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

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.

Level 0 to 1 processing of the imaging Fourier transform spectrometer GLORIA: generation of radiometrically and spectrally calibrated spectra

Directory of Open Access Journals (Sweden)

A. Kleinert

2014-12-01

Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging Fourier transform spectrometer that is capable of operating on various high-altitude research aircraft. It measures the atmospheric emission in the thermal infrared spectral region in limb and nadir geometry. GLORIA consists of a classical Michelson interferometer combined with an infrared camera. The infrared detector has a usable area of 128 × 128 pixels, measuring up to 16 384 interferograms simultaneously. Imaging Fourier transform spectrometers impose a number of challenges with respect to instrument calibration and algorithm development. The optical setup with extremely high optical throughput requires the development of new methods and algorithms for spectral and radiometric calibration. Due to the vast amount of data there is a high demand for scientifically intelligent optimisation of the data processing. This paper outlines the characterisation and processing steps required for the generation of radiometrically and spectrally calibrated spectra. Methods for performance optimisation of the processing algorithm are presented. The performance of the data processing and the quality of the calibrated spectra are demonstrated for measurements collected during the first deployments of GLORIA on aircraft.

Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

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

Fourier transform 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)

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.

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...

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.

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

Pre-processing of Fourier transform infrared spectra by means of multivariate analysis implemented in the R environment.

Science.gov (United States)

Banas, Krzysztof; Banas, Agnieszka; Gajda, Mariusz; Pawlicki, Bohdan; Kwiatek, Wojciech M; Breese, Mark B H

2015-04-21

Pre-processing of Fourier transform infrared (FTIR) spectra is typically the first and crucial step in data analysis. Very often hyperspectral datasets include the regions characterized by the spectra of very low intensity, for example two-dimensional (2D) maps where the areas with only support materials (like mylar foil) are present. In that case segmentation of the complete dataset is required before subsequent evaluation. The method proposed in this contribution is based on a multivariate approach (hierarchical cluster analysis), and shows its superiority when compared to the standard method of cutting-off by using only the mean spectral intensity. Both techniques were implemented and their performance was tested in the R statistical environment - open-source platform - that is a favourable solution if the repeatability and transparency are the key aspects.

Use of fast Fourier transform in gamma-ray spectral analysis

International Nuclear Information System (INIS)

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

1978-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform has been devised. The validity of the method has been confirmed by computer simulation for spectra of a NaI detector. First, it is shown that spectral data can be represented by Fourier series with a reduced number of terms. Then the estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features of the method and a general problem to be solved in relation to a response matrix method are described. (author)

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.

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....

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)

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

Energy Technology Data Exchange (ETDEWEB)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net [NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)

2017-04-10

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

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

International Nuclear Information System (INIS)

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

2017-01-01

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

PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

Science.gov (United States)

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

Floor response spectra for multi-degree-of-freedom systems by Fourier transform

International Nuclear Information System (INIS)

Scanlan, R.H.; Sachs, K.

1975-01-01

A method of generating floor response spectra from a given ground response spectrum is given. This time-saving approach makes use of Fourier spectrum techniques and the randomness of phase angles. In matrix form a structure having many degrees-of-freedom is described by the equation of motion with M, C, K as the mass-, damping-, and stiffness matrices and Z being the acceleration time history of the earthquake and I a direction vector. If the Fourier spectrum FZ of the ground motion is known, then by standard methods the Fourier spectrum of the equipment response can be obtained. The assumption of random phase angles for the synthetic time history Z seems reasonable. The response is then also a superposition of cosine waves. Good agreement with time history methods is obtained. This method is much faster than time history methods, which are being used in most applications

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

Fourier transform infrared studies in solid egg white lysozyme

International Nuclear Information System (INIS)

Rivzi, T.Z.

1994-12-01

Fourier Transform Infrared (FTIR) Spectroscopy is the most recent addition to the arsenal of bioanalytical techniques capable of providing information about the secondary structure of proteins in a variety of environments. FTIR spectra have been obtained in solid egg white lysozyme. The spectra display the usual amide I, II and III bands. Secondary structural information obtained from the spectra after applying resolution enhancement techniques to the amide I band has been found consistent with the x-ray crystallographic data of the protein and also to the spectroscopic data of the protein in aqueous solution. (author). 17 refs, 6 figs, 2 tabs

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.

[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.

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…

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.

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)

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.)

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…

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.

Monitoring wine aging with Fourier transform infrared spectroscopy (FT-IR

Directory of Open Access Journals (Sweden)

Basalekou Marianthi

2015-01-01

Full Text Available Oak wood has commonly been used in wine aging but recently other wood types such as Acacia and Chestnut, have attracted the interest of the researchers due to their possible positive contribution to wine quality. However, only the use of oak and chestnut woods is approved by the International Enological Codex of the International Organisation of Vine and Wine. In this study Fourier Transform (FT-mid-infrared spectroscopy combined with Discriminant Analysis was used to differentiate wines aged in barrels made from French oak, American oak, Acacia and Chestnut and in tanks with oak chips, over a period of 12 months. Two red (Mandilaria, Kotsifali and two white (Vilana, Dafni native Greek grape varieties where used to produce four wines. The Fourier Transform Infrared (FT-IR spectra of the samples were recorded on a Zinc Selenide (ZnSe window after incubation at 40 °C for 30 min. A complete differentiation of the samples according to both the type of wood used and the contact time was achieved based on their FT-IR spectra.

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.

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

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.

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...

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.

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.

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)

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

GROUPING OF ORAL STREPTOCOCCAL SPECIES USING FOURIER-TRANSFORM INFRARED-SPECTROSCOPY IN COMPARISON WITH CLASSICAL MICROBIOLOGICAL IDENTIFICATION

NARCIS (Netherlands)

VANDERMEI, HC; NAUMANN, D; BUSSCHER, HJ

1993-01-01

The grouping and identification made by Fourier-transform infrared spectroscopy (FT-IR) of 40 oral streptococcal strains was compared with their known taxonomic positions. Grouping was obtained by cluster analysis on the spectral distances between the first derivative spectra of the strains. Spectra

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.

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

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.

A rapid method to screen for cell-wall mutants using discriminant analysis of Fourier transform infrared spectra

International Nuclear Information System (INIS)

Chen LiMei; Carpita, N.C.; Reiter, W.D.; Wilson, R.H.; Jeffries, C.; McCann, M.C.

1998-01-01

We have developed a rapid method to screen large numbers of mutant plants for a broad range of cell wall phenotypes using Fourier transform infrared (FTIR) microspectroscopy of leaves. We established and validated a model that can discriminate between the leaves of wild-type and a previously defined set of cell-wall mutants of Arabidopsis. Exploratory principal component analysis indicated that mutants deficient in different cell-wall sugars can be distinguished from each other. Discrimination of cell-wall mutants from wild-type was independent of variability in starch content or additional unrelated mutations that might be present in a heavily mutagenised population. We then developed an analysis of FTIR spectra of leaves obtained from over 1000 mutagenised flax plants, and selected 59 plants whose spectral variation from wild-type was significantly out of the range of a wild-type population, determined by Mahalanobis distance. Cell wall sugars from the leaves of selected putative mutants were assayed by gas chromatography-mass spectrometry and 42 showed significant differences in neutral sugar composition. The FTIR spectra indicated that six of the remaining 17 plants have altered ester or protein content. We conclude that linear discriminant analysis of FTIR spectra is a robust method to identify a broad range of structural and architectural alterations in cell walls, appearing as a consequence of developmental regulation, environmental adaptation or genetic modification. (author)

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

(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

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

Science.gov (United States)

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

1979-01-01

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

On the measurement of Wigner distribution moments in the fractional Fourier transform domain

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2002-01-01

It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed

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

Fourier transform zero field NMR and NQR

International Nuclear Information System (INIS)

Zax, D.B.

1985-01-01

In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI

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)

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.

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.

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.

Fourier transform infrared spectroscopy of dental unit water line biofilm bacteria

OpenAIRE

Liaqat, Iram

2009-01-01

Fourier transform-infrared (FT-IR) spectroscopy has become an important tool for rapid analysis of complex biological samples. The infrared absorbance spectrum could be regarded as a “fingerprint” which is a feature of biochemical substances. The FT-IR spectra of fresh and stored dried samples of six bacterial isolates (Klebsiella sp., Bacillus cereus, Bacillus subtilis, Pseudomonas aeruginosa, Achromobacter xylosoxidans and Achromobacter sp.) were observed by variation in sample preparation....

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.

