae; Cosgrove, Daniel J; Park, Sunkyu; Kim, Seong H

2012-07-01

The non-centrosymmetry requirement of sum frequency generation (SFG) vibration spectroscopy allows the detection and quantification of crystalline cellulose in lignocellulose biomass without spectral interferences from hemicelluloses and lignin. This paper shows a correlation between the amount of crystalline cellulose in biomass and the SFG signal intensity. Model biomass samples were prepared by mixing commercially available cellulose, xylan, and lignin to defined concentrations. The SFG signal intensity was found sensitive to a wide range of crystallinity, but varied non-linearly with the mass fraction of cellulose in the samples. This might be due to the matrix effects such as light scattering and absorption by xylan and lignin, as well as the non-linear density dependence of the SFG process itself. Comparison with other techniques such as XRD, FT-Raman, FT-IR and NMR demonstrate that SFG can be a complementary and sensitive tool to assess crystalline cellulose in biomass. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

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 relationship between shock response spectrum and fast Fourier transform

International Nuclear Information System (INIS)

Zola, Maurizio

2001-01-01

In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)

Instantaneous Purified Orbit: A New Tool for Analysis of Nonstationary Vibration of Rotor System

Directory of Open Access Journals (Sweden)

Shi Dongfeng

2001-01-01

Full Text Available In some circumstances, vibration signals of large rotating machinery possess time-varying characteristics to some extent. Traditional diagnosis methods, such as FFT spectrum and orbit diagram, are confronted with a huge challenge to deal with this problem. This work aims at studying the four intrinsic drawbacks of conventional vibration signal processing method and instantaneous purified orbit (IPO on the basis of improved Fourier spectrum (IFS to analyze nonstationary vibration. On account of integration, the benefits of short period Fourier transform (SPFT and regular holospectrum, this method can intuitively reflect vibration characteristics of’a rotor system by means of parameter analysis for corresponding frequency ellipses. Practical examples, such as transient vibration in run-up stages and bistable condition of rotor show that IPO is a powerful tool for diagnosis and analysis of the vibration behavior of rotor systems.

Closed contour fractal dimension estimation by the Fourier transform

International Nuclear Information System (INIS)

Florindo, J.B.; Bruno, O.M.

2011-01-01

Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.

Structure and orientation of interfacial proteins determined by sum frequency generation vibrational spectroscopy: method and application.

Science.gov (United States)

Ye, Shuji; Wei, Feng; Li, Hongchun; Tian, Kangzhen; Luo, Yi

2013-01-01

In situ and real-time characterization of molecular structures and orientation of proteins at interfaces is essential to understand the nature of interfacial protein interaction. Such work will undoubtedly provide important clues to control biointerface in a desired manner. Sum frequency generation vibrational spectroscopy (SFG-VS) has been demonstrated to be a powerful technique to study the interfacial structures and interactions at the molecular level. This paper first systematically introduced the methods for the calculation of the Raman polarizability tensor, infrared transition dipole moment, and SFG molecular hyperpolarizability tensor elements of proteins/peptides with the secondary structures of α-helix, 310-helix, antiparallel β-sheet, and parallel β-sheet, as well as the methodology to determine the orientation of interfacial protein secondary structures using SFG amide I spectra. After that, recent progresses on the determination of protein structure and orientation at different interfaces by SFG-VS were then reviewed, which provides a molecular-level understanding of the structures and interactions of interfacial proteins, specially understanding the nature of driving force behind such interactions. Although this review has focused on analysis of amide I spectra, it will be expected to offer a basic idea for the spectral analysis of amide III SFG signals and other complicated molecular systems such as RNA and DNA. Copyright © 2013 Elsevier Inc. All rights reserved.

Density functional theory, comparative vibrational spectroscopic studies, highest occupied molecular orbital and lowest unoccupied molecular orbital analysis of Linezolid

Science.gov (United States)

Rajalakshmi, K.; Gunasekaran, S.; Kumaresan, S.

2015-06-01

The Fourier transform infrared spectra and Fourier transform Raman spectra of Linezolid have been recorded in the regions 4,000-400 and 4,000-100 cm-1, respectively. Utilizing the observed Fourier transform infrared spectra and Fourier transform Raman spectra data, a complete vibrational assignment and analysis of the fundamental modes of the compound have been carried out. The optimum molecular geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities, have been calculated by density functional theory with 6-31G(d,p), 6-311G(d,p) and M06-2X/6-31G(d,p) levels. The difference between the observed and scaled wavenumber values of most of the fundamentals is very small. A detailed interpretation of the infrared and Raman spectra of Linezolid is reported. Mulliken's net charges have also been calculated. Ultraviolet-visible spectrum of the title molecule has also been calculated using time-dependent density functional method. Besides, molecular electrostatic potential, highest occupied molecular orbital and lowest unoccupied molecular orbital analysis and several thermodynamic properties have been performed by the density functional theoretical method.

Water Orientation at Ceramide/Water Interfaces Studied by Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy and Molecular Dynamics Simulation

KAUST Repository

Adhikari, Aniruddha

2016-10-10

Lipid/water interaction is essential for many biological processes. The water structure at the nonionic lipid interface remains little known, and there is no scope of a priori prediction of water orientation at nonionic interfaces, either. Here, we report our study combining advanced nonlinear spectroscopy and molecular dynamics simulation on the water orientation at the ceramide/water interface. We measured χ spectrum in the OH stretch region of ceramide/isotopically diluted water interface using heterodyne-detected vibrational sum-frequency generation spectroscopy and found that the interfacial water prefers an overall hydrogen-up orientation. Molecular dynamics simulation indicates that this preferred hydrogen-up orientation of water is determined by a delicate balance between hydrogen-up and hydrogen-down orientation induced by lipid-water and intralipid hydrogen bonds. This mechanism also suggests that water orientation at neutral lipid interfaces depends highly on the chemical structure of the lipid headgroup, in contrast to the charged lipid interfaces where the net water orientation is determined solely by the charge of the lipid headgroup.

Transformation of potential energy surfaces for estimating isotopic shifts in anharmonic vibrational frequency calculations

Energy Technology Data Exchange (ETDEWEB)

Meier, Patrick; Oschetzki, Dominik; Rauhut, Guntram, E-mail: rauhut@theochem.uni-stuttgart.de [Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, Robert [Clemens-Schöpf Institut für Organische Chemie and Biochemie, Technische Universität Darmstadt, Petersenstrasse 22, 64287 Darmstadt (Germany)

2014-05-14

A transformation of potential energy surfaces (PES) being represented by multi-mode expansions is introduced, which allows for the calculation of anharmonic vibrational spectra of any isotopologue from a single PES. This simplifies the analysis of infrared spectra due to significant CPU-time savings. An investigation of remaining deviations due to truncations and the so-called multi-level approximation is provided. The importance of vibrational-rotational couplings for small molecules is discussed in detail. In addition, an analysis is proposed, which provides information about the quality of the transformation prior to its execution. Benchmark calculations are provided for a set of small molecules.

Some notes concerning the fourier transformation of auto-correlation functions; Quelques notes sur la transformee de fourier des fonctions d'autocorrelation

Energy Technology Data Exchange (ETDEWEB)

Froelicher, B; Dalfes, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1968-07-01

A study is made of the passage of the auto-correlation function to the frequency spectrum by a numerical Fourier transformation. Two principal characteristics of auto-correlation functions, the time between two points and the total time, are related to two oscillations which appear in the frequency spectrum and which deform it. Various methods are proposed for reducing the effect of these two parasitic oscillations and for re-obtaining the real spectrum. (authors) [French] On etudie le passage de la fonction d'autocorrelation au spectre de frequence par transformee de Fourier numerique. Deux caracteristiques principales des fonctions d'autocorrelation, la duree entre points et la duree totale sont reliees a deux oscillations qui apparaissent dans le spectre de frequence et le deforment. Diverses methodes sont proposees pour reduire l'effet de ces deux oscillations parasites, et retrouver le spectre reel. (auteurs)

Direct fourier method reconstruction based on unequally spaced fast fourier transform

International Nuclear Information System (INIS)

Wu Xiaofeng; Zhao Ming; Liu Li

2003-01-01

First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)

A fractional Fourier transform analysis of the scattering of ultrasonic waves

Science.gov (United States)

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

2015-01-01

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

A discrete Fourier transform for virtual memory machines

Science.gov (United States)

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.

Imaging vibration of the cochlear partition of an excised guinea pig cochlea using phase-sensitive Fourier domain optical coherence tomography

Science.gov (United States)

Choudhury, Niloy; Zeng, Yaguang; Fridberger, Anders; Chen, Fangyi; Zha, Dingjun; Nuttall, Alfred L.; Wang, Ruikang K.

2011-03-01

Studying the sound stimulated vibrations of various membranes that form the complex structure of the organ of Corti in the cochlea of the inner ear is essential for understanding how the travelling sound wave of the basilar membrane couples its energy to the organ structures. In this paper we report the feasibility of using phase-sensitive Fourier domain optical coherence tomography (FD-OCT) to image the vibration of various micro-structures of the cochlea at the same time. An excised cochlea of a guinea pig was stimulated using sounds at various frequencies and vibration image was obtained. When measuring the apex area, vibration signal from different turns, which have different best response frequencies are obtained in the same image. The method has the potential to measure the response from a much wider region of the cochlea than any other currently used method. The noise floor for vibration image for the system at 200 Hz was ~0.3nm.

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

Energy Technology Data Exchange (ETDEWEB)

Rodriguez G, A.; Bowtell, R.; Mansfield, P. [Area de Procesamiento Digital de Senales e Imagenes Biomedicas. Universidad Autonoma Metropolitana Iztapalapa. Mexico D.F. 09340 Mexico (Mexico)

1998-12-31

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

International Nuclear Information System (INIS)

Rodriguez G, A.; Bowtell, R.; Mansfield, P.

1998-01-01

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Random sampling of evolution time space and Fourier transform processing

International Nuclear Information System (INIS)

Kazimierczuk, Krzysztof; Zawadzka, Anna; Kozminski, Wiktor; Zhukov, Igor

2006-01-01

Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and 15 N-edited NOESY-HSQC spectra of 13 C 15 N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time

Progress report of a static Fourier transform spectrometer breadboard

Science.gov (United States)

Rosak, A.; Tintó, F.

2017-11-01

MOLI instrument -for MOtionLess Interferometer- takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors -integrated into that interference cube- thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

International Nuclear Information System (INIS)

Fan Hongyi; Hao Ren; Lu Hailiang

2008-01-01

Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible

Motor Fault Diagnosis Based on Short-time Fourier Transform and Convolutional Neural Network

Science.gov (United States)

Wang, Li-Hua; Zhao, Xiao-Ping; Wu, Jia-Xin; Xie, Yang-Yang; Zhang, Yong-Hong

2017-11-01

With the rapid development of mechanical equipment, the mechanical health monitoring field has entered the era of big data. However, the method of manual feature extraction has the disadvantages of low efficiency and poor accuracy, when handling big data. In this study, the research object was the asynchronous motor in the drivetrain diagnostics simulator system. The vibration signals of different fault motors were collected. The raw signal was pretreated using short time Fourier transform (STFT) to obtain the corresponding time-frequency map. Then, the feature of the time-frequency map was adaptively extracted by using a convolutional neural network (CNN). The effects of the pretreatment method, and the hyper parameters of network diagnostic accuracy, were investigated experimentally. The experimental results showed that the influence of the preprocessing method is small, and that the batch-size is the main factor affecting accuracy and training efficiency. By investigating feature visualization, it was shown that, in the case of big data, the extracted CNN features can represent complex mapping relationships between signal and health status, and can also overcome the prior knowledge and engineering experience requirement for feature extraction, which is used by traditional diagnosis methods. This paper proposes a new method, based on STFT and CNN, which can complete motor fault diagnosis tasks more intelligently and accurately.

IR visible sum-frequency vibrational spectroscopy of Biphenyl-3 methylene thiol monolayer on gold and silver: effect of the visible wavelength on the SFG spectrum

Science.gov (United States)

Humbert, C.; Dreesen, L.; Mani, A. A.; Caudano, Y.; Lemaire, J.-J.; Thiry, P. A.; Peremans, A.

2002-04-01

We measured IR-visible sum-frequency generation spectra of CH 3-(C 6H 4) 2-(CH 2) 3-S-H (Biphenyl-3) self-assembled monolayers on a silver and a gold substrate. For the latter substrate, we observed different interference patterns between the resonant signal of the CH vibration and the non-resonant contribution of the substrate as a function of the visible beam wavelength. The non-linear response of the gold substrate is enhanced around 480 nm corresponding to the s-d interband transition. Such effect is not observed for the silver substrate the interband transition of which is located out of the investigated visible spectral range of 450-700 nm.

The application and improvement of Fourier transform spectrometer experiment

Science.gov (United States)

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.

Geometric Representations for Discrete Fourier Transforms

Science.gov (United States)

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.

Estimation of Interchannel Time Difference in Frequency Subbands Based on Nonuniform Discrete Fourier Transform

Directory of Open Access Journals (Sweden)

Qiu Bo

2008-01-01

Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

Science.gov (United States)

Morelli, Eugene A.

2013-01-01

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

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

Science.gov (United States)

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",…

Techniques for computing the discrete Fourier transform using the quadratic residue Fermat number systems

Science.gov (United States)

Truong, T. K.; Chang, J. J.; Hsu, I. S.; Pei, D. Y.; Reed, I. S.

1986-01-01

The complex integer multiplier and adder over the direct sum of two copies of finite field developed by Cozzens and Finkelstein (1985) is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplication over the rings of integers modulo Fermat numbers can be performed by means of two integer multiplications, whereas the complex integer multiplication requires three integer multiplications. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed to compute a systolic array of the DFT can be reduced substantially. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

Efficient yellow beam generation by intracavity sum frequency ...

Indian Academy of Sciences (India)

2014-02-06

Feb 6, 2014 ... We present our studies on dual wavelength operation using a single Nd:YVO4 crystal and its intracavity sum frequency generation by considering the influence of the thermal lensing effect on the performance of the laser. A KTP crystal cut for type-II phase matching was used for intracavity sum frequency ...

On integral and finite Fourier transforms of continuous q-Hermite polynomials

International Nuclear Information System (INIS)

Atakishiyeva, M. K.; Atakishiyev, N. M.

2009-01-01

We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

Limited-angle three-dimensional reconstructions using Fourier transform iterations and Radon transform iterations

International Nuclear Information System (INIS)

Tam, K.C.; Perez-Mendez, V.

1981-01-01

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time

Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations

International Nuclear Information System (INIS)

Tam, K.C.; Perez-Mendez, V.

1979-12-01

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables

Natural Frequencies Evaluation on Partially Damaged Building using Ambient Vibration Technique

Science.gov (United States)

Kamarudin, A. F.; Zainal Abidin, M. H.; Daud, M. E.; Noh, M. S. Md; Madun, A.; Ibrahim, A.; Matarul, J.; Mokhatar, S. N.

2018-04-01

Severe damages observed on the school blocks, roads, retaining walls and drainage within the compound of SMK Kundasang Sabah possibly due to the ground movements triggered by the Ranau earthquake in 1991. Ambient vibration measurements were carried on the remaining demolished 3-storey building which partially damaged in order to measure the predominant building frequencies using tri-axial 1 Hz seismometer sensors. Popular methods of Horizontal-to-vertical spectral ratios (HVSR) and Fourier amplitude spectra (FAS) were used to compute the ambient vibration wave fields of each building axes (Transverse or North-South (NS), Longitudinal or East-West (EW) and vertical) into Fourier spectra. Two main modes of translation and torsion were observed from the peaks frequencies obtained at 2.99 to 3.10 Hz (1st mode), 4.85 Hz (2nd mode) and 5.63 to 5.85 Hz (3rd mode). The building experiencing translation modes of bending and shear in the NS and EW directions. It could be seen when the amplitudes tends to increase when the floor are increased. Meanwhile, the torsional bending mode is expected to occur when the deformation amplitudes are found to be increasing horizontally, when moving into partially structural damaged section located on the East wing of building.