On the oxidation mechanism of microcrystalline silicon thin films studied by Fourier transform infrared spectroscopy

NARCIS (Netherlands)

Bronneberg, A. C.; Smets, A. H. M.; Creatore, M.; M. C. M. van de Sanden,

2011-01-01

Insight into the oxidation mechanism of microcrystalline silicon thin films has been obtained by means of Fourier transform infrared spectroscopy. The films were deposited by using the expanding thermal plasma and their oxidation upon air exposure was followed in time. Transmission spectra were

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

Characterisation of Authentic Lignin Biorefinery Samples by Fourier Transform Infrared Spectroscopy and Determination of the Chemical Formula for Lignin

DEFF Research Database (Denmark)

Le, Duy Michael; Damgaard Nielsen, Anders; Sørensen, Hanne

2017-01-01

samples in situ with no prior purification and minimal sample preparation. Lignin chemical formulas and lignin Fourier transform infrared (FTIR) spectra were extracted from mixed spectra by filtering out signals from residual carbohydrates and minerals. From estimations of C, H and O and adjustment...

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 transform infrared spectroscopy in physics laboratory courses

International Nuclear Information System (INIS)

Möllmann, K-P; Vollmer, M

2013-01-01

Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes. (paper)

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

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

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.

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.

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

International Nuclear Information System (INIS)

Stanek, Jan; Kozminski, Wiktor

2010-01-01

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D 15 N- and 13 C-edited NOESY-HSQC spectra of human ubiquitin.

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.

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

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 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.)

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)

Quasiparticle relaxation in Heavy Fermions studied using Inverse Fourier Transform of optical conductivity

International Nuclear Information System (INIS)

Dordevic, S.V.

2012-01-01

Inverse Fourier Transform of optical conductivity is used for studies of quasiparticle relaxation in Heavy Fermions in time domain. We demonstrate the usefulness of the procedure on model spectra and then use it to study quasiparticle relaxation in two Heavy Fermions YbFe 4 Sb 12 and CeRu 4 Sb 12 . Optical conductivity in time domain reveals details of quasiparticle relaxation close to the Fermi level, not readily accessible from the spectra in the frequency domain. In particular, we find that the relaxation of heavy quasiparticles does not start instantaneously, but typically after a few hundred femto-seconds.

Influence of spectral resolution, spectral range and signal-to-noise ratio of Fourier transform infra-red spectra on identification of high explosive substances

Science.gov (United States)

Banas, Krzysztof; Banas, Agnieszka M.; Heussler, Sascha P.; Breese, Mark B. H.

2018-01-01

In the contemporary spectroscopy there is a trend to record spectra with the highest possible spectral resolution. This is clearly justified if the spectral features in the spectrum are very narrow (for example infra-red spectra of gas samples). However there is a plethora of samples (in the liquid and especially in the solid form) where there is a natural spectral peak broadening due to collisions and proximity predominately. Additionally there is a number of portable devices (spectrometers) with inherently restricted spectral resolution, spectral range or both, which are extremely useful in some field applications (archaeology, agriculture, food industry, cultural heritage, forensic science). In this paper the investigation of the influence of spectral resolution, spectral range and signal-to-noise ratio on the identification of high explosive substances by applying multivariate statistical methods on the Fourier transform infra-red spectral data sets is studied. All mathematical procedures on spectral data for dimension reduction, clustering and validation were implemented within R open source environment.

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 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.

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)

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

Far-infrared Fourier Transform Spectroscopy Measurements of Mn12-acetate.

Science.gov (United States)

Tu, Jiufeng; Suzuki, Yoko; Mertes, K. M.; Sarachik, M. P.; Agladze, N. I.; Sievers, A. J.; Rumberger, E. M.; Hendrickson, D. N.; Christou, G.

2004-03-01

The transmission spectra of both powder samples and assemblies of single crystals of Mn_12-acetate were measured in the far infrared region (2.0 - 20 cm-1) using a Fourier transform technique. The energies of the observed aborption lines agree with those obtained by Mukhin et al. [1] using the backwards wave oscillator technique. The temperature dependence of the aborption lines, as well as the presence of additional absorption lines, will be discussed. [1] A. A. Mukhin, V. D. Travkin, A. K. Zvesdin, A. Caneschi, D. Gatteschi and R. Sessoli, Physica B 284-288 (2000) 1221-1222

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

Science.gov (United States)

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

2017-05-01

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

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

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.

Fourier evaluation of broad Moessbauer spectra

International Nuclear Information System (INIS)

Vincze, I.

1981-01-01

It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)

Deconvolution, differentiation and Fourier transformation algorithms for noise-containing data based on splines and global approximation

NARCIS (Netherlands)

Wormeester, Herbert; Sasse, A.G.B.M.; van Silfhout, Arend

1988-01-01

One of the main problems in the analysis of measured spectra is how to reduce the influence of noise in data processing. We show a deconvolution, a differentiation and a Fourier Transform algorithm that can be run on a small computer (64 K RAM) and suffer less from noise than commonly used routines.

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",…

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

Fourier evaluation of broad Moessbauer spectra

International Nuclear Information System (INIS)

Vincze, I.

1981-09-01

It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)

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.

New Measurement of Singly Ionized Selenium Spectra by High Resolution Fourier Transform and Grating Spectroscopy

Science.gov (United States)

Hala, Noman; Nave, G.; Kramida, A.; Ahmad, T.; Nahar, S.; Pradhan, A.

2015-05-01

We report new measurements of singly ionised selenium, an element of the iron group detected in nearly twice as many planetary nebulae as any other trans-iron element. We use the NIST 2 m UV/Vis/IR and FT700 UV/Vis Fourier transform spectrometers over the wavelength range of 2000 Å-2.5 μm, supplemented in the lower wavelength region 300-2400 Å with grating spectra taken on a 3-m normal incidence vacuum spectrograph. The analysis of Se II is being extended, covering the wide spectral region from UV to IR. From our investigation, we found serious inconsistency and incompleteness in the previously published results, where several levels were reported without any designation. The analysis is being revised and extended with the help of semiempirical quasi-relativistic Hartree-Fock calculations, starting with the 4s24p3- [4s24p2(4d +5d +5s +6s) +4s4p4] transition array. Out of fifty-two previously reported levels, we rejected thirteen and found several new level values. With the new measurements, we expect to observe transitions between 4s24p2(4d +5s) and 4s24p2(5p +4f), lying in the visible and IR region. A complete interpretation of the level system of both parities will be assisted by least squares fitted parametric calculations. In all, we have already classified about 450 observed lines involving 89 energy levels.

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....

Chemical fingerprinting of Arabidopsis using Fourier transform infrared (FT-IR) spectroscopic approaches.

Science.gov (United States)

Gorzsás, András; Sundberg, Björn

2014-01-01

Fourier transform infrared (FT-IR) spectroscopy is a fast, sensitive, inexpensive, and nondestructive technique for chemical profiling of plant materials. In this chapter we discuss the instrumental setup, the basic principles of analysis, and the possibilities for and limitations of obtaining qualitative and semiquantitative information by FT-IR spectroscopy. We provide detailed protocols for four fully customizable techniques: (1) Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS): a sensitive and high-throughput technique for powders; (2) attenuated total reflectance (ATR) spectroscopy: a technique that requires no sample preparation and can be used for solid samples as well as for cell cultures; (3) microspectroscopy using a single element (SE) detector: a technique used for analyzing sections at low spatial resolution; and (4) microspectroscopy using a focal plane array (FPA) detector: a technique for rapid chemical profiling of plant sections at cellular resolution. Sample preparation, measurement, and data analysis steps are listed for each of the techniques to help the user collect the best quality spectra and prepare them for subsequent multivariate analysis.

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

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

Science.gov (United States)

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

2015-09-01

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

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.

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

Analysis of phthalate ester content in poly(vinyl chloride) plastics by means of Fourier transform Raman spectroscopy

DEFF Research Database (Denmark)

Nørbygaard, Thomas; Berg, Rolf W.

2004-01-01

Fourier transform (FT) Raman spectroscopy is applied to a range of phthalate ester plasticizers in pure form as well as in poly(vinyl chloride) (PVC) samples. It is found that phthalate esters as a group can be identified by a set of six characteristic Raman bands. FT-Raman spectra of 22 phthalate...

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

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.

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…

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.

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

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

On the Use of Fourier Transform Infrared (FT-IR) Spectroscopy and Synthetic Calibration Spectra to Quantify Gas Concentrations in a Fischer-Tropsch Catalyst System

Science.gov (United States)

Ferguson, Frank T.; Johnson, Natasha M.; Nuth, Joseph A., III

2015-01-01

One possible origin of prebiotic organic material is that these compounds were formed via Fischer-Tropsch-type (FTT) reactions of carbon monoxide and hydrogen on silicate and oxide grains in the warm, inner-solar nebula. To investigate this possibility, an experimental system has been built in which the catalytic efficiency of different grain-analog materials can be tested. During such runs, the gas phase above these grain analogs is sampled using Fourier transform infrared (FT-IR) spectroscopy. To provide quantitative estimates of the concentration of these gases, a technique in which high-resolution spectra of the gases are calculated using the high-resolution transmission molecular absorption (HITRAN) database is used. Next, these spectra are processed via a method that mimics the processes giving rise to the instrumental line shape of the FT-IR spectrometer, including apodization, self-apodization, and broadening due to the finite resolution. The result is a very close match between the measured and computed spectra. This technique was tested using four major gases found in the FTT reactions: carbon monoxide, methane, carbon dioxide, and water. For the ranges typical of the FTT reactions, the carbon monoxide results were found to be accurate to within 5% and the remaining gases accurate to within 10%. These spectra can then be used to generate synthetic calibration data, allowing the rapid computation of the gas concentrations in the FTT experiments.

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.

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)

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

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

Science.gov (United States)

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

2017-06-01

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

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.

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

Science.gov (United States)

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

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

Science.gov (United States)

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

2009-09-01

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

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)

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia

Directory of Open Access Journals (Sweden)

Sri A’jilah Samsir

2016-09-01

Full Text Available In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600–3100 cm−1 in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (South were clustered together in one group while samples from Perak, Kedah, Penang, Selangor, Kelantan, and Terengganu (North and East Coast were in another clustered group. Keywords: Apomictic, Mangosteen, Fourier Transformed-Infrared, Peninsular Malaysia

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

Science.gov (United States)

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

2017-11-27

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

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

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

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

Science.gov (United States)

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

2016-09-19

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

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.

Preservation of information in Fourier theory based deconvolved nuclear spectra

International Nuclear Information System (INIS)

Madan, V.K.; Gopalakrishnan, K.R.; Sharma, R.C.; Rattan, S.S.

1995-01-01

Nuclear spectroscopy is extremely useful to the internal radiation dosimetry for the estimation of body burden due to gamma emitters. Analysis of nuclear spectra is concerned with the extraction of qualitative and quantitative information embedded in the spectra. A spectral deconvolution method based on Fourier theory is probably the simplest method of deconvolving nuclear spectra. It is proved mathematically that the deconvolution method preserves the qualitative information. It is shown by using simulated spectra and an observed gamma ray spectrum that the method preserves the quantitative information. This may provide a novel approach of information extraction from a deconvolved spectrum. The paper discusses the methodology, mathematical analysis, and the results obtained by deconvolving spectra. (author). 6 refs., 2 tabs

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

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

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

Cancerous tissue mapping from random lasing emission spectra

International Nuclear Information System (INIS)

Polson, R C; Vardeny, Z V

2010-01-01

Random lasing emission spectra have been collected from both healthy and cancerous tissues. The two types of tissue with optical gain have different light scattering properties as obtained from an average power Fourier transform of their random lasing emission spectra. The difference in the power Fourier transform leads to a contrast between cancerous and benign tissues, which is utilized for tissue mapping of healthy and cancerous regions of patients

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

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).

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.

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.

Electrostatic ion trap and Fourier transform measurements for high-resolution mass spectrometry

International Nuclear Information System (INIS)

Bhushan, K. G.; Gadkari, S. C.; Yakhmi, J. V.; Sahni, V. C.

2007-01-01

We report on the development of an electrostatic ion trap for high-resolution mass spectrometry. The trap works on purely electrostatic fields and hence trapping and storing of ions is not mass restrictive, unlike other techniques based on Penning, Paul, or radio frequency quadrupole ion traps. It allows simultaneous trapping and studying of multiple mass species over a large mass range. Mass spectra were recorded in ''dispersive'' and ''self-bunching'' modes of ions. Storage lifetimes of about 100 ms and mass resolving power of about 20 000 could be achieved from the fifth harmonic Fourier transform spectrum of Xe ions recorded in the self-bunching mode

Rapid, nondestructive estimation of surface polymer layer thickness using attenuated total reflection fourier transform infrared (ATR FT-IR) spectroscopy and synthetic spectra derived from optical principles.

Science.gov (United States)

Weinstock, B André; Guiney, Linda M; Loose, Christopher

2012-11-01

We have developed a rapid, nondestructive analytical method that estimates the thickness of a surface polymer layer with high precision but unknown accuracy using a single attenuated total reflection Fourier transform infrared (ATR FT-IR) measurement. Because the method is rapid, nondestructive, and requires no sample preparation, it is ideal as a process analytical technique. Prior to implementation, the ATR FT-IR spectrum of the substrate layer pure component and the ATR FT-IR and real refractive index spectra of the surface layer pure component must be known. From these three input spectra a synthetic mid-infrared spectral matrix of surface layers 0 nm to 10,000 nm thick on substrate is created de novo. A minimum statistical distance match between a process sample's ATR FT-IR spectrum and the synthetic spectral matrix provides the thickness of that sample. We show that this method can be used to successfully estimate the thickness of polysulfobetaine surface modification, a hydrated polymeric surface layer covalently bonded onto a polyetherurethane substrate. A database of 1850 sample spectra was examined. Spectrochemical matrix-effect unknowns, such as the nonuniform and molecularly novel polysulfobetaine-polyetherurethane interface, were found to be minimal. A partial least squares regression analysis of the database spectra versus their thicknesses as calculated by the method described yielded an estimate of precision of ±52 nm.

Laser Mode Behavior of the Cassini CIRS Fourier Transform Spectrometer at Saturn

Science.gov (United States)

Brasunas, John C.

2012-01-01

The CIRS Fourier transform spectrometer aboard the NASA/ESA/ASI Cassini orbiter has been acquiring spectra of the Saturnian system since 2004. The CIRS reference interferometer employs a laser diode to trigger the interferogram sampling. Although the control of laser diode drive current and operating temperature are stringent enough to restrict laser wavelength variation to a small fraction of CIRS finest resolution element, the CIRS instrument does need to be restarted every year or two, at which time it may start in a new laser mode. By monitoring the Mylar absorption features in uncalibrated spectra due to the beam splitter Mylar substrate, it can be shown that these jumps are to adjacent modes and that most of the eight-year operation so far is restricted to three adjacent modes. For a given mode, the wavelength stability appears consistent with the stability of the laser diode drive curren.t and operating temperature.

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

Science.gov (United States)

Reed, George H; Poyner, Russell R

2015-01-01

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

Fourier-transform 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.

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 ...

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.

A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

Energy Technology Data Exchange (ETDEWEB)

Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com [Universidade Federal de São Paulo, Depto. Ciências Exatas e da Terra, Rua Prof. Arthur Riedel, 275, Jd. Eldorado, CEP 09972-270 Diadema, SP (Brazil)

2014-12-10

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

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.

Gastric cancer differentiation using Fourier transform near-infrared spectroscopy with unsupervised pattern recognition

Science.gov (United States)

Yi, Wei-song; Cui, Dian-sheng; Li, Zhi; Wu, Lan-lan; Shen, Ai-guo; Hu, Ji-ming

2013-01-01

The manuscript has investigated the application of near-infrared (NIR) spectroscopy for differentiation gastric cancer. The 90 spectra from cancerous and normal tissues were collected from a total of 30 surgical specimens using Fourier transform near-infrared spectroscopy (FT-NIR) equipped with a fiber-optic probe. Major spectral differences were observed in the CH-stretching second overtone (9000-7000 cm-1), CH-stretching first overtone (6000-5200 cm-1), and CH-stretching combination (4500-4000 cm-1) regions. By use of unsupervised pattern recognition, such as principal component analysis (PCA) and cluster analysis (CA), all spectra were classified into cancerous and normal tissue groups with accuracy up to 81.1%. The sensitivity and specificity was 100% and 68.2%, respectively. These present results indicate that CH-stretching first, combination band and second overtone regions can serve as diagnostic markers for gastric cancer.

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.

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)

Characterization of near-infrared nonmetal atomic emission from an atmospheric helium microwave-induced plasma using a Fourier transform spectrophotometer

International Nuclear Information System (INIS)

Hubert, J.; Van Tra, H.; Chi Tran, K.; Baudais, F.L.