Mode shape and natural frequency identification for seismic analysis from background vibration

International Nuclear Information System (INIS)

Bhan, S.; Wozniak, Z.

1986-10-01

Background vibration in a CANDU plant can be used to determine the dynamic characteristics of major items of equipment, such as calandria, the fuelling machines and the primary heat transport pumps. These dynamic characteristics can then be used to verify the seismic response of the equipment which, at present, is based on theoretical models only. The feasibility and basic theory of this new approach (which uses accelerations measured at several points on a structure and does not require knowledge of the source of excitation) was established in Phase I of the study. This report is based on Phase II in which the methods of analysis developed in Phase I were improved and verified experimentally. A Fast Fourier Transform (FFT) algorithm was incorporated and an interactive curve fitting technique was developed to obtain the dynamic characteristics in the form of natural frequencies, mode shapes and damping ratios. The method is now available for use at a CANDU plant

Vibrational analysis of Fourier transform spectrum of the A3Π0–X1Σ ...

Indian Academy of Sciences (India)

Abstract. The emission spectrum of InBr molecule has been recorded in the region. 350–400 nm on BOMEM DA8 Fourier transform spectrometer at an apodized resolu- tion of 0.06 cm−1 using microwave excitation technique. About 61 violet degraded and single headed bands have been recorded and are classified into ...

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

Science.gov (United States)

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.

Vibrational Dynamics of Interfacial Water by Free Induction Decay Sum Frequency Generation (FID-SFG) at the Al2O3(1120)/H2O Interface.

Science.gov (United States)

Boulesbaa, Abdelaziz; Borguet, Eric

2014-02-06

The dephasing dynamics of a vibrational coherence may reveal the interactions of chemical functional groups with their environment. To investigate this process at a surface, we employ free induction decay sum frequency generation (FID-SFG) to measure the time that it takes for free OH stretch oscillators at the charged (pH ≈ 13, KOH) interface of alumina/water (Al2O3/H2O) to lose their collective coherence. By employing noncollinear optical parametric amplification (NOPA) technology and nonlinear vibrational spectroscopy, we showed that the single free OH peak actually corresponds to two distinct oscillators oriented opposite to each other and measured the total dephasing time, T2, of the free OH stretch modes at the Al2O3/H2O interface with a sub-40 fs temporal resolution. Our results suggested that the free OH oscillators associated with interfacial water dephase on the time scale of 89.4 ± 6.9 fs, whereas the homogeneous dephasing of interfacial alumina hydroxyls is an order of magnitude slower.

Spectroscopy and reactions of vibrationally excited transient molecules

Energy Technology Data Exchange (ETDEWEB)

Dai, H.L. [Univ. of Pennsylvania, Philadelphia (United States)

1993-12-01

Spectroscopy, energy transfer and reactions of vibrationally excited transient molecules are studied through a combination of laser-based excitation techniques and efficient detection of emission from the energized molecules with frequency and time resolution. Specifically, a Time-resolved Fourier Transform Emission Spectroscopy technique has been developed for detecting dispersed laser-induced fluorescence in the IR, visible and UV regions. The structure and spectroscopy of the excited vibrational levels in the electronic ground state, as well as energy relaxation and reactions induced by specific vibronic excitations of a transient molecule can be characterized from time-resolved dispersed fluorescence in the visible and UV region. IR emissions from highly vibrational excited levels, on the other hand, reveal the pathways and rates of collision induced vibrational energy transfer.

Frequency adjustable MEMS vibration energy harvester

Science.gov (United States)

Podder, P.; Constantinou, P.; Amann, A.; Roy, S.

2016-10-01

Ambient mechanical vibrations offer an attractive solution for powering the wireless sensor nodes of the emerging “Internet-of-Things”. However, the wide-ranging variability of the ambient vibration frequencies pose a significant challenge to the efficient transduction of vibration into usable electrical energy. This work reports the development of a MEMS electromagnetic vibration energy harvester where the resonance frequency of the oscillator can be adjusted or tuned to adapt to the ambient vibrational frequency. Micro-fabricated silicon spring and double layer planar micro-coils along with sintered NdFeB micro-magnets are used to construct the electromagnetic transduction mechanism. Furthermore, another NdFeB magnet is adjustably assembled to induce variable magnetic interaction with the transducing magnet, leading to significant change in the spring stiffness and resonance frequency. Finite element analysis and numerical simulations exhibit substantial frequency tuning range (25% of natural resonance frequency) by appropriate adjustment of the repulsive magnetic interaction between the tuning and transducing magnet pair. This demonstrated method of frequency adjustment or tuning have potential applications in other MEMS vibration energy harvesters and micromechanical oscillators.

Frequency adjustable MEMS vibration energy harvester

International Nuclear Information System (INIS)

Podder, P; Constantinou, P; Roy, S; Amann, A

2016-01-01

Ambient mechanical vibrations offer an attractive solution for powering the wireless sensor nodes of the emerging “Internet-of-Things”. However, the wide-ranging variability of the ambient vibration frequencies pose a significant challenge to the efficient transduction of vibration into usable electrical energy. This work reports the development of a MEMS electromagnetic vibration energy harvester where the resonance frequency of the oscillator can be adjusted or tuned to adapt to the ambient vibrational frequency. Micro-fabricated silicon spring and double layer planar micro-coils along with sintered NdFeB micro-magnets are used to construct the electromagnetic transduction mechanism. Furthermore, another NdFeB magnet is adjustably assembled to induce variable magnetic interaction with the transducing magnet, leading to significant change in the spring stiffness and resonance frequency. Finite element analysis and numerical simulations exhibit substantial frequency tuning range (25% of natural resonance frequency) by appropriate adjustment of the repulsive magnetic interaction between the tuning and transducing magnet pair. This demonstrated method of frequency adjustment or tuning have potential applications in other MEMS vibration energy harvesters and micromechanical oscillators. (paper)

Generalized Fourier transforms Fk,a

DEFF Research Database (Denmark)

Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent

2009-01-01

We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....

Fourier transform infrared and FT-Raman spectra, assignment, ab initio, DFT and normal co-ordinate analysis of 2-chloro-4-methylaniline and 2-chloro-6-methylaniline.

Science.gov (United States)

Arjunan, V; Mohan, S

2009-03-01

The Fourier transform infrared (FTIR) and FT-Raman spectra of 2-chloro-4-methylaniline and 2-chloro-6-methylaniline have been measured in the range 4000-400 and 4000-100cm(-1), respectively. Utilising the observed FTIR and FT-Raman data, a complete vibrational assignment and analysis of the fundamental modes of the compounds were carried out. The vibrational frequency which were determined experimentally are compared with those obtained theoretically from ab initio HF and DFT gradient calculations employing the HF/6-31G(d,p) and B3LYP/6-31G(d,p) methods for optimised geometries. The geometries and normal modes of vibration obtained from the HF and DFT methods are in good agreement with the experimental data. The normal co-ordinate analysis was also carried out on the basis of ab initio force fields utilising Wilson's FG matrix method. The manifestations of NH-pi interactions and the influence of bulky chlorine and methyl group on the vibrational modes of the amino group are investigated.

The Fourier Transform for Certain HyperKähler Fourfolds

NARCIS (Netherlands)

Shen, M.; Vial, C.

2016-01-01

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle

Amine Chemistry at Aqueous Interfaces: The Study of Organic Amines in Neutralizing Acidic Gases at an Air/Water Surface Using Vibrational Sum Frequency Spectroscopy

Science.gov (United States)

McWilliams, L.; Wren, S. N.; Valley, N. A.; Richmond, G.

2014-12-01

Small organic bases have been measured in atmospheric samples, with their sources ranging from industrial processing to animal husbandry. These small organic amines are often highly soluble, being found in atmospheric condensed phases such as fogwater and rainwater. Additionally, they display acid-neutralization ability often greater than ammonia, yet little is known regarding their kinetic and thermodynamic properties. This presentation will describe the molecular level details of a model amine system at the vapor/liquid interface in the presence of acidic gas. We find that this amine system shows very unique properties in terms of its bonding, structure, and orientation at aqueous surfaces. The results of our studies using a combination of computation, vibrational sum frequency spectroscopy, and surface tension will report the properties inherent to these atmospherically relevant species at aqueous surfaces.

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

Science.gov (United States)

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.

Simplification of gamma-ray spectral data by using Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

A method is proposed to represent γ-ray response spectra by Fourier series for the purpose of compressing spectral data. The usefulness of the method was confirmed by applying it to a spectral library of a NaI detector. In the method, a response spectrum as a wave is described by superposition of sine (cosine) waves with low frequencies, whose coefficient parameters can be obtained by a Fast Fourier Transform program. The relation between the number of parameters and the fitting error is discussed, and as the result, it is shown that the number of parameters can be reduced to about a half. The merits and features are presented in practical application of the method to the analysis of γ-ray spectra. (auth.)

From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

International Nuclear Information System (INIS)

Ganapol, B.D.

2001-01-01

A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

Comparative study on γ energy spectrum denoise by fourier and wavelet transforms

International Nuclear Information System (INIS)

Shi Dongsheng; Di Yuming; Zhou Chunlin

2007-01-01

This paper introduces the basic principle of wavelet and Fourier transforms, applies wavelet transform method to denoise γ energy spectrum of 60 Co and compares it with Fourier transform method. The result of simulation with MATLAB software tool showed that as compared with traditional Fourier transform, wavelet transform has comparatively higher accuracy for γ energy spectrum denoising and is more feasible to γ energy spectrum denoising. (authors)

On the Scaled Fractional Fourier Transformation Operator

International Nuclear Information System (INIS)

Hong-Yi, Fan; Li-Yun, Hu

2008-01-01

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched

Sum Frequency Generation Studies of Hydrogenation Reactions on Platinum Nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Krier, James M. [Univ. of California, Berkeley, CA (United States)

2013-08-31

Sum Frequency Generation (SFG) vibrational spectroscopy is used to characterize intermediate species of hydrogenation reactions on the surface of platinum nanoparticle catalysts. In contrast to other spectroscopy techniques which operate in ultra-high vacuum or probe surface species after reaction, SFG collects information under normal conditions as the reaction is taking place. Several systems have been studied previously using SFG on single crystals, notably alkene hydrogenation on Pt(111). In this thesis, many aspects of SFG experiments on colloidal nanoparticles are explored for the first time. To address spectral interference by the capping agent (PVP), three procedures are proposed: UV cleaning, H2 induced disordering and calcination (core-shell nanoparticles). UV cleaning and calcination physically destroy organic capping while disordering reduces SFG signal through a reversible structural change by PVP.

Fourier transformations for difference analogs of the harmonic oscillator

International Nuclear Information System (INIS)

Askey, R.; Atakishiyev, N.M.

1995-01-01

The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs

The finite Fourier transform of classical polynomials

OpenAIRE

Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

2014-01-01

The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

Fourier Transform Ultrasound Spectroscopy for the determination of wave propagation parameters.

Science.gov (United States)

Pal, Barnana

2017-01-01

The reported results for ultrasonic wave attenuation constant (α) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a consequence of the inherent wave propagation characteristics in a bounded medium. In the present work Fourier Transform Ultrasound Spectroscopy (FTUS) is adopted to determine ultrasonic wave propagation parameters, the wave number (k) and attenuation constant (α) at 1MHz frequency in tri-distilled water at room temperature (25°C). Pulse-echo signals obtained under same experimental conditions regarding the exciting input signal and reflecting boundary wall of the water container for various lengths of water columns are captured. The Fast Fourier Transform (FFT) components of the echo signals are taken to compute k, α and r, the reflection constant at the boundary, using Oak Ridge and Oxford method. The results are compared with existing literature values. Copyright © 2016 Elsevier B.V. All rights reserved.

Low energy electron diffraction (LEED) and sum frequency generation (SFG) vibrational spectroscopy studies of solid-vacuum, solid-air and solid-liquid interfaces

Energy Technology Data Exchange (ETDEWEB)

Hoffer, Saskia [Univ. of California, Berkeley, CA (United States)

2002-01-01

Electron based surface probing techniques can provide detailed information about surface structure or chemical composition in vacuum environments. The development of new surface techniques has made possible in situ molecular level studies of solid-gas interfaces and more recently, solid-liquid interfaces. The aim of this dissertation is two-fold. First, by using novel sample preparation, Low Energy Electron Diffraction (LEED) and other traditional ultra high vacuum (UHV) techniques are shown to provide new information on the insulator/vacuum interface. The surface structure of the classic insulator NaCl has been determined using these methods. Second, using sum frequency generation (SFG) surface specific vibrational spectroscopy studies were performed on both the biopolymer/air and electrode/electrolyte interfaces. The surface structure and composition of polyetherurethane-silicone copolymers were determined in air using SFG, atomic force microscopy (AFM), and X-ray photoelectron spectroscopy (XPS). SFG studies of the electrode (platinum, gold and copper)/electrolyte interface were performed as a function of applied potential in an electrochemical cell.

Sum frequency generation vibrational spectroscopy (SFG-VS) for complex molecular surfaces and interfaces: Spectral lineshape measurement and analysis plus some controversial issues

Science.gov (United States)

Wang, Hong-Fei

2016-12-01

Sum-frequency generation vibrational spectroscopy (SFG-VS) was first developed in the 1980s and it has been proven a uniquely sensitive and surface/interface selective spectroscopic probe for characterization of the structure, conformation and dynamics of molecular surfaces and interfaces. In recent years, there have been many progresses in the development of methodology and instrumentation in the SFG-VS toolbox that have significantly broadened the application to complex molecular surfaces and interfaces. In this review, after presenting a unified view on the theory and methodology focusing on the SFG-VS spectral lineshape, as well as the new opportunities in SFG-VS applications with such developments, some of the controversial issues that have been puzzling the community are discussed. The aim of this review is to present to the researchers and students interested in molecular surfaces and interfacial sciences up-to-date perspectives complementary to the existing textbooks and reviews on SFG-VS.

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

Science.gov (United States)

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.

Fast Fourier transform telescope

International Nuclear Information System (INIS)

Tegmark, Max; Zaldarriaga, Matias

2009-01-01

We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

Analysis of tokamak plasma confinement modes using the fast Fourier transformation

International Nuclear Information System (INIS)

Mirmoeini, S.R.; Salar Elahi, A.; Ghoranneviss, M.

2016-01-01

The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and without external field (electric biasing), and then compared it with each other. After the Fourier analysis of Mirnov coil data, the diagram of power spectrum density was depicted in different angles of Mirnov coils in the 'presence of external field' as well as in the 'absence of external field'. The power spectrum density (PSD) interprets the manner of power distribution of a signal with frequency. In this article, the number of plasma modes and the safety factor q were obtained by using the mode number of q = m/n (m is the mode number). The maximum MHD activity was obtained in 30-35 kHz frequency, using the density of the energy spectrum. In addition, the number of different modes across 0-35 ms time was compared with each other in the presence and absence of the external field. (author)

Vibrational Characterizations of Zn0.72Li0.28O/Si Thin Films Studied by Fourier Transform Raman Spectroscopy

International Nuclear Information System (INIS)

Myo Myat Thet; Win Kyaw; Yin Maung Maung; Ko Ko Kyaw Soe

2008-03-01

The Zn0.72Li0.28O/Si (x = 0.28mol%) thin layers were fabricated on p-Si(100) substrate with five different process temperature. Vibrational characterizations of those thin films were investigated by FT- Raman spectroscopy. The resulted spectral line characters have been compared with that of Zn0.72Li0.28O/Glass thin films. Some vibrational motions of starting materials and final(candidate) thin films molecules were found in two substrates of glass and Si and vibrational frequencies were assigned by using molecular spectroscopy. Most of the frequencies of starting and final materials were found to be shifted in each of the films of two different substrates.

Fourier transforms and convolutions for the experimentalist

CERN Document Server

Jennison, RC

1961-01-01

Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t

High-speed digital holographic interferometry for vibration measurement

International Nuclear Information System (INIS)

Pedrini, Giancarlo; Osten, Wolfgang; Gusev, Mikhail E.

2006-01-01

A system based on digital holographic interferometry for the measurement of vibrations is presented. A high-power continuous laser(10 W) and a high-speed CCD camera are used. Hundreds of holograms of an object that has been subjected to dynamic deformation are recorded. The acquisition speed and the time of exposure of the detector are determined by the vibration frequency. Two methods are presented for triggering the camera in order to acquire at a given phase of the vibration. The phase of the wavefront is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. The deformation of the object is obtained from the phase. By combination of the deformations recorded at different times it is possible to reconstruct the vibration of the object

Elucidation of Compression-Induced Surface Crystallization in Amorphous Tablets Using Sum Frequency Generation (SFG) Microscopy.

Science.gov (United States)

Mah, Pei T; Novakovic, Dunja; Saarinen, Jukka; Van Landeghem, Stijn; Peltonen, Leena; Laaksonen, Timo; Isomäki, Antti; Strachan, Clare J

2017-05-01

To investigate the effect of compression on the crystallization behavior in amorphous tablets using sum frequency generation (SFG) microscopy imaging and more established analytical methods. Tablets containing neat amorphous griseofulvin with/without excipients (silica, hydroxypropyl methylcellulose acetate succinate (HPMCAS), microcrystalline cellulose (MCC) and polyethylene glycol (PEG)) were prepared. They were analyzed upon preparation and storage using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy, scanning electron microscopy (SEM) and SFG microscopy. Compression-induced crystallization occurred predominantly on the surface of the neat amorphous griseofulvin tablets, with minimal crystallinity being detected in the core of the tablets. The presence of various types of excipients was not able to mitigate the compression-induced surface crystallization of the amorphous griseofulvin tablets. However, the excipients affected the crystallization rate of amorphous griseofulvin in the core of the tablet upon compression and storage. SFG microscopy can be used in combination with ATR-FTIR spectroscopy and SEM to understand the crystallization behaviour of amorphous tablets upon compression and storage. When selecting excipients for amorphous formulations, it is important to consider the effect of the excipients on the physical stability of the amorphous formulations.

FOURIER SERIES MODELS THROUGH TRANSFORMATION

African Journals Online (AJOL)

DEPT

monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.

Fourier transform in multimode systems in the Bargmann representation

International Nuclear Information System (INIS)

Lei, C; Vourdas, A

2007-01-01

A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed

Sum-frequency generation from molecular monolayers using 14 μm radiation from the FELIX free-electron laser

International Nuclear Information System (INIS)

Van der Ham, E.W.M.; Vrehen, Q.H.F.; Eliel, E.R.

1995-01-01

Sum-frequency generation (SFG) has developed into a widely applied tool for study of surfaces and interfaces where molecules are present. It combines the surface specificity of a second-order nonlinear optical technique with the power of a spectroscopic method, and it can be used under widely varying experimental conditions ranging from UHV to electrochemical cells. The important characteristic of SFG is that it allows one to study the average spatial orientation of a molecular bond in a monolayer of molecules at an interface. Until recently SFG measurements were confined to the frequency interval Y μ > 1700 cm -1 because of a lack of suitable laser sources at wave-lengths λ > 6 μm. So for most molecules only a few vibrational modes and thus intramolecular bonds can be studied. We have developed a universal sum-frequency spectrometer around the FELIX free-electron law that covers the complete molecular fingerprint since we can generate any IR wavelength between 2.75 and 110 fμ at the FELIX facility. We have used this setup for a series of exploratory SFG experiments in a frequency range that was hitherto unexplored in the study of molecular monolayers. We have studied thiol monolayers chemisorbed on a variety of noble metals (Au, Ag, Pt) where we focussed on the C-S stretch vibration at ν = 702 cm -1 (λ = 14.3 μm). We have found spectroscopic features revealing the presence of both the trane and gauche conformers of the adsorbed molecules. The present measurements open a whole new wavelength range for nonlinear optical studies of interfaces

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

Ferraro, John R

1978-01-01

Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

Ferraro, John R

1985-01-01

The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry.Presenting current information from leading experts in the field, Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-Infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography - Fourier Transform Interferometry.Volume 4 especially benefits spectroscopists and physicists, as well as researchers

Frequency analysis for the thermal hydraulic characterization of a natural circulation circuit

Energy Technology Data Exchange (ETDEWEB)

Torres, Walmir M.; Macedo, Luiz A.; Sabundjian, Gaiane; Andrade, Delvonei A.; Umbehaun, Pedro E.; Conti, Thadeu N.; Mesquita, Roberto N.; Masotti, Paulo H.; Angelo, Gabriel, E-mail: wmtorres@ipen.b, E-mail: lamacedo@ipen.b, E-mail: gdjian@ipen.b, E-mail: delvonei@ipen.b, E-mail: umbehaun@ipen.b, E-mail: tnconti@ipen.b, E-mail: , E-mail: rnavarro@ipen.b, E-mail: pmasotti@ipen.b, E-mail: gabriel.angelo@usp.b [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)

2011-07-01

This paper presents the frequency analysis studies of the pressure signals from an experimental natural circulation circuit during a heating process. The main objective is to identify the characteristic frequencies of this process using fast Fourier transform. Video images are used to associate these frequencies to the observed phenomenology in the circuit during the process. Sub-cooled and saturated flow boiling, heaters vibrations, overall circuit vibrations, chugging and geysering were observed. Each phenomenon has its specific frequency associated. Some phenomena and their frequencies must be avoided or attenuated since they can cause damages to the natural circulation circuit and its components. Special operation procedures and devices can be developed to avoid these undesirable frequencies. (author)

Frequency analysis for the thermal hydraulic characterization of a natural circulation circuit

International Nuclear Information System (INIS)

Torres, Walmir M.; Macedo, Luiz A.; Sabundjian, Gaiane; Andrade, Delvonei A.; Umbehaun, Pedro E.; Conti, Thadeu N.; Mesquita, Roberto N.; Masotti, Paulo H.; Angelo, Gabriel

2011-01-01

This paper presents the frequency analysis studies of the pressure signals from an experimental natural circulation circuit during a heating process. The main objective is to identify the characteristic frequencies of this process using fast Fourier transform. Video images are used to associate these frequencies to the observed phenomenology in the circuit during the process. Sub-cooled and saturated flow boiling, heaters vibrations, overall circuit vibrations, chugging and geysering were observed. Each phenomenon has its specific frequency associated. Some phenomena and their frequencies must be avoided or attenuated since they can cause damages to the natural circulation circuit and its components. Special operation procedures and devices can be developed to avoid these undesirable frequencies. (author)

Multichannel Dynamic Fourier-Transform IR Spectrometer

Science.gov (United States)

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.

Low-frequency characteristics extension for vibration sensors

Institute of Scientific and Technical Information of China (English)

杨学山; 高峰; 候兴民

2004-01-01

Traditional magneto-electric vibration sensors and servo accelerometers have severe shortcomings when used to measure vibration where low frequency components predominate. A low frequency characteristic extension for velocity vibration sensors is presented in this paper. The passive circuit technology, active compensation technology and the closedcycle pole compensation technology are used to extend the measurable range and to improve low frequency characteristics of sensors. Thses three types of low frequency velocity vibration sensors have been developed and widely adopted in China.

Fourier domain optical coherence tomography achieves full range complex imaging in vivo by introducing a carrier frequency during scanning

International Nuclear Information System (INIS)

Wang, Ruikang K

2007-01-01

The author describes a Fourier domain optical coherence tomography (FDOCT) system that is capable of full range complex imaging in vivo. This is achieved by introducing a constant carrier frequency into the OCT spectral interferograms at the time when imaging is performed. The complex functions of the spatial interferograms formed by each single wavelength are constructed before performing the Fourier transformation to localize the scatters within a sample. Two algorithms, based on Fourier filtering and Hilbert transformation, respectively, are described to achieve the full range complex FDOCT imaging. It is shown that the Hilbert transformation approach delivers better performance than the Fourier filtering method does in terms of tolerating the sample movement in vivo. The author finally demonstrates experimentally the system and algorithms for true in vivo imaging at a rate of 20 000 axial scans per second

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Double Fourier analysis for Emotion Identification in Voiced Speech

International Nuclear Information System (INIS)

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

2016-01-01

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. (paper)

Novel 2D representation of vibration for local damage detection

Directory of Open Access Journals (Sweden)

Grzegorz Żak

2014-07-01

Full Text Available In this paper a new 2D representation for local damage detection is presented. It is based on a vibration time series analysis. A raw vibration signal is decomposed via short-time Fourier transform and new time series for each frequency bin are differentiated to decorrelate them. For each time series, autocorrelation function is calculated. In the next step ACF maps are constructed. For healthy bearing ACF map should not have visible horizontal lines indicating damage. The method is illustrated by analysis of real data containing signals from damaged bearing and healthy for comparison.

Fourier transforms in NMR, optical, and mass spectrometry

International Nuclear Information System (INIS)

Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH

1990-01-01

This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs

Simple optical setup implementation for digital Fourier transform holography

Energy Technology Data Exchange (ETDEWEB)

De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)

2011-01-01

In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.

Hydration of Sulphobetaine (SB) and Tetra(ethylene glycol) (EG4)-Terminated Self-Assembled Monolayers Studied by Sum Frequency Generation (SFG) Vibrational Spectroscopy

Science.gov (United States)

Stein, M. Jeanette; Weidner, Tobias; McCrea, Keith; Castner, David G.; Ratner, Buddy D.

2010-01-01

Sum frequency generation (SFG) vibrational spectroscopy is used to study the surface and the underlying substrate of both homogeneous and mixed self-assembled monolayers (SAMs) of 11-mercaptoundecyl-1-sulphobetainethiol (HS(CH2)11N+(CH3)2(CH2)3SO3−, SB) and 1-mercapto-11-undecyl tetra(ethylene glycol) (HS(CH2)11O(CH2CH2O)4OH, EG4) with an 11-mercapto-1-undecanol (HS(CH2)11OH, MCU) diluent. SFG results on the C–H region of the dry and hydrated SAMs gave an in situ look into the molecular orientation and suggested an approach to maximize signal-to-noise ratio on these difficult to analyze hydrophilic SAMs. Vibrational fingerprint studies in the 3000–3600 cm−1 spectral range for the SAMs exposed serially to air, water, and deuterated water revealed that a layer of tightly-bound structured water was associated with the surface of a non-fouling monolayer but was not present on a hydrophobic N-undecylmercaptan (HS(CH2)10CH3, UnD) control. The percentage of water retained upon submersion in D2O correlated well with the relative amount of protein that was previously shown to absorb onto the monolayers. These results provide evidence supporting the current theory regarding the role of a tightly-bound vicinal water layer in the protein resistance of a non-fouling group. PMID:19639981

Perceptual Space of Superimposed Dual-Frequency Vibrations in the Hands.

Science.gov (United States)

Hwang, Inwook; Seo, Jeongil; Choi, Seungmoon

2017-01-01

The use of distinguishable complex vibrations that have multiple spectral components can improve the transfer of information by vibrotactile interfaces. We investigated the qualitative characteristics of dual-frequency vibrations as the simplest complex vibrations compared to single-frequency vibrations. Two psychophysical experiments were conducted to elucidate the perceptual characteristics of these vibrations by measuring the perceptual distances among single-frequency and dual-frequency vibrations. The perceptual distances of dual-frequency vibrations between their two frequency components along their relative intensity ratio were measured in Experiment I. The estimated perceptual spaces for three frequency conditions showed non-linear perceptual differences between the dual-frequency and single-frequency vibrations. A perceptual space was estimated from the measured perceptual distances among ten dual-frequency compositions and five single-frequency vibrations in Experiment II. The effect of the component frequency and the frequency ratio was revealed in the perceptual space. In a percept of dual-frequency vibration, the lower frequency component showed a dominant effect. Additionally, the perceptual difference among single-frequency and dual-frequency vibrations were increased with a low relative difference between two frequencies of a dual-frequency vibration. These results are expected to provide a fundamental understanding about the perception of complex vibrations to enrich the transfer of information using vibrotactile stimuli.

Some Notes on the Use of theWindowed Fourier Transform for Spectral Analysis of Discretely Sampled Data

Directory of Open Access Journals (Sweden)

Robert W. Johnson

2013-06-01

Full Text Available The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numerically the energy and reconstruction theorems; however, transform pairs based on a variable window or nonuniform frequency sampling in general do not. Instead of selecting the shape of the window as some function of the central frequency, we propose constructing a single window with unit energy from an arbitrary set of windows that is applied over the entire frequency axis. By virtue of using a fixed window with uniform frequency sampling, such a transform satisfies the energy and reconstruction theorems. The shape of the window can be tailored to meet the requirements of the investigator in terms of time/frequency resolution. The algorithm extends naturally to the case of nonuniform signal sampling without modification beyond identification of the Nyquist interval.

Automatic picking of the first arrival event using the unwrapped-phase of the Fourier transformed wavefield

KAUST Repository

Choi, Yun Seok; Alkhalifah, Tariq Ali; Saragiotis, Christos

2011-01-01

an approach based on unwrapping the phase. We unwrap the phase by taking the derivative of the Fourier-transformed wavefield with respect to the angular frequency and isolate its amplitude component. To do so, we first apply a damping function to the seismic

The Fourier transform of tubular densities

KAUST Repository

Prior, C B; Goriely, A

2012-01-01

molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one

On the Laplace transform of the Weinberg type sum rules

International Nuclear Information System (INIS)

Narison, S.

1981-09-01

We consider the Laplace transform of various sum rules of the Weinberg type including the leading non-perturbative effects. We show from the third type Weinberg sum rules that 7.5 to 8.9 1 coupling to the W boson, while the second sum rule gives an upper bound on the A 1 mass (Msub(A 1 ) < or approx. 1.25 GeV). (author)

Detection of 320 Gb/s Nyquist OTDM by polarization-insensitive time-domain optical Fourier transformation

DEFF Research Database (Denmark)

Hu, Hao; Kong, Deming; Palushani, Evarist

2013-01-01

320 Gb/s Nyquist-OTDM is generated by rectangular filtering with a bandwidth of 320 GHz and received by polarization-insensitive time-domain optical Fourier transformation (TD-OFT) followed by passive filtering. After the time-to-frequency mapping in the TD-OFT, the Nyquist-OTDM is converted into...

An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations

International Nuclear Information System (INIS)

Golubov, B I

1998-01-01

Let f-hat c be the Fourier cosine transform of f. Then, as proved for functions of class L p (R + ) in Titchmarsh's book 'Introduction to the theory of Fourier integrals' (1937), the Hardy operator and the Hardy-Littlewood operator can be defined. In the present paper similar equalities are proved for functions of class L p (R + ), 1< p≤2, and the Walsh-Fourier transformation

Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform

Directory of Open Access Journals (Sweden)

Zohreh Moghareh Abed

2010-01-01

Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.

Electro-optic imaging Fourier transform spectrometer

Science.gov (United States)

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.