1986-01-01

A new approach for using Fourier transform spectroscopy (FTS) for the detection of atomic emission from an atmospheric helium plasma has been developed and the results obtained are described. Among the different types of plasma source available, the atmospheric pressure microwave helium plasma appears to be an efficient excitation source for the determination of nonmetal species. The more complete microwave plasma emission spectra of Cl, Br, I, S, O, P, C, N, and He in the near-infrared region were obtained and their corrected relative emission intensities are reported. This makes qualitative identification simple, and aids in the quantitative analysis of atomic species. The accuracy of the emission wavelengths obtained with the Fourier transform spectrophotometer was excellent and the resolution provided by the FTS allowed certain adjacent emission lines to be adequate for analytical applications

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

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.

Fourier-transform infrared spectroscopic studies of dithia ...

Indian Academy of Sciences (India)

Unknown

limited region 1000–1150 cm–1.10 Therefore, in the present paper we report and analyse Fourier-trans- form infrared (FT-IR) spectra of S2TPP and its chemically prepared cation. 2. Experimental. Dithia tetraphenyl porphyrine was received from. Professor A L Verma as a gift and used without fur- ther purification. However ...

Depth resolved hyperspectral imaging spectrometer based on structured light illumination and Fourier transform interferometry

Science.gov (United States)

Choi, Heejin; Wadduwage, Dushan; Matsudaira, Paul T.; So, Peter T.C.

2014-01-01

A depth resolved hyperspectral imaging spectrometer can provide depth resolved imaging both in the spatial and the spectral domain. Images acquired through a standard imaging Fourier transform spectrometer do not have the depth-resolution. By post processing the spectral cubes (x, y, λ) obtained through a Sagnac interferometer under uniform illumination and structured illumination, spectrally resolved images with depth resolution can be recovered using structured light illumination algorithms such as the HiLo method. The proposed scheme is validated with in vitro specimens including fluorescent solution and fluorescent beads with known spectra. The system is further demonstrated in quantifying spectra from 3D resolved features in biological specimens. The system has demonstrated depth resolution of 1.8 μm and spectral resolution of 7 nm respectively. PMID:25360367

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.

Measurement of surface temperature and emissivity by a multitemperature method for Fourier-transform infrared spectrometers

DEFF Research Database (Denmark)

Clausen, Sønnik; Morgenstjerne, Axel; Rathmann, Ole

1996-01-01

Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single...... of blackbody sources are estimated with an uncertainty of 0.2-2 K. The method is demonstrated for measuring the spectral emissivity of a brass specimen and an oxidized nickel specimen. (C) 1996 Optical Society of America...... measurement at a known sample temperature, for example, at ambient temperature. The temperature of the sample surface can be measured rather easily at ambient temperature. The spectrum at ambient temperature is used to eliminate background effects from spectra as measured at other surface temperatures...

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

International Nuclear Information System (INIS)

Kroon, John J.; Becker, Peter A.

2014-01-01

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

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)

The influence of incident beam's angle offset of Fourier transform infrared spectrometer on the spectrum measurement explored with synchrotron radiation

International Nuclear Information System (INIS)

Chen Wenhao; Chen Min; Xiao Tiqiao

2011-01-01

Effects of the incident angle offset on FT-IR spectra are investigated in this paper. The simulated FT-IR spectra are obtained by Fourier inverse transform. The results show that this frequency shift varies with the angle offset of the incident beam in FT-IR. As an example,the factors that affect the angle of incident IR light at SSRF are analyzed. According to performance specifications of the IR beamline, requirements of the optical component installation precision and position drift of the light source are given. (authors)

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.

Broadband Chirped-Pulse Fourier-Transform Microwave Spectroscopic Investigation of the Structures of Three Diethylsilane Conformers

Science.gov (United States)

Steber, Amanda L.; Obenchain, Daniel A.; Peebles, Rebecca A.; Peebles, Sean A.; Neill, Justin L.; Muckle, Matt T.; Pate, Brooks H.; Guirgis, Gamil A.

2009-06-01

The rotational spectrum of diethylsilane has been assigned using broadband chirped-pulse Fourier-transform microwave (CP-FTMW) spectroscopy. Previously, Fourier-transform microwave rotational spectra were observed using a Balle-Flygare type instrument for the ^{28}Si isotopologues of the gauche-gauche, trans-gauche, and trans-trans conformers. In the present study, a broadband microwave spectrum was obtained at the University of Virginia, taking advantage of the ability to perform deep signal averaging to increase the measurement sensitivity. To obtain a full structural determination of the conformers of this molecule, spectra for the ^{29}Si, ^{30}Si, and single ^{13}C substitutions for the gauche-gauche, the trans-gauche, and the trans-trans species were assigned. Substitution (r_s) structures and inertial fit (r_0) structures were determined and a comparison between the experimental and ab initio structures will be presented. For the ^{28}Si isotopologues, the percent differences between the experimental and ab initio rotational constants are less than 1.5% for the trans-trans and trans-gauche and are between 2.0 and 5.0% for the gauche-gauche conformer. The structural parameters will be compared between this molecule, diethylgermane and other silicon containing molecules and the relative abundances of the three conformers will be discussed. S.A. Peebles, M.M. Serafin, R.A. Peebles, G.A. Guirgis, and H.D. Stidham J. Phys. Chem. A, (2009), DOI: 10.1021/jp811049n.

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

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

Science.gov (United States)

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

2014-10-01

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

Analysis of bacteria on steel surfaces using reflectance micro-Fourier transform infrared spectroscopy.

Science.gov (United States)

Ojeda, Jesús J; Romero-González, María E; Banwart, Steven A

2009-08-01

Reflectance micro-Fourier transform infrared (FT-IR) analysis has been applied to characterize biofilm formation of Aquabacterium commune, a common microorganism present on drinking water distribution systems, onto the increasingly popular pipe material stainless steel EN1.4307. The applicability of the reflectance micro-FT-IR technique for analyzing the bacterial functional groups is discussed, and the results are compared to spectra obtained using more conventional FT-IR techniques: transmission micro-FT-IR, attenuated transmitted reflectance (ATR), and KBr pellets. The differences between the infrared spectra of wet and dried bacteria, as well as free versus attached bacteria, are also discussed. The spectra obtained using reflectance micro-FT-IR spectroscopy were comparable to those obtained using other FT-IR techniques. The absence of sample preparation, the potential to analyze intact samples, and the ability to characterize opaque and thick samples without the need to transfer the bacterial samples to an infrared transparent medium or produce a pure culture were the main advantages of reflectance micro-FT-IR spectroscopy.

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

2014-10-07

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

A Fourier transform spectrometer for visible and near ultra-violet measurements of atmospheric absorption

Science.gov (United States)

Parsons, C. L.; Gerlach, J. C.; Whitehurst, M.

1982-01-01

The development of a prototype, ground-based, Sun-pointed Michelson interferometric spectrometer is described. Its intended use is to measure the atmospheric amount of various gases which absorb in the near-infrared, visible, and near-ultraviolet portions of the electromagnetic spectrum. Preliminary spectra which contain the alpha, 0.8 micrometer, and rho sigma tau water vapor absorption bands in the near-infrared are presented to indicate the present capability of the system. Ultimately, the spectrometer can be used to explore the feasible applications of Fourier transform spectroscopy in the ultraviolet where grating spectrometers were used exclusively.

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

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

Discrimination of different red wine by Fourier-transform infrared and two-dimensional infrared correlation spectroscopy

Science.gov (United States)

Zhang, Yan-ling; Chen, Jian-bo; Lei, Yu; Zhou, Qun; Sun, Su-qin; Noda, Isao

2010-06-01

Fourier-transform infrared spectroscopy (FT-IR) and two-dimensional infrared (2D IR) correlation spectroscopy were applied to analyze main components of liquid red wine with different sugar contents and volatilization residues of dry red wine from different manufactures. The infrared spectra, second derivative spectra of dry red wine show the typical peaks of alcohol, while the spectra of sweet wine are composed of the peaks of both alcohol and sugar, and the contribution of sugar enhanced as the increase of sugar content. Using principal component analysis (PCA) method, dry and sweet wine can be readily classified. Analysis of the infrared spectra of the volatilization residues of dry red wine samples from five different manufactures indicates that dry red wine may be composed of glycerol, carboxylic acids or esters and carboxyl ate, at the same time, different dry red wine show different characteristic peaks in the second derivative spectra and 2D IR correlation spectra, which can be used to discriminate the different manufactures and evaluate the quality of wine samples. The results suggested that infrared spectroscopy is a direct and effective method for the analysis of principle components of different red wines and discrimination of different red wines.

Diffuse reflectance infrared Fourier-Transform spectra of selected organic compounds

Energy Technology Data Exchange (ETDEWEB)

Harmon, S.H.; Caton, J.E.