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

International Nuclear Information System (INIS)

Freedman, Michael H.; Wang, Zhenghan

2007-01-01

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks

Balancing Vibrations at Harmonic Frequencies by Injecting Harmonic Balancing Signals into the Armature of a Linear Motor/Alternator Coupled to a Stirling Machine

Science.gov (United States)

Holliday, Ezekiel S. (Inventor)

2014-01-01

Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.

The deconvolution of Doppler-broadened positron annihilation measurements using fast Fourier transforms and power spectral analysis

International Nuclear Information System (INIS)

Schaffer, J.P.; Shaughnessy, E.J.; Jones, P.L.

1984-01-01

A deconvolution procedure which corrects Doppler-broadened positron annihilation spectra for instrument resolution is described. The method employs fast Fourier transforms, is model independent, and does not require iteration. The mathematical difficulties associated with the incorrectly posed first order Fredholm integral equation are overcome by using power spectral analysis to select a limited number of low frequency Fourier coefficients. The FFT/power spectrum method is then demonstrated for an irradiated high purity single crystal sapphire sample. (orig.)

Broadband electromagnetic power harvester from vibrations via frequency conversion by impact oscillations

International Nuclear Information System (INIS)

Yuksek, N. S.; Almasri, M.; Feng, Z. C.

2014-01-01

In this paper, we propose an electromagnetic power harvester that uses a transformative multi-impact approach to achieve a wide bandwidth response from low frequency vibration sources through frequency-up conversion. The device consists of a pick-up coil, fixed at the free edge of a cantilever beam with high resonant frequency, and two cantilever beams with low excitation frequencies, each with an impact mass attached at its free edge. One of the two cantilevers is designed to resonate at 25 Hz, while the other resonates at 50 Hz within the range of ambient vibration frequency. When the device is subjected to a low frequency vibration, the two low-frequency cantilevers responded by vibrating at low frequencies, and thus their thick metallic masses made impacts with the high resonance frequency cantilever repeatedly at two locations. This has caused it along with the pick-up coil to oscillate, relative to the permanent magnet, with decaying amplitude at its resonance frequency, and results in a wide bandwidth response from 10 to 63 Hz at 2 g. A wide bandwidth response between 10–51 Hz and 10–58 Hz at acceleration values of 0.5 g and 2 g, respectively, were achieved by adjusting the impact cantilever frequencies closer to each other (25 Hz and 45 Hz). A maximum output power of 85 μW was achieved at 5 g at 30 Hz across a load resistor, 2.68 Ω.

Difference frequency generation spectroscopy as a vibrational optical activity measurement tool.

Science.gov (United States)

Cheon, Sangheon; Cho, Minhaeng

2009-03-19

Vibrational optical activity (VOA) of chiral molecules in condensed phases can be studied by using vibrational circular dichroism and Raman optical activity measurement techniques. Recently, IR-vis sum frequency generation has shown to be an alternative VOA measurement method. Such a three-wave-mixing method employing a polarization modulation technique can be a potentially useful VOA measurement tool. Here, a theoretical description of difference frequency generation (DFG) employing circularly polarized visible radiations is presented. Frequency scanning to obtain a VOA-DFG spectrum is achieved by controlling the difference between the two electronically nonresonant incident radiation frequencies. If the two incident beams are linearly polarized and their polarization directions are perpendicular to each other, one can selectively measure the all-electric-dipole-allowed chiral component of the DFG susceptibility. In addition, by using circularly polarized beams and taking the DFG difference intensity signal, which is defined as the difference between left and right circularly polarized DFG signals, additional chiral susceptibility components originating from the electric quadrupole transition can be measured. The DFG as a novel VOA measurement technique for solution samples containing chiral molecules will therefore be a useful coherent spectroscopic tool for determining absolute configuration of chiral molecules in condensed phases.

Removal of Stationary Sinusoidal Noise from Random Vibration Signals.

Energy Technology Data Exchange (ETDEWEB)

Johnson, Brian; Cap, Jerome S.

2018-02-01

In random vibration environments, sinusoidal line noise may appear in the vibration signal and can affect analysis of the resulting data. We studied two methods which remove stationary sine tones from random noise: a matrix inversion algorithm and a chirp-z transform algorithm. In addition, we developed new methods to determine the frequency of the tonal noise. The results show that both of the removal methods can eliminate sine tones in prefabricated random vibration data when the sine-to-random ratio is at least 0.25. For smaller ratios down to 0.02 only the matrix inversion technique can remove the tones, but the metrics to evaluate its effectiveness also degrade. We also found that using fast Fourier transforms best identified the tonal noise, and determined that band-pass-filtering the signals prior to the process improved sine removal. When applied to actual vibration test data, the methods were not as effective at removing harmonic tones, which we believe to be a result of mixed-phase sinusoidal noise.

The RC Circuit: An Approach with Fourier Transforms In this article ...

Indian Academy of Sciences (India)

CLASSROOM. Mitrajyoti Ghosh. 83, Mitrapara 2nd Lane, Harinavi,. Kolkata 700148, West Bengal,. India. Email: mijospeakingnow@gmail.com. The RC Circuit: An Approach with Fourier Transforms. In this article we shall mathematically analyse the Resistor-. Capacitor (RC) circuit with the help of Fourier transforms. (FT).

Cooperative Effects of Zwitterionic-Ionic Surfactant Mixtures on the Interfacial Water Structure Revealed by Sum Frequency Generation Vibrational Spectroscopy.

Science.gov (United States)

Pan, Xuecong; Yang, Fangyuan; Chen, Shunli; Zhu, Xuefeng; Wang, Chuanyi

2018-05-08

Cooperative effects of a series of equimolar binary zwitterionic-ionic surfactant mixtures on the interfacial water structure at the air-water interfaces have been studied by sum frequency generation vibrational spectroscopy (SFG-VS). For zwitterionic surfactant palmityl sulfobetaine (SNC 16 ), anionic surfactant sodium hexadecyl sulfate (SHS), and cationic surfactant cetyltrimethylammonium bromide (CTAB) with the same length of alkyl chain, significantly enhanced ordering of interfacial water molecules was observed for the zwitterionic-anionic surfactant mixtures SNC 16 -SHS, indicating that SNC 16 interacts more strongly with SHS than with CTAB because of the strong headgroup-headgroup electrostatic attraction for SNC 16 -SHS. Meanwhile, the SFG amplitude ratio of methyl and methylene symmetric stretching modes was used to verify the stronger interaction between SNC 16 and SHS. The conformational order indicator increased from 0.64 for SNC 16 to 7.17 for SNC 16 -SHS but only 0.94 for SNC 16 -CTAB. In addition, another anionic surfactant sodium dodecyl sulfate (SDS) was introduced to study the influence of chain-chain interaction. Decreased SFG amplitude of interfacial water molecules for SNC 16 -SDS was observed. Therefore, both the headgroup-headgroup electrostatic interaction and chain-chain van der Waals attractive interaction of the surfactants play an important role in enhancing the ordering of interfacial water molecules. The results provided experimental and theoretical bases for practical applications of the surfactants.

Limitations on continuous variable quantum algorithms with Fourier transforms

International Nuclear Information System (INIS)

Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C

2009-01-01

We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.

HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS

Directory of Open Access Journals (Sweden)

Endah Purwanti

2014-05-01

Full Text Available Health problems with cardiovascular system disorder are still ranked high globally. One way to detect abnormalities in the cardiovascular system especially in the heart is through the electrocardiogram (ECG reading. However, reading ECG recording needs experience and expertise, software-based neural networks has designed to help identify any abnormalities ofthe heart through electrocardiogram digital image. This image is processed using image processing methods to obtain ordinate chart which representing the heart’s electrical potential. Feature extraction using Fourier transforms which are divided into several numbers of coefficients. As the software input, Fourier transforms coefficient have been normalized. Output of this software is divided into three classes, namely heart with atrial fibrillation, coronary heart disease and normal. Maximum accuracy rate ofthis software is 95.45%, with the distribution of the Fourier transform coefficients 1/8 and number of nodes 5, while minimum accuracy rate of this software at least 68.18% by distribution of the Fourier transform coefficients 1/32 and the number of nodes 32. Overall result accuracy rate of this software has an average of86.05% and standard deviation of7.82.

Fourier transform spectra of quantum dots

Science.gov (United States)

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.

Fourier-transform optical microsystems

Science.gov (United States)

Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.

1999-01-01

The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.

Micro-scale piezoelectric vibration energy harvesting: From fixed-frequency to adaptable-frequency devices

Science.gov (United States)

Miller, Lindsay Margaret

Wireless sensor networks (WSNs) have the potential to transform engineering infrastructure, manufacturing, and building controls by allowing condition monitoring, asset tracking, demand response, and other intelligent feedback systems. A wireless sensor node consists of a power supply, sensor(s), power conditioning circuitry, radio transmitter and/or receiver, and a micro controller. Such sensor nodes are used for collecting and communicating data regarding the state of a machine, system, or process. The increasing demand for better ways to power wireless devices and increase operation time on a single battery charge drives an interest in energy harvesting research. Today, wireless sensor nodes are typically powered by a standard single-charge battery, which becomes depleted within a relatively short timeframe depending on the application. This introduces tremendous labor costs associated with battery replacement, especially when there are thousands of nodes in a network, the nodes are remotely located, or widely-distributed. Piezoelectric vibration energy harvesting presents a potential solution to the problems associated with too-short battery life and high maintenance requirements, especially in industrial environments where vibrations are ubiquitous. Energy harvester designs typically use the harvester to trickle charge a rechargeable energy storage device rather than directly powering the electronics with the harvested energy. This allows a buffer between the energy harvester supply and the load where energy can be stored in a "tank". Therefore, the harvester does not need to produce the full required power at every instant to successfully power the node. In general, there are tens of microwatts of power available to be harvested from ambient vibrations using micro scale devices and tens of milliwatts available from ambient vibrations using meso scale devices. Given that the power requirements of wireless sensor nodes range from several microwatts to about one

Calibration and fluctuation of the secular frequency peak amplitude versus initial condition distribution of the ion cloud confined into a three-dimensional quadrupole ion trap using a fourier transform operating mode and a steady ion flow injection mode

International Nuclear Information System (INIS)

Janulyte, A.; Andre, J.; Carette, M.; Mercury, M.; Reynard, C; Zerega, Y.

2009-01-01

A specific Fourier transform operating mode is applied to a 3-dimensional quadrupolar ion trap for mass analysis (Fourier Transform Quadrupolar Ion Trap (FTQIT) Operating Mode or Mass Spectrometer). With this operating mode, an image signal, which is representative of the collective motion of simultaneously confined ions, is made up from a set of recorded time-of-flight histograms. In an ion trap, the secular frequency of ion motion depends on m/Z ratio of the ion. By Fourier transformation of the image signal, one observes the frequency peak of each confined ionic species. When only one ionic species is confined, the peak amplitude is proportional to the maximal amplitude of the image signal. The maximal amplitude of the image signal is expressed according to the operating parameters, the initial conditions of the ions and the number of ions. Simulation tools lead to fluctuation calculation of the maximal amplitude of the image signal. Two origins are explored: (1) the fluctuation of the numbers of ions according to the steady ion flow injection mode (SIFIM) used with this operating mode and (2) the distribution fluctuation of the initial positions and velocities. Initial confinement conditions, obtained with SIFIM injection mode, lead to optimal detection with small fluctuations of the peak amplitude for Fourier transform operating mode applied to an ion trap. (authors)

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

Science.gov (United States)

Yan, Xin-Zhong

2011-07-01

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

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

Science.gov (United States)

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

2018-02-13

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

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

Science.gov (United States)

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.

Suppressing carrier removal error in the Fourier transform method for interferogram analysis

International Nuclear Information System (INIS)

Fan, Qi; Yang, Hongru; Li, Gaoping; Zhao, Jianlin

2010-01-01

A new carrier removal method for interferogram analysis using the Fourier transform is presented. The proposed method can be used to suppress the carrier removal error as well as the spectral leakage error. First, the carrier frequencies are estimated with the spectral centroid of the up sidelobe of the apodized interferogram, and then the up sidelobe can be shifted to the origin in the frequency domain by multiplying the original interferogram by a constructed plane reference wave. The influence of the carrier frequencies without an integer multiple of the frequency interval and the window function for apodization of the interferogram can be avoided in our work. The simulation and experimental results show that this method is effective for phase measurement with a high accuracy from a single interferogram

Semiclassical quantization of vibrational systems using fast-Fourier transform methods: Application to HDO stretches

International Nuclear Information System (INIS)

Pickett, T.J.; Shirts, R.B.

1991-01-01

Based on work by Martens and Ezra and partially developed independently by Eaker, we apply an improved method of approximating the quantum energy levels of a system of coupled oscillators using the fast-Fourier transform of classical coordinates and momenta to find quantizing trajectories. Application is made to a two-dimensional system modeling the stretching motions of the HDO molecule. The results are in excellent agreement with quantum calculations. This method is useful because: (1) it gives results which are independent of any separability of the Hamiltonian, (2) it is not limited in the number of degrees of freedom that can be handled, and (3) no zero-order approximation to the system is necessary. Results are equally valid inside and outside of resonance zones

Effect of surface structure on catalytic reactions: A sum frequency generation surface vibrational spectroscopy study

International Nuclear Information System (INIS)

McCrea, Keith R.

2001-01-01

In the results discussed above, it is clear that Sum Frequency Generation (SFG) is a unique tool that allows the detection of vibrational spectra of adsorbed molecules present on single crystal surfaces under catalytic reaction conditions. Not only is it possible to detect active surface intermediates, it is also possible to detect spectator species which are not responsible for the measured turnover rates. By correlating high-pressure SFG spectra under reaction conditions and gas chromatography (GC) kinetic data, it is possible to determine which species are important under reaction intermediates. Because of the flexibility of this technique for studying surface intermediates, it is possible to determine how the structures of single crystal surfaces affect the observed rates of catalytic reactions. As an example of a structure insensitive reaction, ethylene hydrogenation was explored on both Pt(111) and Pt(100). The rates were determined to be essentially the same. It was observed that both ethylidyne and di-(sigma) bonded ethylene were present on the surface under reaction conditions on both crystals, although in different concentrations. This result shows that these two species are not responsible for the measured turnover rate, as it would be expected that one of the two crystals would be more active than the other, since the concentration of the surface intermediate would be different on the two crystals. The most likely active intermediates are weakly adsorbed molecules such as(pi)-bonded ethylene and ethyl. These species are not easily detected because their concentration lies at the detection limit of SFG. The SFG spectra and GC data essentially show that ethylene hydrogenation is structure insensitive for Pt(111) and Pt(100). SFG has proven to be a unique and excellent technique for studying adsorbed species on single crystal surfaces under high-pressure catalytic reactions. Coupled with kinetic data obtained from gas chromatography measurements, it can

Polarization entanglement of sum-frequency photons: A tool to probe the Markovian limit

Science.gov (United States)

Volkov, Victor; Chelli, Riccardo

2015-06-01

The article addresses the possibility of entanglement-specific infrared-visible sum-frequency generation spectroscopy. In the case of an anisotropic interface, it is possible to employ SSS and PSS polarizations to detect responses not only specific to χY Y Y and χX Y Y nonlinearities, but also to higher-order χ(Y Y Y )(X Y Y ) and χ(X Y Y )(Y Y Y ) nonlinearities. Using quantum mechanical studies of the rhenium complex [Re (OH) 3(CO) 3] as a molecular model, we demonstrate that if such complexes would form an anisotropic orientational distribution at a surface, under the considered geometry and the polarization settings, we may prepare quantum correlated C =O vibrational states to emit polarization-entangled photons. Accordingly, we explore the possibility of a polarization-measurement protocol to extract spectral signatures of the entangled states. The response would be informative on intramolecular interactions. As a result, we discuss the possible practical implications in probing dynamics at interfaces, and different opportunities in the preparation of entangled vibrational states of quantified fidelity.

An Image Matching Method Based on Fourier and LOG-Polar Transform

Directory of Open Access Journals (Sweden)

Zhijia Zhang

2014-04-01

Full Text Available This Traditional template matching methods are not appropriate for the situation of large angle rotation between two images in the online detection for industrial production. Aiming at this problem, Fourier transform algorithm was introduced to correct image rotation angle based on its rotatary invariance in time-frequency domain, orienting image under test in the same direction with reference image, and then match these images using matching algorithm based on log-polar transform. Compared with the current matching algorithms, experimental results show that the proposed algorithm can not only match two images with rotation of arbitrary angle, but also possess a high matching accuracy and applicability. In addition, the validity and reliability of algorithm was verified by simulated matching experiment targeting circular images.

Discrete Fourier Transform Analysis in a Complex Vector Space

Science.gov (United States)

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.

Complex nonlinear Fourier transform and its inverse

International Nuclear Information System (INIS)

Saksida, Pavle

2015-01-01

We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)

Two-dimensional vibrational-electronic spectroscopy

Science.gov (United States)

Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira

2015-10-01

Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([FeIII(CN)6]3- dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5FeIICNRuIII(NH3)5]- dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

Two-dimensional vibrational-electronic spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira, E-mail: mkhalil@uw.edu [Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195 (United States)

2015-10-21

Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (ν{sub CN}) and either a ligand-to-metal charge transfer transition ([Fe{sup III}(CN){sub 6}]{sup 3−} dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN){sub 5}Fe{sup II}CNRu{sup III}(NH{sub 3}){sub 5}]{sup −} dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific ν{sub CN} modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a

Monitoring of vibrating machinery using artificial neural networks

International Nuclear Information System (INIS)

Alguindigue, I.E.; Loskiewicz-Buczak, A.

1991-01-01

The primary source of vibration in complex engineering systems is rotating machinery. Vibration signatures collected from these components render valuable information about the operational state of the system and may be used to perform diagnostics. For example, the low frequency domain contains information about unbalance, misalignment, instability in journal bearing and mechanical looseness; analysis of the medium frequency range can render information about faults in meshing gear teeth; while the high frequency domain will contain information about incipient faults in rolling-element bearings. Trend analysis may be performed by comparing the vibration spectrum for each machine with a reference spectrum and evaluating the vibration magnitude changes at different frequencies. This form of analysis for diagnostics is often performed by maintenance personnel monitoring and recording transducer signals and analyzing the signals to identify the operating condition of the machine. With the advent of portable fast Fourier transform (FFT) analyzers and ''laptop'' computers, it is possible to collect and analyze vibration data an site and detect incipient failures several weeks or months before repair is necessary. It is often possible to estimate the remaining life of certain systems once a fault has been detected. RMS velocity, acceleration, displacements, peak value, and crest factor readings can be collected from vibration sensors. To exploit all the information embedded in these signals, a robust and advanced analysis technique is required. Our goal is to design a diagnostic system using neural network technology, a system such as this would automate the interpretation of vibration data coming from plant-wide machinery and permit efficient on-line monitoring of these components

Fourier transforms in spectroscopy

CERN Document Server

Kauppinen, Jyrki

2000-01-01

This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi

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

Science.gov (United States)

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.

Sum Frequency Generation Vibrational Spectroscopy of 1,3-Butadiene Hydrogenation on 4 nm Pt@SiO 2 , Pd@SiO 2 , and Rh@SiO 2 Core–Shell Catalysts

KAUST Repository

Krier, James M.

2015-01-14

© 2014 American Chemical Society. 1,3-Butadiene (1,3-BD) hydrogenation was performed on 4 nm Pt, Pd, and Rh nanoparticles (NPs) encapsulated in SiO2 shells at 20, 60, and 100 °C. The core-shells were grown around polyvinylpyrrolidone (PVP) coated NPs (Stöber encapsulation) prepared by colloidal synthesis. Sum frequency generation (SFG) vibrational spectroscopy was performed to correlate surface intermediates observed in situ with reaction selectivity. It is shown that calcination is effective in removing PVP, and the SFG signal can be generated from the metal surface. Using SFG, it is possible to compare the surface vibrational spectrum of Pt@SiO2 (1,3-BD is hydrogenated through multiple paths and produces butane, 1-butene, and cis/trans-2-butene) to Pd@SiO2 (1,3-BD favors one path and produces 1-butene and cis/trans-2-butene). In contrast to Pt@SiO2 and Pd@SiO2, SFG and kinetic experiments of Rh@SiO2 show a permanent accumulation of organic material.

Decay of the Fourier transform analytic and geometric aspects

CERN Document Server

Iosevich, Alex

2014-01-01

The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware

DEFF Research Database (Denmark)

Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard

2008-01-01

We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe the performa......We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe...

Functional differential equations for the q-Fourier transform of q-Gaussians

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Functional differential equations for the q-Fourier transform of q-Gaussians

Energy Technology Data Exchange (ETDEWEB)

Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

2010-02-05

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Experiences with non-intrusive monitoring of distribution transformers based on the on-line frequency response

OpenAIRE

Eduardo Gomez Luna

2015-01-01

The following article presents the results obtained in experiences that use the Impulse Frequency Response Analysis (IFRA) method with a transformer in service. The IFRA method has been implemented in order to transform the transient signals to the frequency domain using Discrete Fourier Transform (DFT). However, it can be considered that the DFT is not the most suitable tool for this type of analysis, since, by definition, this tool is useful for processing stationary signals. Taking that in...

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

Science.gov (United States)

Li, Min; Zhang, Yanchi; Xie, Da

2018-04-01

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

Direct comparison of phase-sensitive vibrational sum frequency generation with maximum entropy method: case study of water.

Science.gov (United States)

de Beer, Alex G F; Samson, Jean-Sebastièn; Hua, Wei; Huang, Zishuai; Chen, Xiangke; Allen, Heather C; Roke, Sylvie

2011-12-14

We present a direct comparison of phase sensitive sum-frequency generation experiments with phase reconstruction obtained by the maximum entropy method. We show that both methods lead to the same complex spectrum. Furthermore, we discuss the strengths and weaknesses of each of these methods, analyzing possible sources of experimental and analytical errors. A simulation program for maximum entropy phase reconstruction is available at: http://lbp.epfl.ch/. © 2011 American Institute of Physics

The determination of frequency response function of the RSG Gas by laplace transform analysis

International Nuclear Information System (INIS)

Tukiran, S.; Surian, P.; Jujuratisbela, U.

1997-01-01

The response function of the RSG-GAS reactor system to the reactivity perturbations is necessary to be analyzed due to the interrelation with reliability and safety of reactor operation. the response depends on the power frequency response function H(s), while H(s) depends on the zero power frequency response function Z(s) and dynamic power coefficient of reactivity Kp(s) determination of the frequency response function of the RSG-GAS reactor was done by Fourier transform analysis method. Z(s) was obtained by fourier transform of P(t) and Cj(t) became P(S) and Cj(s) in point kinetic equations. Second order of simpson rule was used for completion of its numerical integration. then. LYMPR (Laplace transform for multipurpose reactor) code was made with fortran 77 computer language in vax 8550 system. the LTMPR code is able to determine the frequency response function and period-reactivity relation of RSG-GAS reactor by rod drop method. Profile of power as rod drop, zero power (without reactivity feedback) was used for determination frequency response of RSG-GAS reactor. The results of calculations are in a good agreement with experiment result, so the LTMPR code can be used for analysis response frequency of the RSG-GAS reactor

Fourier transform methods for calculating action variables and semiclassical eigenvalues for coupled oscillator systems

International Nuclear Information System (INIS)

Eaker, C.W.; Schatz, G.C.; De Leon, N.; Heller, E.J.

1984-01-01

Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method

Raman spectroscopy of gases with a Fourier transform spectrometer: the spectrum of D2

International Nuclear Information System (INIS)

Jennings, D.E.; Weber, A.; Brault, J.W.

1986-01-01

A high-resolution Fourier transform spectrometer (FTS) has been used to record spontaneous incoherent laser Raman spectra of gases. The resolution, sensitivity, calibration accuracy, and spectral coverage achieved in these spectra demonstrate the viability of the FTS for Raman spectroscopy. Measurements from a spectrum of D 2 containing both v = 0-0 and v = 1-0 transitions were fitted to the Dunham expansion of the vibration--rotation energy levels. The coefficients are (in cm -1 ) Y 10 = 2993.6060(67), Y 01 = 30.4401 (89), Y 11 = -1.0538(17), Y 02 = -0.011590(41), Y 12 = 2.02(80) x 10 -4 , and Y 03 = 5.83(11) x 10 -6 . Errors in parentheses are one standard deviation

Band Width of Acoustic Resonance Frequency Relatively Natural Frequency of Fuel Rod Vibration

Energy Technology Data Exchange (ETDEWEB)

Proskuryakov, Konstantin Nicolaevich; Moukhine, V.S.; Novikov, K.S.; Galivets, E.Yu. [MPEI - TU, 14, Krasnokazarmennaya str., Moscow, 111250 (Russian Federation)

2009-06-15

In flow induced vibrations the fluid flow is the energy source that causes vibration. Acoustic resonance in piping may lead to severe problems due to over-stressing of components or significant losses of efficiency. Steady oscillatory flow in NPP primary loop can be induced by the pulsating flow introduced by reactor circulating pump or may be set up by self-excitation. Dynamic forces generated by the turbulent flow of coolant in reactor cores cause fuel rods (FR) and fuel assembly (FA) to vibrate. Flow-induced FR and FA vibrations can generally be broken into three groups: large amplitude 'resonance type' vibrations, which can cause immediate rod failure or severe damage to the rod and its support structure, middle amplitude 'within bandwidth of resonance frequency type' vibrations responsible for more gradual wear and fatigue at the contact surface between the fuel cladding and rod support and small amplitude vibrations, 'out of bandwidth of resonance frequency type' responsible for permissible wear and fatigue at the contact surface between the fuel cladding and rod support. Ultimately, these vibration types can result in a cladding breach, and therefore must be accounted for in the thermal hydraulic design of FR and FA and reactor internals. In paper the technique of definition of quality factor (Q) of acoustic contour of the coolant is presented. The value of Q defines a range of frequencies of acoustic fluctuations of the coolant within which the resonance of oscillations of the structure and the coolant is realized. Method of evaluation of so called band width (BW) of acoustic resonance frequency is worked out and presented in the paper. BW characterises the range of the frequency of coolant pressure oscillations within which the frequency of coolant pressure oscillations matches the fuel assembly's natural frequency of vibration (its resonance frequency). Paper show the way of detuning acoustic resonance from natural

Second harmonic generation and sum frequency generation

International Nuclear Information System (INIS)

Pellin, M.J.; Biwer, B.M.; Schauer, M.W.; Frye, J.M.; Gruen, D.M.

1990-01-01

Second harmonic generation and sum frequency generation are increasingly being used as in situ surface probes. These techniques are coherent and inherently surface sensitive by the nature of the mediums response to intense laser light. Here we will review these two techniques using aqueous corrosion as an example problem. Aqueous corrosion of technologically important materials such as Fe, Ni and Cr proceeds from a reduced metal surface with layer by layer growth of oxide films mitigated by compositional changes in the chemical makeup of the growing film. Passivation of the metal surface is achieved after growth of only a few tens of atomic layers of metal oxide. Surface Second Harmonic Generation and a related nonlinear laser technique, Sum Frequency Generation have demonstrated an ability to probe the surface composition of growing films even in the presence of aqueous solutions. 96 refs., 4 figs

Fourier Transform and Photoacoustic Absorption Spectra of Ethylene within 6035 6210 cm-1: Comparative Measurements

International Nuclear Information System (INIS)

Kapitanov, V.A.; Solodov, A.M.; Petrova, T.M.; Ponomarev, Y.N.

2010-01-01

Measurements of ethylene absorption spectra with Fourier Transform (FT) and Photoacoustic (PA) spectrometers within 6035-6210 cm -1 are described. The methodology used for building the frequency scale for both spectrometers is presented. The methane absorption spectrum, included into the HITRAN database, was used in both cases to calibrate the frequency scale. Ethylene absorption spectra were obtained with the two recording methods; a coincidence of the measured line center positions was obtained with an accuracy of 0.0005 cm -1

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

An introduction to Laplace transforms and Fourier series

CERN Document Server

Dyke, Phil

2014-01-01

Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...

The Fourier transform of tubular densities

International Nuclear Information System (INIS)

Prior, C B; Goriely, A

2012-01-01

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)

The Fourier transform of tubular densities

KAUST Repository

Prior, C B

2012-05-18

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.

Phase transition behaviors of the supported DPPC bilayer investigated by sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM).

Science.gov (United States)

Wu, Heng-Liang; Tong, Yujin; Peng, Qiling; Li, Na; Ye, Shen

2016-01-21

The phase transition behaviors of a supported bilayer of dipalmitoylphosphatidyl-choline (DPPC) have been systematically evaluated by in situ sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM). By using an asymmetric bilayer composed of per-deuterated and per-protonated monolayers, i.e., DPPC-d75/DPPC and a symmetric bilayer of DPPC/DPPC, we were able to probe the molecular structural changes during the phase transition process of the lipid bilayer by SFG spectroscopy. It was found that the DPPC bilayer is sequentially melted from the top (adjacent to the solution) to bottom leaflet (adjacent to the substrate) over a wide temperature range. The conformational ordering of the supported bilayer does not decrease (even slightly increases) during the phase transition process. The conformational defects in the bilayer can be removed after the complete melting process. The phase transition enthalpy for the bottom leaflet was found to be approximately three times greater than that for the top leaflet, indicating a strong interaction of the lipids with the substrate. The present SFG and AFM observations revealed similar temperature dependent profiles. Based on these results, the temperature-induced structural changes in the supported lipid bilayer during its phase transition process are discussed in comparison with previous studies.

Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

Science.gov (United States)

Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

2017-12-01

This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

Fourier transform Raman spectroscopy of synthetic and biological calcium phosphates.

Science.gov (United States)

Sauer, G R; Zunic, W B; Durig, J R; Wuthier, R E

1994-05-01

Fourier-transform (FT) Raman spectroscopy was used to characterize the organic and mineral components of biological and synthetic calcium phosphate minerals. Raman spectroscopy provides information on biological minerals that is complimentary to more widely used infrared methodologies as some infrared-inactive vibrational modes are Raman-active. The application of FT-Raman technology has, for the first time, enabled the problems of high sample fluorescence and low signal-to-noise that are inherent in calcified tissues to be overcome. Raman spectra of calcium phosphates are dominated by a very strong band near 960 cm-1 that arises from the symmetric stretching mode (v1) of the phosphate group. Other Raman-active phosphate vibrational bands are seen at approximately 1075 (v3), 590 (v4), and 435 cm-1 (v2). Minerals containing acidic phosphate groups show additional vibrational modes. The different calcium phosphate mineral phases can be distinguished from one another by the relative positions and shapes of these bands in the Raman spectra. FT-Raman spectra of nascent, nonmineralized matrix vesicles (MV) show a distinct absence of the phosphate v1 band even though these structures are rich in calcium and phosphate. Similar results were seen with milk casein and synthetic Ca-phosphatidyl-serine-PO4 complexes. Hence, the phosphate and/or acidic phosphate ions in these noncrystalline biological calcium phosphates is in a molecular environment that differs from that in synthetic amorphous calcium phosphate. In MV, the first distinct mineral phase to form contained acidic phosphate bands similar to those seen in octacalcium phosphate. The mineral phase present in fully mineralized MV was much more apatitic, resembling that found in bones and teeth.(ABSTRACT TRUNCATED AT 250 WORDS)

The use of Fourier eigen transform to the boundary element method for transient elastodynamic problems

International Nuclear Information System (INIS)

Ji, X.; Chen, Y.M.