1982-05-01

Diffuse reflectance infrared spectra of a variety of different organic compounds have been determined. Profiles of the spectra along with the location and relative intensity of the principal bands have been included for each compound studied. In addition both diffuse reflectance and transmittance infrared spectra were obtained for the same samples, and the spectral results were compared. Although some minor variations are observed between a diffuse reflectance spectrum and the corresponding transmittance spectrum, the diffuse reflectance is quite useful and may be a superior technique for the study of many samples because it possesses an inherently higher signal-to-noise response, requires less sample preparation and allows a very wide range of samples (solids, liquids of low volatility, neat sample, or sample diluted in a reflecting medium) to be studied under very similar conditions.

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

[Identification of Dendrobium varieties by Fourier transform infrared spectroscopy combined with spectral retrieval].

Science.gov (United States)

Liu, Fei; Wang, Yuan-zhong; Deng, Xing-yan; Jin, Hang; Yang, Chun-yan

2014-06-01

The infrared spectral of stems of 165 trees of 23 Dendrobium varieties were obtained by means of Fourier transform infrared spectroscopy technique. The spectra show that the spectra of all the samples were similar, and the main components of stem of Dendrobium is cellulose. By the spectral professional software Omnic8.0, three spectral databases were constructed. Lib01 includes of the average spectral of the first four trees of every variety, while Lib02 and Lib03 are constructed from the first-derivative spectra and the second-derivative spectra of average spectra, separately. The correlation search, the square difference retrieval and the square differential difference retrieval of the spectra are performed with the spectral database Lib01 in the specified range of 1 800-500 cm(-1), and the yield correct rate of 92.7%, 74.5% and 92.7%, respectively. The square differential difference retrieval of the first-derivative spectra and the second-derivative spectra is carried out with Lib02 and Lib03 in the same specified range 1 800-500 cm(-1), and shows correct rate of 93.9% for the former and 90.3% for the later. The results show that the first-derivative spectral retrieval of square differential difference algorithm is more suitabe for discerning Dendrobium varieties, and FTIR combining with the spectral retrieval method can identify different varieties of Dendrobium, and the correlation retrieval, the square differential retrieval, the first-derivative spectra and second-derivative spectra retrieval in the specified spectral range are effective and simple way of distinguishing different varieties of Dendrobium.

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.

Studies on Fourier amplitude spectra of accelerograms recorded on rock sites

International Nuclear Information System (INIS)

Ghosh, A.K.; Rao, K.S.

1990-01-01

Fourier spectra of 54 earthquake accelerograms recorded on rock sites in the U.S.A. have been analysed. These could be used in generation of synthetic accelerogramms for seismic design. (author). 19 figs., 1 tab., 1 appendix, 19 re fs

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)

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

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.

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.

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...

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)

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

Monitoring breast cancer treatment using a Fourier transform infrared spectroscopy-based computational model.

Science.gov (United States)

Depciuch, J; Kaznowska, E; Golowski, S; Koziorowska, A; Zawlik, I; Cholewa, M; Szmuc, K; Cebulski, J

2017-09-05

Breast cancer affects one in four women, therefore, the search for new diagnostic technologies and therapeutic approaches is of critical importance. This involves the development of diagnostic tools to facilitate the detection of cancer cells, which is useful for assessing the efficacy of cancer therapies. One of the major challenges for chemotherapy is the lack of tools to monitor efficacy during the course of treatment. Vibrational spectroscopy appears to be a promising tool for such a purpose, as it yields Fourier transformation infrared (FTIR) spectra which can be used to provide information on the chemical composition of the tissue. Previous research by our group has demonstrated significant differences between the infrared spectra of healthy, cancerous and post-chemotherapy breast tissue. Furthermore, the results obtained for three extreme patient cases revealed that the infrared spectra of post-chemotherapy breast tissue closely resembles that of healthy breast tissue when chemotherapy is effective (i.e., a good therapeutic response is achieved), or that of cancerous breast tissue when chemotherapy is ineffective. In the current study, we compared the infrared spectra of healthy, cancerous and post-chemotherapy breast tissue. Characteristic parameters were designated for the obtained spectra, spreading the function of absorbance using the Kramers-Kronig transformation and the best fit procedure to obtain Lorentz functions, which represent components of the bands. The Lorentz function parameters were used to develop a physics-based computational model to verify the efficacy of a given chemotherapy protocol in a given case. The results obtained using this model reflected the actual patient data retrieved from medical records (health improvement or no improvement). Therefore, we propose this model as a useful tool for monitoring the efficacy of chemotherapy in patients with breast cancer. Copyright © 2017 Elsevier B.V. All rights reserved.

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

Science.gov (United States)

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

2014-01-01

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

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

H∞ Robust Control of a Large-Piston MEMS Micromirror for Compact Fourier Transform Spectrometer Systems

Directory of Open Access Journals (Sweden)

Huipeng Chen

2018-02-01

Full Text Available Incorporating linear-scanning micro-electro-mechanical systems (MEMS micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large-piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and proportional-integral-derivative (PID closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with a full width at half maximum (FWHM spectral linewidth of 96 cm−1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

H∞ Robust Control of a Large-Piston MEMS Micromirror for Compact Fourier Transform Spectrometer Systems.

Science.gov (United States)

Chen, Huipeng; Li, Mengyuan; Zhang, Yi; Xie, Huikai; Chen, Chang; Peng, Zhangming; Su, Shaohui

2018-02-08

Incorporating linear-scanning micro-electro-mechanical systems (MEMS) micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS) possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large-piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and proportional-integral-derivative (PID) closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with a full width at half maximum (FWHM) spectral linewidth of 96 cm -1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

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....

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)

[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.

Rapid detection of foodborne microorganisms on food surface using Fourier transform Raman spectroscopy

Science.gov (United States)

Yang, Hong; Irudayaraj, Joseph

2003-02-01

Fourier transform (FT) Raman spectroscopy was used for non-destructive characterization and differentiation of six different microorganisms including the pathogen Escherichia coli O157:H7 on whole apples. Mahalanobis distance metric was used to evaluate and quantify the statistical differences between the spectra of six different microorganisms. The same procedure was extended to discriminate six different strains of E. coli. The FT-Raman procedure was not only successful in discriminating the different E. coli strain but also accurately differentiated the pathogen from non-pathogens. Results demonstrate that FT-Raman spectroscopy can be an excellent tool for rapid examination of food surfaces for microorganism contamination and for the classification of microbial cultures.

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.

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

Quantitative analysis of red wine tannins using Fourier-transform mid-infrared spectrometry.

Science.gov (United States)

Fernandez, Katherina; Agosin, Eduardo

2007-09-05

Tannin content and composition are critical quality components of red wines. No spectroscopic method assessing these phenols in wine has been described so far. We report here a new method using Fourier transform mid-infrared (FT-MIR) spectroscopy and chemometric techniques for the quantitative analysis of red wine tannins. Calibration models were developed using protein precipitation and phloroglucinolysis as analytical reference methods. After spectra preprocessing, six different predictive partial least-squares (PLS) models were evaluated, including the use of interval selection procedures such as iPLS and CSMWPLS. PLS regression with full-range (650-4000 cm(-1)), second derivative of the spectra and phloroglucinolysis as the reference method gave the most accurate determination for tannin concentration (RMSEC = 2.6%, RMSEP = 9.4%, r = 0.995). The prediction of the mean degree of polymerization (mDP) of the tannins also gave a reasonable prediction (RMSEC = 6.7%, RMSEP = 10.3%, r = 0.958). These results represent the first step in the development of a spectroscopic methodology for the quantification of several phenolic compounds that are critical for wine quality.

An attempt at predicting blood β-hydroxybutyrate from Fourier-transform mid-infrared spectra of milk using multivariate mixed models in Polish dairy cattle.