1989-01-01

The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes

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

Science.gov (United States)

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.

Reduction and coding of synthetic aperture radar data with Fourier transforms

Science.gov (United States)

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.

Imaging properties of the mesooptical Fourier transform microscope for nuclear research emulsion

International Nuclear Information System (INIS)

Bencze, Gy.L.; Soroko, L.M.

1987-01-01

The optical signal transformation in the Mesooptical Fourier Transform Microscope (MFTM) for nuclear emulsion is treated in terms of Fourier Optics. A continuous conversion of the traditional optical microscope into the MFTM is followed. The images of dot-like and straight line objects given by the MFTM are discussed

On QCD sum rules of the Laplace transform type and light quark masses

International Nuclear Information System (INIS)

Narison, S.

1981-04-01

We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in quantum chromodynamics. Two specific examples corresponding to the S-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given

Application of Fourier transforms for microwave radiometric inversions

Science.gov (United States)

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 Spectroscopy of the A {sup 3}Π– X {sup 3}Σ{sup −} Transition of OH{sup +}

Energy Technology Data Exchange (ETDEWEB)

Hodges, James N.; Bernath, Peter F. [Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529 (United States)

2017-05-10

The OH{sup +} ion is of critical importance to the chemistry in the interstellar medium and is a prerequisite for the generation of more complex chemical species. Submillimeter and ultraviolet observations rely on high quality laboratory spectra. Recent measurements of the fundamental vibrational band and previously unanalyzed Fourier transform spectra of the near-ultraviolet A {sup 3}Π− X {sup 3}Σ{sup −} electronic spectrum, acquired at the National Solar Observatory at Kitt Peak in 1989, provide an excellent opportunity to perform a global fit of the available data. These new optical data are approximately four times more precise as compared to the previous values. The fit to the new data provides updated molecular constants, which are necessary to predict the OH{sup +} transition frequencies accurately to support future observations. These new constants are the first published using the modern effective Hamiltonian for a linear molecule. These new molecular constants allow for easy simulation of transition frequencies and spectra using the PGOPHER program. The new constants improve simulations of higher J -value infrared transitions, and represent an improvement of an order of magnitude for some constants pertaining to the optical transitions.

Realization of quantum Fourier transform over ZN

International Nuclear Information System (INIS)

Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao

2014-01-01

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)

Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

Science.gov (United States)

Scheibler, Robin; Hurley, Paul

2012-03-01

We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.

Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.

1998-01-01

Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays

A Novel Hybrid Error Criterion-Based Active Control Method for on-Line Milling Vibration Suppression with Piezoelectric Actuators and Sensors

Directory of Open Access Journals (Sweden)

Xingwu Zhang

2016-01-01

Full Text Available Milling vibration is one of the most serious factors affecting machining quality and precision. In this paper a novel hybrid error criterion-based frequency-domain LMS active control method is constructed and used for vibration suppression of milling processes by piezoelectric actuators and sensors, in which only one Fast Fourier Transform (FFT is used and no Inverse Fast Fourier Transform (IFFT is involved. The correction formulas are derived by a steepest descent procedure and the control parameters are analyzed and optimized. Then, a novel hybrid error criterion is constructed to improve the adaptability, reliability and anti-interference ability of the constructed control algorithm. Finally, based on piezoelectric actuators and acceleration sensors, a simulation of a spindle and a milling process experiment are presented to verify the proposed method. Besides, a protection program is added in the control flow to enhance the reliability of the control method in applications. The simulation and experiment results indicate that the proposed method is an effective and reliable way for on-line vibration suppression, and the machining quality can be obviously improved.

Reconstruction of on-axis lensless Fourier transform digital hologram with the screen division method

Science.gov (United States)

Jiang, Hongzhen; Liu, Xu; Liu, Yong; Li, Dong; Chen, Zhu; Zheng, Fanglan; Yu, Deqiang

2017-10-01

An effective approach for reconstructing on-axis lensless Fourier Transform digital hologram by using the screen division method is proposed. Firstly, the on-axis Fourier Transform digital hologram is divided into sub-holograms. Then the reconstruction result of every sub-hologram is obtained according to the position of corresponding sub-hologram in the hologram reconstruction plane with Fourier transform operation. Finally, the reconstruction image of on-axis Fourier Transform digital hologram can be acquired by the superposition of the reconstruction result of sub-holograms. Compared with the traditional reconstruction method with the phase shifting technology, in which multiple digital holograms are required to record for obtaining the reconstruction image, this method can obtain the reconstruction image with only one digital hologram and therefore greatly simplify the recording and reconstruction process of on-axis lensless Fourier Transform digital holography. The effectiveness of the proposed method is well proved with the experimental results and it will have potential application foreground in the holographic measurement and display field.

Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

Directory of Open Access Journals (Sweden)

Darian M. Onchiș

2011-09-01

Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

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

Science.gov (United States)

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.

Experimental vibration analysis for a 3D scaled model of a three-floor steel structure

Directory of Open Access Journals (Sweden)

Ernesto F. Castillo

Full Text Available In this paper we present an experimental study of a three dimensional physical model of a three-floor structure subjected to forced vibrations by imposing displacements in its support. The aim of this work is to analyze the behavior of the building when a dynamic vibration absorber (DVA is acting. An analytic simplified analysis and a numerical study are developed to obtain the natural frequencies of the structure. Experiments are carried out in a vibrating table. The frequency range to be experimentally analyzed is determined by the first natural frequency of the structure for which the DVA damping effects are verified. The equipment capabilities, i.e. the frequencies, amplitudes and admissible load, limit the analyses. Nevertheless, satisfactory results are obtained for the study of the first mode of vibration. The effect of different amplitudes of the imposed support motion is also analyzed. In addition, the damping effect of the DVA device is evaluated upon varying its mass and its location in the structure. The characteristic curves in the frequency domain are obtained computing the Fast Fourier Transformation (FFT of the acceleration history registered with piezoelectric accelerometers at different checkpoints for the cases analyzed.

Two dimensional vibrations of the guinea pig apex organ of Corti measured in vivo using phase sensitive Fourier domain optical coherence tomography

Science.gov (United States)

Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Fridberger, Anders; Ren, Tianying; Wang, Ruikang; Jacques, Steven L.; Nuttall, Alfred L.

2015-02-01

In this study, we measure the in vivo apical-turn vibrations of the guinea pig organ of Corti in both axial and radial directions using phase-sensitive Fourier domain optical coherence tomography. The apical turn in guinea pig cochlea has best frequencies around 100 - 500 Hz which are relevant for human speech. Prior measurements of vibrations in the guinea pig apex involved opening the otic capsule, which has been questioned on the basis of the resulting changes to cochlear hydrodynamics. Here this limitation is overcome by measuring the vibrations through bone without opening the otic capsule. Furthermore, we have significantly reduced the surgery needed to access the guinea pig apex in the axial direction by introducing a miniature mirror inside the bulla. The method and preliminary data are discussed in this article.

Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

Science.gov (United States)

Huang, Lin; Lenells, Jonatan

2018-03-01

Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.

Sum Frequency Generation Vibrational Spectroscopy Studies on ModelPeptide Adsorption at the Hydrophobic Solid-Water and HydrophilicSolid-Water Interfaces

Energy Technology Data Exchange (ETDEWEB)

York, Roger L. [Univ. of California, Berkeley, CA (United States)

2007-01-01

Sum frequency generation (SFG) vibrational spectroscopy has been used to study the interfacial structure of several polypeptides and amino acids adsorbed to hydrophobic and hydrophilic surfaces under a variety of experimental conditions. Peptide sequence, peptide chain length, peptide hydrophobicity, peptide side-chain type, surface hydrophobicity, and solution ionic strength all affect an adsorbed peptide's interfacial structure. Herein, it is demonstrated that with the choice of simple, model peptides and amino acids, surface specific SFG vibrational spectroscopy can be a powerful tool to elucidate the interfacial structure of these adsorbates. Herein, four experiments are described. In one, a series of isosequential amphiphilic peptides are synthesized and studied when adsorbed to both hydrophobic and hydrophilic surfaces. On hydrophobic surfaces of deuterated polystyrene, it was determined that the hydrophobic part of the peptide is ordered at the solid-liquid interface, while the hydrophilic part of the peptide appears to have a random orientation at this interface. On a hydrophilic surface of silica, it was determined that an ordered peptide was only observed if a peptide had stable secondary structure in solution. In another experiment, the interfacial structure of a model amphiphilic peptide was studied as a function of the ionic strength of the solution, a parameter that could change the peptide's secondary structure in solution. It was determined that on a hydrophobic surface, the peptide's interfacial structure was independent of its structure in solution. This was in contrast to the adsorbed structure on a hydrophilic surface, where the peptide's interfacial structure showed a strong dependence on its solution secondary structure. In a third experiment, the SFG spectra of lysine and proline amino acids on both hydrophobic and hydrophilic surfaces were obtained by using a different experimental geometry that increases the SFG signal

Development and testing of a fast Fourier transform high dynamic-range spectral diagnostics for millimeter wave characterization

International Nuclear Information System (INIS)

Thoen, D. J.; Bongers, W. A.; Westerhof, E.; Baar, M. R. de; Berg, M. A. van den; Beveren, V. van; Goede, A. P. H.; Graswinckel, M. F.; Schueller, F. C.; Oosterbeek, J. W.; Buerger, A.; Hennen, B. A.

2009-01-01

A fast Fourier transform (FFT) based wide range millimeter wave diagnostics for spectral characterization of scattered millimeter waves in plasmas has been successfully brought into operation. The scattered millimeter waves are heterodyne downconverted and directly digitized using a fast analog-digital converter and a compact peripheral component interconnect computer. Frequency spectra are obtained by FFT in the time domain of the intermediate frequency signal. The scattered millimeter waves are generated during high power electron cyclotron resonance heating experiments on the TEXTOR tokamak and demonstrate the performance of the diagnostics and, in particular, the usability of direct digitizing and Fourier transformation of millimeter wave signals. The diagnostics is able to acquire 4 GHz wide spectra of signals in the range of 136-140 GHz. The rate of spectra is tunable and has been tested between 200 000 spectra/s with a frequency resolution of 100 MHz and 120 spectra/s with a frequency resolution of 25 kHz. The respective dynamic ranges are 52 and 88 dB. Major benefits of the new diagnostics are a tunable time and frequency resolution due to postdetection, near-real time processing of the acquired data. This diagnostics has a wider application in astrophysics, earth observation, plasma physics, and molecular spectroscopy for the detection and analysis of millimeter wave radiation, providing high-resolution spectra at high temporal resolution and large dynamic range.

Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

International Nuclear Information System (INIS)

Nogueira, Pedro H F; Castro, Antonio S de

2016-01-01

The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)

Nanoscale chemical and mechanical characterization of thin films:sum frequency generation (SFG) vibrational spectroscopy at buriedinterfaces

Energy Technology Data Exchange (ETDEWEB)

Kweskin, Sasha Joseph [Univ. of California, Berkeley, CA (United States)

2006-01-01

Sum frequency generation (SFG) surface vibrational spectroscopy was used to characterize interfaces pertinent to current surface engineering applications, such as thin film polymers and novel catalysts. An array of advanced surface science techniques like scanning probe microscopy (SPM), x-ray photoelectron spectroscopy (XPS), gas chromatography (GC) and electron microscopy were used to obtain experimental measurements complementary to SFG data elucidating polymer and catalyst surface composition, surface structure, and surface mechanical behavior. Experiments reported in this dissertation concentrate on three fundamental questions: (1) How does the interfacial molecular structure differ from that of the bulk in real world applications? (2) How do differences in chemical environment affect interface composition or conformation? (3) How do these changes correlate to properties such as mechanical or catalytic performance? The density, surface energy and bonding at a solid interface dramatically alter the polymer configuration, physics and mechanical properties such as surface glass transition, adhesion and hardness. The enhanced sensitivity of SFG at the buried interface is applied to three systems: a series of acrylates under compression, the compositions and segregation behavior of binary polymer polyolefin blends, and the changes in surface structure of a hydrogel as a function of hydration. In addition, a catalytically active thin film of polymer coated nanoparticles is investigated to evaluate the efficacy of SFG to provide in situ information for catalytic reactions involving small mass adsorption and/or product development. Through the use of SFG, in situ total internal reflection (TIR) was used to increase the sensitivity of SFG and provide the necessary specificity to investigate interfaces of thin polymer films and nanostructures previously considered unfeasible. The dynamic nature of thin film surfaces is examined and it is found that the non

Surface and buried interfacial structures of epoxy resins used as underfills studied by sum frequency generation vibrational spectroscopy.

Science.gov (United States)

Vázquez, Anne V; Holden, Brad; Kristalyn, Cornelius; Fuller, Mike; Wilkerson, Brett; Chen, Zhan

2011-05-01

Flip chip technology has greatly improved the performance of semiconductor devices, but relies heavily on the performance of epoxy underfill adhesives. Because epoxy underfills are cured in situ in flip chip semiconductor devices, understanding their surface and interfacial structures is critical for understanding their adhesion to various substrates. Here, sum frequency generation (SFG) vibrational spectroscopy was used to study surface and buried interfacial structures of two model epoxy resins used as underfills in flip chip devices, bisphenol A digylcidyl ether (BADGE) and 1,4-butanediol diglycidyl ether (BDDGE). The surface structures of these epoxies were compared before and after cure, and the orientations of their surface functional groups were deduced to understand how surface structural changes during cure may affect adhesion properties. Further, the effect of moisture exposure, a known cause of adhesion failure, on surface structures was studied. It was found that the BADGE surface significantly restructured upon moisture exposure while the BDDGE surface did not, showing that BADGE adhesives may be more prone to moisture-induced delamination. Lastly, although surface structure can give some insight into adhesion, buried interfacial structures more directly correspond to adhesion properties of polymers. SFG was used to study buried interfaces between deuterated polystyrene (d-PS) and the epoxies before and after moisture exposure. It was shown that moisture exposure acted to disorder the buried interfaces, most likely due to swelling. These results correlated with lap shear adhesion testing showing a decrease in adhesion strength after moisture exposure. The presented work showed that surface and interfacial structures can be correlated to adhesive strength and may be helpful in understanding and designing optimized epoxy underfill adhesives.

Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

International Nuclear Information System (INIS)

Miao, J.; Sayre, D.; Chapman, H.N.

1998-01-01

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2x in each dimension (i.e., oversampling by 4x for 2D and 8x for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. copyright 1998 Optical Society of America

Meso-optical Fourier transform microscope with double focusing

International Nuclear Information System (INIS)

Batusov, Yu.A.; Soroko, L.M.; Tereshchenko, V.V.

1992-01-01

The meso-optical Fourier transform microscope (MFTM) with double focusing for particle tracks of low ionization level in the nuclear emulsion is described. It is shown experimentally that this device enables one to get high concentration of information about the position of the particle track in the nuclear emulsion and thus to increase the signal-to-noise ratio. It is shown that spreading of the meso-optical image of the particle track in the sagittal section of the MFTM can be eliminated completely in the frame of the diffraction limit. The number of the additional degrees of freedom in this new MFTM system along depth coordinate is equal to 20 in comparison to single degree of freedom in the Fourier transform microscope of the direct observation. 10 refs.; 15 figs

Improved Fourier-transform profilometry

International Nuclear Information System (INIS)

Mao Xianfu; Chen Wenjing; Su Xianyu

2007-01-01

An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object

Pi, Fourier Transform and Ludolph van Ceulen

NARCIS (Netherlands)

Vajta, Miklos

2000-01-01

The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as

Fourier series and orthogonal polynomials

CERN Document Server

Jackson, Dunham

2004-01-01

This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe

DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael

2011-01-01

We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated.......We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated....

Electromechanical characteristics of piezoelectric ceramic transformers in radial vibration composed of concentric piezoelectric ceramic disk and ring

International Nuclear Information System (INIS)

Lin, Shuyu; Hu, Jing; Fu, Zhiqiang

2013-01-01

A new type of piezoelectric ceramic transformer in radial vibration is presented. The piezoelectric transformer consists of a pairing of a concentric piezoelectric ceramic circular disk and ring. The inner piezoelectric ceramic disk is axially polarized and the outer piezoelectric ring is radially polarized. Based on the plane stress theory, the exact analytical theory for the piezoelectric transformer is developed and its electromechanical equivalent circuit is introduced. The resonance/anti-resonance frequency equations of the transformer are obtained and the relationship between the resonance/anti-resonance frequency, the effective electromechanical coupling coefficient and the geometrical dimensions of the piezoelectric transformer is analyzed. The dependency of the voltage transformation ratio on the frequency is obtained. To verify the analytical theory, a numerical method is used to simulate the electromechanical characteristics of the piezoelectric transformer. It is shown that the analytical resonance/anti-resonance frequencies are in good agreement with the numerical results. (paper)

Application of finite Fourier transformation for the solution of the diffusion equation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1991-01-01

The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

Examination and vibration characteristics of gas circulator (B1) of HENDEL

International Nuclear Information System (INIS)

Shimomura, Hiroaki; Izawa, Naoki; Ihzuka, Takayuki; Kawaji, Satoshi; Kunitama, Takehiko; Hayashi, Haruyoshi; Kobayashi, Toshiaki; Katoh, Michio

1985-06-01

An examination and vibration measurements were conducted on the gas bearing type high speed helium gas circulator after the failure on April 1984 and the repairing on August 1984. The examination made clear that the cause of the failure and scratching of gas bearing pads and journal shaft was found. The vibrational spectra showed a clear difference between failed and repaired conditions, and a frequency analysis technique by means of fast Fourier transform and a small-scale computer is expected as a useful method of diagnosis for circulators. A conceptual scheme of gas circulator diagnostic system based on above principle is shown, and a basic process of diagnostic software is described. (author)

Some applications of Fourier's great discovery for beginners

International Nuclear Information System (INIS)

Kraftmakher, Yaakov

2012-01-01

Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations. (paper)

Measurements of bridges' vibration characteristics using a mobile phone

Directory of Open Access Journals (Sweden)

Z. M. C. Pravia

Full Text Available ABSTRACTThis research presents an alternative way to perform a bridge inspection, which considers the dynamics parameters from the structure. It shows an experimental phase with use of a mobile phone to extract the accelerations answers from two concrete bridges, from those records is feasible to obtain natural frequencies using the Fast Fourier Transform (FFT.Numerical models with uses finite element model (FEM allow to determine the natural frequencies from the two concrete bridges and compare with the experimental phase of each one. The final results shows it's possible to use mobiles phones to extract vibration answers from concrete bridges and define the structural behavior of bridges from natural frequencies, this procedure could be used to evaluate bridges with lower costs.

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

Science.gov (United States)

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.

Modeling and analysis of circular flexural-vibration-mode piezoelectric transformer.

Science.gov (United States)

Huang, Yihua; Huang, Wei

2010-12-01

We propose a circular flexural-vibration-mode piezoelectric transformer and perform a theoretical analysis of the transformer. An equivalent circuit is derived from the equations of piezoelectricity and the Hamilton's principle. With this equivalent circuit, the voltage gain ratio, input impedance, and the efficiency of the circular flexural-vibration-mode piezoelectric transformer can be determined. The basic behavior of the transformer is shown by numerical results.

Experimental evidence for an optical interference model for vibrational sum frequency generation on multilayer organic thin film systems. I. Electric dipole approximation

International Nuclear Information System (INIS)

O’Brien, Daniel B.; Massari, Aaron M.

2015-01-01

In the field of vibrational sum frequency generation spectroscopy (VSFG) applied to organic thin film systems, a significant challenge to data analysis is in the accurate description of optical interference effects. Herein, we provide experimental evidence that a model recently developed in our lab provides an accurate description of this phenomenon. We studied the organic small molecule N,N′-dioctyl-3,4,9,10-perylenedicarboximide vapor deposited as a thickness gradient on silicon wafer substrates with two oxide thicknesses and two surface preps. VSFG data were obtained using the ssp and the sps polarization combinations in the imide carbonyl stretching region as a function of organic thickness. In this first of two reports, the data are modeled and interpreted within the ubiquitous electric dipole approximation for VSFG. The intrinsic sample responses are parameterized during the fitting routines while optical interference effects are simply calculated from the model using known refractive indices, thin film thicknesses, and beam angles. The results indicate that the thin film model provides a good description of optical interferences, indicating that interfacial terms are significant. Inconsistencies between the fitting results within the bounds of the electric dipole response motivate deliberation for additional effects to be considered in the second report

Experimental evidence for an optical interference model for vibrational sum frequency generation on multilayer organic thin film systems. I. Electric dipole approximation.

Science.gov (United States)

O'Brien, Daniel B; Massari, Aaron M

2015-01-14

In the field of vibrational sum frequency generation spectroscopy (VSFG) applied to organic thin film systems, a significant challenge to data analysis is in the accurate description of optical interference effects. Herein, we provide experimental evidence that a model recently developed in our lab provides an accurate description of this phenomenon. We studied the organic small molecule N,N'-dioctyl-3,4,9,10-perylenedicarboximide vapor deposited as a thickness gradient on silicon wafer substrates with two oxide thicknesses and two surface preps. VSFG data were obtained using the ssp and the sps polarization combinations in the imide carbonyl stretching region as a function of organic thickness. In this first of two reports, the data are modeled and interpreted within the ubiquitous electric dipole approximation for VSFG. The intrinsic sample responses are parameterized during the fitting routines while optical interference effects are simply calculated from the model using known refractive indices, thin film thicknesses, and beam angles. The results indicate that the thin film model provides a good description of optical interferences, indicating that interfacial terms are significant. Inconsistencies between the fitting results within the bounds of the electric dipole response motivate deliberation for additional effects to be considered in the second report.

Experimental evidence for an optical interference model for vibrational sum frequency generation on multilayer organic thin film systems. I. Electric dipole approximation

Energy Technology Data Exchange (ETDEWEB)

O’Brien, Daniel B.; Massari, Aaron M., E-mail: massari@umn.edu [Department of Chemistry, University of Minnesota—Twin Cities, 207 Pleasant Street SE, Minneapolis, Minnesota 55455 (United States)

2015-01-14

In the field of vibrational sum frequency generation spectroscopy (VSFG) applied to organic thin film systems, a significant challenge to data analysis is in the accurate description of optical interference effects. Herein, we provide experimental evidence that a model recently developed in our lab provides an accurate description of this phenomenon. We studied the organic small molecule N,N′-dioctyl-3,4,9,10-perylenedicarboximide vapor deposited as a thickness gradient on silicon wafer substrates with two oxide thicknesses and two surface preps. VSFG data were obtained using the ssp and the sps polarization combinations in the imide carbonyl stretching region as a function of organic thickness. In this first of two reports, the data are modeled and interpreted within the ubiquitous electric dipole approximation for VSFG. The intrinsic sample responses are parameterized during the fitting routines while optical interference effects are simply calculated from the model using known refractive indices, thin film thicknesses, and beam angles. The results indicate that the thin film model provides a good description of optical interferences, indicating that interfacial terms are significant. Inconsistencies between the fitting results within the bounds of the electric dipole response motivate deliberation for additional effects to be considered in the second report.

The periodogram at the Fourier frequencies

NARCIS (Netherlands)

Kokoszka, P; Mikosch, T

In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,

Spectral sum rules and search for periodicities in DNA sequences

International Nuclear Information System (INIS)

Chechetkin, V.R.

2011-01-01

Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory. - Highlights: → We study the significance criteria for latent periodicities in DNA sequences. → The constraints imposed by sum rules can be described with De Finetti distribution. → It is intermediate between Rayleigh distribution and exact combinatoric theory. → Theory is applicable to the study of correlations between different periodicities. → The approach can be generalized to the arbitrary discrete Fourier transform.

Studies of Heterogeneously Catalyzed Liquid-Phase Alcohol Oxidation on Platinum bySum-frequency Generation Vibrational Spectroscopy and Reaction Rate Measurements

Energy Technology Data Exchange (ETDEWEB)

Thompson, Christopher [Univ. of California, Berkeley, CA (United States)

2014-05-15

Compared to many branches of chemistry, the molecular level study of catalytically active surfaces is young. Only with the invention of ultrahigh vacuum technology in the past half century has it been possible to carry out experiments that yield useful molecular information about the reactive occurrences at a surface. The reason is two-fold: low pressure is necessary to keep a surface clean for an amount of time long enough to perform an experiment, and most atomic scale techniques that are surface speci c (x-ray photoelectron spectroscopy, electron energy loss spectroscopy, Auger electron spectroscopy, etc.) cannot be used at ambient pressures, because electrons, which act as chemical probes in these techniques, are easily scattered by molecules. Sum-frequency generation (SFG) vibrational spectroscopy is one technique that can provide molecular level information from the surface without the necessity for high vacuum. Since the advent of SFG as a surface spectroscopic tool it has proved its worth in the studies of surface catalyzed reactions in the gas phase, with numerous reactions in the gas phase having been investigated on a multitude of surfaces. However, in situ SFG characterization of catalysis at the solid-liquid interface has yet to be thoroughly pursued despite the broad interest in the use of heterogeneous catalysts in the liquid phase as replacements for homogeneous counterparts. This work describes an attempt to move in that direction, applying SFG to study the solid-liquid interface under conditions of catalytic alcohol oxidation on platinum.

Practical protocols for fast histopathology by Fourier transform infrared spectroscopic imaging

Science.gov (United States)

Keith, Frances N.; Reddy, Rohith K.; Bhargava, Rohit

2008-02-01

Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that combines the molecular selectivity of spectroscopy with the spatial specificity of optical microscopy. We demonstrate a new concept in obtaining high fidelity data using commercial array detectors coupled to a microscope and Michelson interferometer. Next, we apply the developed technique to rapidly provide automated histopathologic information for breast cancer. Traditionally, disease diagnoses are based on optical examinations of stained tissue and involve a skilled recognition of morphological patterns of specific cell types (histopathology). Consequently, histopathologic determinations are a time consuming, subjective process with innate intra- and inter-operator variability. Utilizing endogenous molecular contrast inherent in vibrational spectra, specially designed tissue microarrays and pattern recognition of specific biochemical features, we report an integrated algorithm for automated classifications. The developed protocol is objective, statistically significant and, being compatible with current tissue processing procedures, holds potential for routine clinical diagnoses. We first demonstrate that the classification of tissue type (histology) can be accomplished in a manner that is robust and rigorous. Since data quality and classifier performance are linked, we quantify the relationship through our analysis model. Last, we demonstrate the application of the minimum noise fraction (MNF) transform to improve tissue segmentation.

Fourier transform of momentum distribution in vanadium

International Nuclear Information System (INIS)

Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.

1985-01-01

Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

Science.gov (United States)

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.

Modification of the fast fourier transform-based method by signal mirroring for accuracy quantification of thermal-hydraulic system code

Energy Technology Data Exchange (ETDEWEB)

Ha, Tae Wook; Jeong, Jae Jun [School of Mechanical Engineering, Pusan National University, Busan (Korea, Republic of); Choi, Ki Yong [Korea Atomic Energy Research Institute (KAERI), Daejeon (Korea, Republic of)

2017-08-15

A thermal–hydraulic system code is an essential tool for the design and safety analysis of a nuclear power plant, and its accuracy quantification is very important for the code assessment and applications. The fast Fourier transform-based method (FFTBM) by signal mirroring (FFTBM-SM) has been used to quantify the accuracy of a system code by using a comparison of the experimental data and the calculated results. The method is an improved version of the FFTBM, and it is known that the FFTBM-SM judges the code accuracy in a more consistent and unbiased way. However, in some applications, unrealistic results have been obtained. In this study, it was found that accuracy quantification by FFTBM-SM is dependent on the frequency spectrum of the fast Fourier transform of experimental and error signals. The primary objective of this study is to reduce the frequency dependency of FFTBM-SM evaluation. For this, it was proposed to reduce the cut off frequency, which was introduced to cut off spurious contributions, in FFTBM-SM. A method to determine an appropriate cut off frequency was also proposed. The FFTBM-SM with the modified cut off frequency showed a significant improvement of the accuracy quantification.

Modification of the fast fourier transform-based method by signal mirroring for accuracy quantification of thermal-hydraulic system code

International Nuclear Information System (INIS)

Ha, Tae Wook; Jeong, Jae Jun; Choi, Ki Yong

2017-01-01

A thermal–hydraulic system code is an essential tool for the design and safety analysis of a nuclear power plant, and its accuracy quantification is very important for the code assessment and applications. The fast Fourier transform-based method (FFTBM) by signal mirroring (FFTBM-SM) has been used to quantify the accuracy of a system code by using a comparison of the experimental data and the calculated results. The method is an improved version of the FFTBM, and it is known that the FFTBM-SM judges the code accuracy in a more consistent and unbiased way. However, in some applications, unrealistic results have been obtained. In this study, it was found that accuracy quantification by FFTBM-SM is dependent on the frequency spectrum of the fast Fourier transform of experimental and error signals. The primary objective of this study is to reduce the frequency dependency of FFTBM-SM evaluation. For this, it was proposed to reduce the cut off frequency, which was introduced to cut off spurious contributions, in FFTBM-SM. A method to determine an appropriate cut off frequency was also proposed. The FFTBM-SM with the modified cut off frequency showed a significant improvement of the accuracy quantification

A low frequency vibration energy harvester using magnetoelectric laminate composite

International Nuclear Information System (INIS)

Ju, Suna; Chae, Song Hee; Choi, Yunhee; Lee, Seungjun; Ji, Chang-Hyeon; Lee, Hyang Woon

2013-01-01

In this paper, we present a vibration energy harvester using magnetoelectric laminate composite and a springless spherical permanent magnet as a proof mass. The harvester utilizes a freely movable spherical permanent magnet to transform external vibration into a time varying magnetic field applied to the magnetoelectric transducer. The laminate composite consists of a Ni–Mn–Ga-based MSMA (magnetic shape memory alloy) element and a PZT (lead zirconate titanate) plate. A proof-of-concept harvester has been fabricated and characterized at various input accelerations and frequencies. A maximum open circuit voltage of 1.18 V has been obtained in response to a 3g vibration at 17 Hz with the fabricated device. Moreover, a maximum output voltage of 10.24 V and output power of 4.1 μW have been achieved on a 950 Ω load, when the fabricated energy harvester was mounted on a smartphone and shaken by hand. (paper)

Fourier transform nuclear magnetic resonance studies of 199Hg

International Nuclear Information System (INIS)

Krueger, H.; Lutz, O.; Nolle, A.; Schwenk, A.