Science.gov (United States)

Belay, T K; Dagnachew, B S; Kowalski, Z M; Ådnøy, T

2017-08-01

Fourier transform mid-infrared (FT-MIR) spectra of milk are commonly used for phenotyping of traits of interest through links developed between the traits and milk FT-MIR spectra. Predicted traits are then used in genetic analysis for ultimate phenotypic prediction using a single-trait mixed model that account for cows' circumstances at a given test day. Here, this approach is referred to as indirect prediction (IP). Alternatively, FT-MIR spectral variable can be kept multivariate in the form of factor scores in REML and BLUP analyses. These BLUP predictions, including phenotype (predicted factor scores), were converted to single-trait through calibration outputs; this method is referred to as direct prediction (DP). The main aim of this study was to verify whether mixed modeling of milk spectra in the form of factors scores (DP) gives better prediction of blood β-hydroxybutyrate (BHB) than the univariate approach (IP). Models to predict blood BHB from milk spectra were also developed. Two data sets that contained milk FT-MIR spectra and other information on Polish dairy cattle were used in this study. Data set 1 (n = 826) also contained BHB measured in blood samples, whereas data set 2 (n = 158,028) did not contain measured blood values. Part of data set 1 was used to calibrate a prediction model (n = 496) and the remaining part of data set 1 (n = 330) was used to validate the calibration models, as well as to evaluate the DP and IP approaches. Dimensions of FT-MIR spectra in data set 2 were reduced either into 5 or 10 factor scores (DP) or into a single trait (IP) with calibration outputs. The REML estimates for these factor scores were found using WOMBAT. The BLUP values and predicted BHB for observations in the validation set were computed using the REML estimates. Blood BHB predicted from milk FT-MIR spectra by both approaches were regressed on reference blood BHB that had not been used in the model development. Coefficients of determination in cross

Large Molecule Structures by Broadband Fourier Transform Molecular Rotational Spectroscopy

Science.gov (United States)

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

2016-06-01

Fourier transform molecular rotational resonance spectroscopy (FT-MRR) using pulsed jet molecular beam sources is a high-resolution spectroscopy technique that can be used for chiral analysis of molecules with multiple chiral centers. The sensitivity of the molecular rotational spectrum pattern to small changes in the three dimensional structure makes it possible to identify diastereomers without prior chemical separation. For larger molecules, there is the additional challenge that different conformations of each diastereomer may be present and these need to be differentiated from the diastereomers in the spectral analysis. Broadband rotational spectra of several larger molecules have been measured using a chirped-pulse FT-MRR spectrometer. Measurements of nootkatone (C15H22O), cedrol (C15H26O), ambroxide (C16H28O) and sclareolide (C16H26O2) are presented. These spectra are measured with high sensitivity (signal-to-noise ratio near 1,000:1) and permit structure determination of the most populated isomers using isotopic analysis of the 13C and 18O isotopologues in natural abundance. The accuracy of quantum chemistry calculations to identify diastereomers and conformers and to predict the dipole moment properties needed for three wave mixing measurements is examined.

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.)

Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy.

Science.gov (United States)

Liu, Yan-De; Ying, Yi-Bin; Fu, Xia-Ping

2005-03-01

To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji apples were tested and 80 of them were used to form a calibration data set. The influences of different data preprocessing and spectra treatments were also quantified. Calibration models based on smoothing spectra were slightly worse than that based on derivative spectra, and the best result was obtained when the segment length was 5 nm and the gap size was 10 points. Depending on data preprocessing and PLS method, the best prediction model yielded correlation coefficient of determination (r2) of 0.759, low root mean square error of prediction (RMSEP) of 0.0677, low root mean square error of calibration (RMSEC) of 0.0562. The results indicated the feasibility of FT-NIR spectral analysis for predicting apple valid acidity in a nondestructive way.

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.

Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory.

Science.gov (United States)

Spencer, Austin P; Li, Hebin; Cundiff, Steven T; Jonas, David M

2015-04-30

A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.

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.

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...

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.

Evaluation of plasma-wave spectral density from cross-power spectra

International Nuclear Information System (INIS)

Ilic, D.B.; Harker, K.J.

1975-01-01

The plasma-wave spectral density is evaluated by performing a spatial Fourier transform on experimental cross-power spectra of ion acoustic waves. The cross-power spectra are recorded on analog magnetic tape, converted to digital form, transferred to digital magnetic tape, and Fourier transformed on a digital computer. The important effects of sampling, finite data strings, and data smoothing on the end results are discussed and illustrated. The results indicate the usefulness of the spectral density method for the study of nonlinear wave phenomena. (auth)

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)

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 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

Evaluation of Fourier and Response Spectra at Ichihasama and Koromogawa Seismic Intensity Observation Sites During the Iwate-Miyagi Nairiku Earthquake in 2008

Science.gov (United States)

Nishikawa, Hayato; Miyajima, Masakatsu

In this study, we evaluate an acceleration Fourier and response spectra at Ichihasama and Koromogawa seismic intensity observation sites which observed JMA seismic intensity of 6 upper but seismic waveform records don't exist during the Iwate-Miyagi Nairiku earthquake in 2008. Firstly, formula to evaluate acceleration Fourier and response spectra are developed using peak ground acceleration, JMA seismic intensity and predominant period of earthquake spectra based on records obtained from crustal earthquakes with Magnitude of 6 to 7. Acceleration Fourier and response spectra are evaluated for another local government site which are not chosen for development of the formula. The evaluated values mostly agree with the observed ones. Finally, acceleration Fourier and response spectra are evaluated for Ichihasama and Koromogawa observation sites. It is clarified that short period below 1 second was predominated in the evaluated spectra.

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)

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)

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.

Ultra High-Mass Resolution Paper Spray by Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

Directory of Open Access Journals (Sweden)

Kevin D. Quinn

2012-01-01

Full Text Available Paper Spray Ionization is an atmospheric pressure ionization technique that utilizes an offline electro-osmotic flow to generate ions off a paper medium. This technique can be performed on a Bruker SolariX Fourier transform ion cyclotron resonance mass spectrometer by modifying the existing nanospray source. High-resolution paper spray spectra were obtained for both organic and biological samples to demonstrate the benefit of linking the technique with a high-resolution mass analyzer. Error values in the range 0.23 to 2.14 ppm were obtained for calf lung surfactant extract with broadband mass resolving power (m/Δm50% above 60,000 utilizing an external calibration standard.

Internal rotation in trifluoromethylsulfur pentafluoride: CF3SF5 by Fourier transform microwave spectroscopy

Science.gov (United States)

Hirota, Eizi; Kawasima, Yoshiyuki; Ajiki, Ken

2017-12-01

Trifluoromethylsulfur pentafluoride CF3SF5, which has been attracting much attention because of its unusually large global warming potential, was investigated by Fourier transform microwave spectroscopy in order to determine the twelve-fold potential barrier to internal rotation in this molecule. We have found the V12 value to be close to zero. Relaxation among internal-rotation and overall-rotation levels was found inhomogeneous, resulting in distributions quite different from thermal in low-temperature molecular beam, which might affect significantly thermodynamic properties of the molecule. Rotational spectra of the 13C species and the 34S species were also observed in natural abundance, leading to the rs Csbnd S bond length of 1.8808 (7) Å.

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..

Fourier–transform infrared spectroscopic characterization of natu ...

Indian Academy of Sciences (India)

We present here the characterization of the fulgurites by Fourier transform infrared (FTIR) absorption, X-ray diffraction and X-ray fluorescence methods. The amorphous nature of the substance has been confirmed by Fourier transform infrared spectra of the fulgurites, which exhibit prominent absorption band in the region ...

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia

OpenAIRE

Samsir, Sri A’jilah; Bunawan, Hamidun; Yen, Choong Chee; Noor, Normah Mohd

2016-01-01

In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600–3100 cm−1 in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA) of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (S...

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....

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

Directory of Open Access Journals (Sweden)

Branko Saric

2002-01-01

Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.

The Fourier transform for certain hyperkähler fourfolds

CERN Document Server

Shen, Mingmin

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 \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

International Nuclear Information System (INIS)

Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

2011-01-01

According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

[A study of Boletus bicolor from different areas using Fourier transform infrared spectrometry].

Science.gov (United States)

Zhou, Zai-Jin; Liu, Gang; Ren, Xian-Pei

2010-04-01

It is hard to differentiate the same species of wild growing mushrooms from different areas by macromorphological features. In this paper, Fourier transform infrared (FTIR) spectroscopy combined with principal component analysis was used to identify 58 samples of boletus bicolor from five different areas. Based on the fingerprint infrared spectrum of boletus bicolor samples, principal component analysis was conducted on 58 boletus bicolor spectra in the range of 1 350-750 cm(-1) using the statistical software SPSS 13.0. According to the result, the accumulated contributing ratio of the first three principal components accounts for 88.87%. They included almost all the information of samples. The two-dimensional projection plot using first and second principal component is a satisfactory clustering effect for the classification and discrimination of boletus bicolor. All boletus bicolor samples were divided into five groups with a classification accuracy of 98.3%. The study demonstrated that wild growing boletus bicolor at species level from different areas can be identified by FTIR spectra combined with principal components analysis.

On the physical relevance of the discrete Fourier transform

CSIR Research Space (South Africa)

Greben, JM

1991-11-01

Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...

A Fourier-Transform Infrared Study of Biochar Aging in Soils

Science.gov (United States)

Singh, B.; Fang, Y.; Johnston, C.T.