1975-01-01

199 Hg Fourier Transform NMR studies of various solutions of diverse mercury salts in H 2 O and D 2 O or in the appropriate protonated and deuterated acids are reported for both Hg 2 ++ and Hg ++ . In the different solutions investigated the 199 Hg line positions depend on the concentration of the solution, on the solvents and their isotopic composition and on the temperature of the sample. A ratio of the Larmor frequency of 199 Hg and of 2 H in a Hg(NO 3 ) 2 solution in dilute DNO 3 is given. Using this ratio and the measured chemical shifts, a ratio of the Larmor frequencies of 199 Hg for infinite dilution relative to 2 H in pure D 2 O is given. From this a g 1 -factor for 199 Hg is derived and compared with the g 1 -factor of an optical pumping experiment. The resulting shielding constant is sigma (hydrated 199 Hg ++ versus 199 Hg atom) = -24.32(5) x 10 -4 . This yields an atomic reference scale for all measured NMR line shifts of mercury. (orig.) [de

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

Science.gov (United States)

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

2018-03-01

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

An innovative MRE absorber with double natural frequencies for wide frequency bandwidth vibration absorption

International Nuclear Information System (INIS)

Sun, Shuaishuai; Yang, Jian; Li, Weihua; Alici, Gursel; Deng, Huaxia; Du, Haiping; Yan, Tianhong

2016-01-01

A new design of adaptive tuned vibration absorber was proposed in this study for vibration reduction. The innovation of the new absorber is the adoption of the eccentric mass on the top of the multilayered magnetorheological elastomer (MRE) structure so that this proposed absorber has two vibration modes: one in the torsional direction and the other in translational direction. This property enables the absorber to expand its effective bandwidth and to be more capable of reducing the vibrations especially dealing with those vibrations with multi-frequencies. The innovative MRE absorber was designed and tested on a horizontal vibration table. The test results illustrate that the MRE absorber realized double natural frequencies, both of which are controllable. Inertia’s influence on the dynamic behavior of the absorber is also investigated in order to guide the design of the innovative MRE absorber. Additionally, the experimentally obtained natural frequencies coincide with the theoretical data, which sufficiently verifies the feasibility of this new design. The last part in terms of the vibration absorption ability also proves that both of these two natural frequencies play a great role in absorbing vibration energy. (paper)

A fourier transform quality measure for iris images

CSIR Research Space (South Africa)

Makinana, S

2014-08-01

Full Text Available to ensure that good quality images are selected for feature extraction, in order to improve iris recognition system. In addition, this research proposes a measure of iris image quality using a Fourier Transform. The experimental results demonstrate...

Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.

Science.gov (United States)

Tang, Heng-He; Liu, Pu-Kun

2015-09-07

A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

VUV Fourier-transform absorption study of the Lyman and Werner bands in D2

Science.gov (United States)

de Lange, Arno; Dickenson, Gareth D.; Salumbides, Edcel J.; Ubachs, Wim; de Oliveira, Nelson; Joyeux, Denis; Nahon, Laurent

2012-06-01

An extensive survey of the D2 absorption spectrum has been performed with the high-resolution VUV Fourier-transform spectrometer employing synchrotron radiation. The frequency range of 90 000-119 000 cm-1 covers the full depth of the potential wells of the B sideset{^1}{+u}{Σ}, B^' } sideset{^1}{+u}{Σ}, and C 1Πu electronic states up to the D(1s) + D(2ℓ) dissociation limit. Improved level energies of rovibrational levels have been determined up to respectively v = 51, v = 13, and v = 20. Highest resolution is achieved by probing absorption in a molecular gas jet with slit geometry, as well as in a liquid helium cooled static gas cell, resulting in line widths of ≈0.35 cm-1. Extended calibration methods are employed to extract line positions of D2 lines at absolute accuracies of 0.03 cm-1. The D 1Πu and B^' ' } sideset{^1}{+u}{Σ} electronic states correlate with the D(1s) + D(3ℓ) dissociation limit, but support a few vibrational levels below the second dissociation limit, respectively, v = 0-3 and v = 0-1, and are also included in the presented study. The complete set of resulting level energies is the most comprehensive and accurate data set for D2. The observations are compared with previous studies, both experimental and theoretical.

Combustion stratification study of partially premixed combustion using Fourier transform analysis of OH* chemiluminescence images

KAUST Repository

Izadi Najafabadi, Mohammad

2017-11-06

A relatively high level of stratification (qualitatively: lack of homogeneity) is one of the main advantages of partially premixed combustion over the homogeneous charge compression ignition concept. Stratification can smooth the heat release rate and improve the controllability of combustion. In order to compare stratification levels of different partially premixed combustion strategies or other combustion concepts, an objective and meaningful definition of “stratification level” is required. Such a definition is currently lacking; qualitative/quantitative definitions in the literature cannot properly distinguish various levels of stratification. The main purpose of this study is to objectively define combustion stratification (not to be confused with fuel stratification) based on high-speed OH* chemiluminescence imaging, which is assumed to provide spatial information regarding heat release. Stratification essentially being equivalent to spatial structure, we base our definition on two-dimensional Fourier transforms of photographs of OH* chemiluminescence. A light-duty optical diesel engine has been used to perform the OH* bandpass imaging on. Four experimental points are evaluated, with injection timings in the homogeneous regime as well as in the stratified partially premixed combustion regime. Two-dimensional Fourier transforms translate these chemiluminescence images into a range of spatial frequencies. The frequency information is used to define combustion stratification, using a novel normalization procedure. The results indicate that this new definition, based on Fourier analysis of OH* bandpass images, overcomes the drawbacks of previous definitions used in the literature and is a promising method to compare the level of combustion stratification between different experiments.

Discrete Fourier Transform in a Complex Vector Space

Science.gov (United States)

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.

Retina as Reciprocal Spatial Fourier Transform Space Implies ``Wave-transformation'' Functions, String Theory, the Inappropriate Uncertainty Principle, and Predicts ``Quarked'' Protons.

Science.gov (United States)

Mc Leod, Roger David; Mc Leod, David M.

2007-10-01

Vision, via transform space: ``Nature behaves in a reciprocal way;' also, Rect x pressure-input sense-reports as Sinc p, indicating brain interprets reciprocal ``p'' space as object space. Use Mott's and Sneddon's Wave Mechanics and Its Applications. Wave transformation functions are strings of positron, electron, proton, and neutron; uncertainty is a semantic artifact. Neutrino-string de Broglie-Schr"odinger wave-function models for electron, positron, suggest three-quark models for protons, neutrons. Variably vibrating neutrino-quills of this model, with appropriate mass-energy, can be a vertical proton string, quills leftward; thread string circumferentially, forming three interlinked circles with ``overpasses''. Diameters are 2:1:2, center circle has quills radially outward; call it a down quark, charge --1/3, charge 2/3 for outward quills, the up quarks of outer circles. String overlap summations are nodes; nodes also far left and right. Strong nuclear forces may be --px. ``Dislodging" positron with neutrino switches quark-circle configuration to 1:2:1, `downers' outside. Unstable neutron charge is 0. Atoms build. With scale factors, retinal/vision's, and quantum mechanics,' spatial Fourier transforms/inverses are equivalent.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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)

Fourier Transform Infrared and Resonance Raman Spectroscopic Studies of Bacteriorhodopsin.

Science.gov (United States)

Earnest, Thomas Nixon

Fourier transform infrared and resonance Raman spectroscopy were used to investigate the structure and function of the light-activated, transmembrane proton pump, bacteriorhodopsin, from the purple membrane of Halobacterium halobium. Bacteriorhodopsin (bR) is a 27,000 dalton integral membrane protein consisting of 248 amino acids with a retinylidene chromophore. Absorption of a photon leads to the translocation of one or two protons from the inside of the cell to the outside. Resonance Raman spectroscopy allows for the study of the configuration of retinal in bR and its photointermediates by the selective enhancement of vibrational modes of the chromophore. This technique was used to determine that the chromophore is attached to lysine-216 in both the bR _{570} and the M _{412} intermediates. In bR with tyrosine-64 selectively nitrated or aminated, the chromophore appears to have the same configuration in that bR _{570} (all- trans) and M _{412} (13- cis) states as it does in unmodified bR. Polarized Fourier transform infrared spectroscopy (FTIR) permits the study of the direction of transition dipole moments arising from molecular vibrations of the protein and the retinal chromophore. The orientation of alpha helical and beta sheet components was determined for bR with the average helical tilt found to lie mostly parallel to the membrane normal. The beta sheet structures also exhibit an IR linear dichroism for the amide I and amide II bands which suggest that the peptide backbone is mostly perpendicular to the membrane plane although it is difficult to determine whether the bands originate from sheet or turn components. The orientation of secondary structure components of the C-1 (residues 72-248) and C-2 (residues 1-71) fragments were also investigated to determine the structure of these putative membrane protein folding intermediates. Polarized, low temperature FTIR -difference spectroscopy was then used to investigate the structure of bR as it undergoes

Dual beam encoded extended fractional Fourier transform security ...

Indian Academy of Sciences (India)

This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...

Fourier transform infrared spectrometery: an undergraduate experiment

International Nuclear Information System (INIS)

Lerner, L

2016-01-01

Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory. (paper)

Fourier transforms on a semisimple symmetric space

NARCIS (Netherlands)

Ban, E.P. van den; Schlichtkrull, H.

1994-01-01

Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation

Fourier transforms on a semisimple symmetric space

NARCIS (Netherlands)

Ban, E.P. van den; Carmona, J.; Delorme, P.

1997-01-01

Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation

The gridding method for image reconstruction by Fourier transformation

International Nuclear Information System (INIS)

Schomberg, H.; Timmer, J.

1995-01-01

This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f. The method involves a window function w and proceeds in three steps. First, the convolution g = w * f is computed numerically on a Cartesian grid, using the available samples of f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w * f is much less error prone than merely interpolating f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform

Efficient yellow beam generation by intracavity sum frequency ...

Indian Academy of Sciences (India)

2014-02-06

Feb 6, 2014 ... petition leading to instability in the output sum frequency power and ... Nd:YVO4 crystal has been identified as one of the promising laser materials for diode ... very important to achieve small laser mode size as well as proper ...

A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform

Science.gov (United States)

Cai, Jianhua

2017-05-01

The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.

Sum frequency generation image reconstruction: Aliphatic membrane under spherical cap geometry

Energy Technology Data Exchange (ETDEWEB)

Volkov, Victor [Bereozovaya 2A, Konstantinovo, Moscow Region 140207 (Russian Federation)

2014-10-07

The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal – a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance.

Vibrational frame transformation for electron-molecule scattering

International Nuclear Information System (INIS)

Greene, C.H.; Jungen, C.

1985-01-01

The frame-transformation theory of electron interaction with a vibrating diatomic core is extended to allow for energy dependence of its parameters. The Born-Oppenheimer separation of electron and nuclear motion is preserved when the electron penetrates the molecular core. The extended theory reproduces the boomerang-model treatment of vibrational excitation in resonant e-N 2 collisions

Design and implementation in VHDL code of the two-dimensional fast Fourier transform for frequency filtering, convolution and correlation operations

Science.gov (United States)

Vilardy, Juan M.; Giacometto, F.; Torres, C. O.; Mattos, L.

2011-01-01

The two-dimensional Fast Fourier Transform (FFT 2D) is an essential tool in the two-dimensional discrete signals analysis and processing, which allows developing a large number of applications. This article shows the description and synthesis in VHDL code of the FFT 2D with fixed point binary representation using the programming tool Simulink HDL Coder of Matlab; showing a quick and easy way to handle overflow, underflow and the creation registers, adders and multipliers of complex data in VHDL and as well as the generation of test bench for verification of the codes generated in the ModelSim tool. The main objective of development of the hardware architecture of the FFT 2D focuses on the subsequent completion of the following operations applied to images: frequency filtering, convolution and correlation. The description and synthesis of the hardware architecture uses the XC3S1200E family Spartan 3E FPGA from Xilinx Manufacturer.

Fourier transform infrared spectrophotometry and X-ray powder ...

African Journals Online (AJOL)

This study aimed at demonstrating complementary roles offered by both Fourier transform infrared (FTIR) spectrophotometry and x-ray powder diffraction (XRPD) techniques in characterizing clay size fraction of kaolins. The clay size fraction of kaolin samples obtained from Kgwakgwe, Makoro, Lobatse and Serule kaolin ...

Fourier transform infrared (FTIR) spectroscopy for identification of ...

African Journals Online (AJOL)

Fourier transform infrared (FTIR) spectroscopy was used in this study to identify and determine spectral features of Chlorella vulgaris Beijerinck 1890 and Scenedesmus obliquus (Turpin) Kützing 1833. Two cultures were grown in a chemically-defined media under photoautotrophic culture conditions isolated from eutrophic ...

S-duality as Fourier transform for arbitrary ϵ1, ϵ2

International Nuclear Information System (INIS)

N Nemkov

2014-01-01

The Alday–Gaiotto–Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ −ϵ 1 /ϵ 2 = 1. Here I extend this conjecture to general values of ϵ 1 , ϵ 2 . Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ϵ 1 , ϵ 2 . The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g 2 ≡ −ϵ 1 ϵ 2 and hypermultiplet masses. (paper)

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

Science.gov (United States)

Yin, Changchuan; Yau, Stephen S-T

2015-10-07

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

The Pegg–Barnett phase operator and the discrete Fourier transform

International Nuclear Information System (INIS)

Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2016-01-01

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)

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

Science.gov (United States)

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.

Fourier Transform Spectrometer System

Science.gov (United States)

Campbell, Joel F. (Inventor)

2014-01-01

A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.

The su(2)α Hahn oscillator and a discrete Fourier-Hahn transform

International Nuclear Information System (INIS)

Jafarov, E I; Stoilova, N I; Van der Jeugt, J

2011-01-01

We define the quadratic algebra su(2) α which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2) α . We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2) α . It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Fourier-Hahn transform is computed explicitly. The matrix of this discrete Fourier-Hahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform. (paper)

Quantum Fourier Transform Over Galois Rings

OpenAIRE

Zhang, Yong

2009-01-01

Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...

Fourier Transform Methods. Chapter 4

Science.gov (United States)

Kaplan, Simon G.; Quijada, Manuel A.

2015-01-01

This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..

Harmonic analysis from Fourier to wavelets

CERN Document Server

Pereyra, Maria Cristina

2012-01-01

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...

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

Science.gov (United States)

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.

Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

2011-01-01

Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....

Quantum Mechanical Calculations of Vibrational Sum-Frequency-Generation (SFG) Spectra of Cellulose: Dependence of the CH and OH Peak Intensity on the Polarity of Cellulose Chains within the SFG Coherence Domain.

Science.gov (United States)

Lee, Christopher M; Chen, Xing; Weiss, Philip A; Jensen, Lasse; Kim, Seong H

2017-01-05

Vibrational sum-frequency-generation (SFG) spectroscopy is capable of selectively detecting crystalline biopolymers interspersed in amorphous polymer matrices. However, the spectral interpretation is difficult due to the lack of knowledge on how spatial arrangements of crystalline segments influence SFG spectra features. Here we report time-dependent density functional theory (TD-DFT) calculations of cellulose crystallites in intimate contact with two different polarities: parallel versus antiparallel. TD-DFT calculations reveal that the CH/OH intensity ratio is very sensitive to the polarity of the crystallite packing. Theoretical calculations of hyperpolarizability tensors (β abc ) clearly show the dependence of SFG intensities on the polarity of crystallite packing within the SFG coherence length, which provides the basis for interpretation of the empirically observed SFG features of native cellulose in biological systems.

Ultrafast and versatile spectroscopy by temporal Fourier transform

Science.gov (United States)

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.

Fourier transform digital holographic adaptive optics imaging system

Science.gov (United States)

Liu, Changgeng; Yu, Xiao; Kim, Myung K.

2013-01-01

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541

On the finite Fourier transforms of functions with infinite discontinuities