2018-01-01

We used diffuse reflectance Fourier-transform infrared (DR-FTIR) spectroscopy, X-ray diffraction (XRD), and chemical and isotopic analyses to characterize the light fraction of four contrasting soils (control and biocharamended soils) to determine changes in biochar properties after aging. Two Eucalyptus saligna Sm. wood biochars, produced at 450°C (B450) and 550°C (B550), were incubated separately in each of the four soils for up to 12 mo at 20, 40, and 60°C. Total C and isotopic (δ13C) methods were used to quantify the amounts of biochar C and native C mineralized during incubation. The DR-FTIR spectra of the light fraction showed distinct absorption bands representing native soil organic C, biochar C, and mineral constituents present in the soils; the mineral bands were consistent with XRD data of the clay fraction of the four soils. Analysis of the DR-FTIR spectra in the ν(C–H) bands showed that the ratio of the aromatic ν(C–H) bands systematically increased relative to the aliphatic ν(C–H) bands with increasing mineralization of biochar C in the B550 amended soils, and this relationship was unique for each soil type. In contrast, this relationship was not observed for the B450 amended soils that contained a relatively smaller proportion of aromatic C. PMID:29657354

SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design

NARCIS (Netherlands)

Dool, T.C. van den; Kruizinga, B.; Braam, B.C.; Hamelinck, R.F.M.M.; Loix, N.; Loon, D. van; Dams, J.

2012-01-01

TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme in 2022. JAXA leads the development

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

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

Fourier transform ion cyclotron resonance mass spectrometry

Science.gov (United States)

Marshall, Alan G.

1998-06-01

As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.

Verification of Ganoderma (lingzhi) commercial products by Fourier Transform infrared spectroscopy and two-dimensional IR correlation spectroscopy

Science.gov (United States)

Choong, Yew-Keong; Sun, Su-Qin; Zhou, Qun; Lan, Jin; Lee, Han-Lim; Chen, Xiang-Dong

2014-07-01

Ganoderma commercial products are typically based on two sources, raw material (powder form and/or spores) and extract (water and/or solvent). This study compared three types of Ganoderma commercial products using 1 Dimensional Fourier Transform infrared and second derivative spectroscopy. The analyzed spectra of Ganoderma raw material products were compared with spectra of cultivated Ganoderma raw material powder from different mushroom farms in Malaysia. The Ganoderma extract product was also compared with three types of cultivated Ganoderma extracts. Other medicinal Ganoderma contents in commercial extract product that included glucan and triterpenoid were analyzed by using FTIR and 2DIR. The results showed that water extract of cultivated Ganoderma possessed comparable spectra with that of Ganoderma product water extract. By comparing the content of Ganoderma commercial products using FTIR and 2DIR, product content profiles could be detected. In addition, the geographical origin of the Ganoderma products could be verified by comparing their spectra with Ganoderma products from known areas. This study demonstrated the possibility of developing verification tool to validate the purity of commercial medicinal herbal and mushroom products.

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.

Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform

International Nuclear Information System (INIS)

Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid

2014-01-01

We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)

The RC Circuit: An Approach with Fourier Transforms

Indian Academy of Sciences (India)

The RC Circuit: An Approach with Fourier Transforms. Classroom Volume 21 Issue 11 November 2016 pp 1029-1042 ... But a lot of things, (including the complex impedanceitself, and some insight into complex analysis) can be understoodbetter if we use the FT approach to solve the differentialequations that come up in ...

Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

KAUST Repository

Lin, Sian-Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.; Chung, Wei-Ho

2016-01-01

In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h

Application of linear discriminant analysis and Attenuated Total Reflectance Fourier Transform Infrared microspectroscopy for diagnosis of colon cancer.

Science.gov (United States)

Khanmohammadi, Mohammadreza; Bagheri Garmarudi, Amir; Samani, Simin; Ghasemi, Keyvan; Ashuri, Ahmad

2011-06-01

Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) microspectroscopy was applied for detection of colon cancer according to the spectral features of colon tissues. Supervised classification models can be trained to identify the tissue type based on the spectroscopic fingerprint. A total of 78 colon tissues were used in spectroscopy studies. Major spectral differences were observed in 1,740-900 cm(-1) spectral region. Several chemometric methods such as analysis of variance (ANOVA), cluster analysis (CA) and linear discriminate analysis (LDA) were applied for classification of IR spectra. Utilizing the chemometric techniques, clear and reproducible differences were observed between the spectra of normal and cancer cases, suggesting that infrared microspectroscopy in conjunction with spectral data processing would be useful for diagnostic classification. Using LDA technique, the spectra were classified into cancer and normal tissue classes with an accuracy of 95.8%. The sensitivity and specificity was 100 and 93.1%, respectively.

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.

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

Science.gov (United States)

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

2009-06-01

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

Fourier transform wavefront control with adaptive prediction of the atmosphere.

Science.gov (United States)

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

2007-09-01

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

Fourier-transforming with quantum annealers

Directory of Open Access Journals (Sweden)

Itay eHen

2014-07-01

Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.

Transformation of a Free-Wilson matrix into Fourier coefficients

Czech Academy of Sciences Publication Activity Database

Holík, M.; Halámek, Josef

2002-01-01

Roč. 20, - (2002), s. 422 - 428 ISSN 0931-8771 Institutional research plan: CEZ:AV0Z2065902 Keywords : Free-Wilson matrix * Fourier transform * multivariate regression Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.558, year: 2002

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

Science.gov (United States)

Pezzolo, Alessandra De Lorenzi

2011-01-01

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

From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation

NARCIS (Netherlands)

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

1998-01-01

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

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.

q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity

NARCIS (Netherlands)

Atakishiyeva, M.K.; Atakishiyev, N.M.; Koornwinder, T.H.

2009-01-01

It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

Detecting the quality of glycerol monolaurate: a method for using Fourier transform infrared spectroscopy with wavelet transform and modified uninformative variable elimination.

Science.gov (United States)

Chen, Xiaojing; Wu, Di; He, Yong; Liu, Shou

2009-04-06

Glycerol monolaurate (GML) products contain many impurities, such as lauric acid and glucerol. The GML content is an important quality indicator for GML production. A hybrid variable selection algorithm, which is a combination of wavelet transform (WT) technology and modified uninformative variable eliminate (MUVE) method, was proposed to extract useful information from Fourier transform infrared (FT-IR) transmission spectroscopy for the determination of GML content. FT-IR spectra data were compressed by WT first; the irrelevant variables in the compressed wavelet coefficients were eliminated by MUVE. In the MUVE process, simulated annealing (SA) algorithm was employed to search the optimal cutoff threshold. After the WT-MUVE process, variables for the calibration model were reduced from 7366 to 163. Finally, the retained variables were employed as inputs of partial least squares (PLS) model to build the calibration model. For the prediction set, the correlation coefficient (r) of 0.9910 and root mean square error of prediction (RMSEP) of 4.8617 were obtained. The prediction result was better than the PLS model with full-spectra data. It was indicated that proposed WT-MUVE method could not only make the prediction more accurate, but also make the calibration model more parsimonious. Furthermore, the reconstructed spectra represented the projection of the selected wavelet coefficients into the original domain, affording the chemical interpretation of the predicted results. It is concluded that the FT-IR transmission spectroscopy technique with the proposed method is promising for the fast detection of GML content.

Hochauflösende Fourier-Transform-Emissionsspektroskopie

OpenAIRE

Uibel, Christian

2000-01-01

Mittels hochauflösender Fourier-Transform-Infrarot-Emissionsspektroskopie wurden tiefliegende elektronische Anregungszustände der mittelschweren zweiatomigen Radikale As2, Sb2 und TeF untersucht. Dabei lag das Interesse vor allem bei den Emissionen nicht voll erlaubter Übergänge wie beispielsweise der 3Σ +u →  1Σ +g- bzw. (1u) →  (0+g)-Übergänge bei den Stickstoff-Homologen. Dieses besondere Interesse an der genauen Analyse der 3Σ +u-Zustände liegt in ihrem metastab...

Application of Migration Velocity Using Fourier Transform Approach ...

African Journals Online (AJOL)

Application of velocity by Fourier transform to process 3-D unmigrated seismic sections has been carried out in Fabi Field, Niger Delta – Nigeria. Usually, all seismic events (sections) are characterized by spikes or noise (random or coherent), multiples and shear waves so that when a seismic bed is dipping, the apparent ...

FREQUENCY COMPONENT EXTRACTION OF HEARTBEAT CUES WITH SHORT TIME FOURIER TRANSFORM (STFT

Directory of Open Access Journals (Sweden)

Sumarna Sumarna

2017-01-01

  Electro-acoustic human heartbeat detector have been made with the main parts : (a stetoscope (piece chest, (b mic condenser, (c transistor amplifier, and (d cues analysis program with MATLAB. The frequency components that contained in heartbeat. cues have also been extracted with Short Time Fourier Transform (STFT from 9 volunteers. The results of the analysis showed that heart rate appeared in every cue frequency spectrum with their harmony. The steps of the research were including detector instrument design, test and instrument repair, cues heartbeat recording with Sound Forge 10 program and stored in wav file ; cues breaking at the start and the end, and extraction/cues analysis using MATLAB. The MATLAB program included filter (bandpass filter with bandwidth between 0.01 – 110 Hz, cues breaking with hamming window and every part was calculated using Fourier Transform (STFT mechanism and the result were shown in frequency spectrum graph.   Keywords: frequency components extraction, heartbeat cues, Short Time Fourier Transform

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)

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.

Soft x-ray microscope using Fourier transform holography

International Nuclear Information System (INIS)

McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H.

1989-01-01

A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 x 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs

Application of the fourier and wavelet transforms in noise reduction of the out of the ordinary data

International Nuclear Information System (INIS)

Tafreshi, M. A.; Sadeghi, Y.

2006-01-01

In this article the noise reduction of the experimental data by the Fourier and the wavelet transforms has been investigated. Using both simulated and experimental data (from the plasma focus facility, Dena), the sensitive features of the application of the Fourier transform are visualized and discussed. Then, the main idea of the wavelet transform and the results of the noise reduction with this transform are presented. Due to this investigation, for the cases such as the current derivative of the Dena facility, where the reliability of the Fourier transform can be doubtful, the wavelet transform can be considered as a more accurate alternative approach

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

Science.gov (United States)

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

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

Fourier-transform spectroscopy of HD in the vacuum ultraviolet at λ = 87-112 nm

Science.gov (United States)

Ivanov, T. I.; Dickenson, G. D.; Roudjane, M.; de Oliveira, N.; Joyeux, D.; Nahon, L.; Tchang-Brillet, W.-Ü. L.; Ubachs, W.

2010-03-01

Absorption spectroscopy in the vacuum ultraviolet (VUV) domain was performed on the hydrogen-deuteride molecule with a novel Fourier-transform spectrometer based upon wavefront division interferometry. This unique instrument, which is a permanent endstation of the undulator-based beamline DESIRS on the synchrotron SOLEIL facility, opens the way to Fourier-transform spectroscopy in the VUV range. The HD spectral lines in the Lyman and Werner bands were recorded in the 87-112 nm range from a quasi-static gas sample in a windowless configuration and with a Doppler-limited resolution. Line positions of some 268 transitions in the ? Lyman bands and 141 transitions in the ? Werner bands were deduced with uncertainties of 0.04 cm-1 (1σ) which correspond to Δλ/λ ∼ 4 × 10-7. This extensive laboratory database is of relevance for comparison with astronomical observations of H2 and HD spectra from highly redshifted objects, with the goal of extracting a possible variation of the proton-to-electron mass ratio (μ = m p /m e ) on a cosmological time scale. For this reason also calculations of the so-called sensitivity coefficients K i were performed in order to allow for deducing constraints on Δμ/μ. The K i coefficients, associated with the line shift that each spectral line undergoes as a result of a varying value for μ, were derived from calculations as a function of μ solving the Schrödinger equation using ab initio potentials.

Fourier Transform Spectrometer Controller for Partitioned Architectures

DEFF Research Database (Denmark)

Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.

2013-01-01

The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....

Fourier transformation methods in the field of gamma spectrometry

Indian Academy of Sciences (India)

The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.

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.

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.

OTDM-WDM Conversion Based on Time-Domain Optical Fourier Transformation with Spectral Compression

DEFF Research Database (Denmark)

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

2011-01-01

We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown.......We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown....

Nonlinear Fourier transform for dual-polarization optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone

communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...

Fourier transform infrared spectroscopy combined with chemometrics for discrimination of Curcuma longa, Curcuma xanthorrhiza and Zingiber cassumunar

Science.gov (United States)

Rohaeti, Eti; Rafi, Mohamad; Syafitri, Utami Dyah; Heryanto, Rudi

2015-02-01

Turmeric (Curcuma longa), java turmeric (Curcuma xanthorrhiza) and cassumunar ginger (Zingiber cassumunar) are widely used in traditional Indonesian medicines (jamu). They have similar color for their rhizome and possess some similar uses, so it is possible to substitute one for the other. The identification and discrimination of these closely-related plants is a crucial task to ensure the quality of the raw materials. Therefore, an analytical method which is rapid, simple and accurate for discriminating these species using Fourier transform infrared spectroscopy (FTIR) combined with some chemometrics methods was developed. FTIR spectra were acquired in the mid-IR region (4000-400 cm-1). Standard normal variate, first and second order derivative spectra were compared for the spectral data. Principal component analysis (PCA) and canonical variate analysis (CVA) were used for the classification of the three species. Samples could be discriminated by visual analysis of the FTIR spectra by using their marker bands. Discrimination of the three species was also possible through the combination of the pre-processed FTIR spectra with PCA and CVA, in which CVA gave clearer discrimination. Subsequently, the developed method could be used for the identification and discrimination of the three closely-related plant species.

Pulse shaping using the optical Fourier transform technique - for ultra-high-speed signal processing

DEFF Research Database (Denmark)

Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

2009-01-01

This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment.......This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment....

Quaternion Fourier transforms for signal and image processing

CERN Document Server

Ell, Todd A; Sangwine, Stephen J

2014-01-01

Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.

Simple surface structure determination from Fourier transforms of angle-resolved photoemission extended fine structure

Energy Technology Data Exchange (ETDEWEB)

Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)

1995-02-01

The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.

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.

Estimation of burst-mode LDA power spectra

DEFF Research Database (Denmark)

Velte, Clara Marika; George, William K.; Buchhave, Preben

2014-01-01

. The signal can be interpreted correctly by applying residence time weighting to all statistics and using the residence time-weighted discrete Fourier transform to compute the Fourier transform. A new spectral algorithm using the latter is applied to two experiments: a cylinder wake and an axisymmetric......The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons: acquisition is dictated by randomly arriving particles, the registered particle velocities tend to be biased toward higher values, and the signal is highly intermittent...

Improving interpretation of infrared spectra for OM characterization by subtraction of spectra from incinerated samples

Science.gov (United States)

Ellerbrock, Ruth H.; Gerke, Horst H.; Leue, Martin

2017-04-01

Non-destructive methods such as diffuse reflectance infrared Fourier transform spectroscopy (DRIFT) have been applied to characterize organic matter (OM) at intact structural surfaces among others. However, it is often difficult to distinguish effects of organic components on DRIFT signal intensities from those of mineral components. The objective of this study was to re-evaluate DRIFT spectra from intact earthworm burrow walls and coated cracks to improve the interpretation of C-H and C=O bands. We compared DRIFT and transmission Fourier transform infrared (FTIR) spectra of entire samples that were from the same pedogenetic soil horizon, but different in mineral composition and texture (i.e., glacial till versus loess). Spectra of incinerated samples were subtracted from the original spectra. Transmission FTIR and DRIFT spectra were almost identical for entire soil samples. However, the DRIFT spectra were affected by the bulk mode bands (i.e., wavenumbers 2000 to 1700 cm-1) that affected spectral resolution and reproducibility. The ratios between C-H and C=O band intensities as indicator for OM quality obtained with DRIFT were smaller than those obtained from transmission FTIR. A spectral subtraction procedure was found to reduce effects of mineral absorption bands on DRIFT spectra allowing an improved interpretation. DRIFT spectroscopy as a non-destructive method for analyzing OM composition at intact surfaces in structured soils could be calibrated with information obtained with the more detailed transmission FTIR and complementary methods.

Dual-polarization nonlinear Fourier transform-based optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

2018-01-01

communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek; Kuna, Maciej

2016-01-01

Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

International Nuclear Information System (INIS)

Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning

2009-01-01

The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe 3 O 4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.

Laser ablation of an indium target: time-resolved Fourier-transform infrared spectra of In I in the 700–7700 cm−1 range

Czech Academy of Sciences Publication Activity Database

Civiš, Svatopluk; Kubelík, Petr; Ferus, Martin; Chernov, Vladislav E.; Zanozina, Ekaterina M.; Juha, Libor

2014-01-01

Roč. 29, č. 12 (2014), s. 2275-2283 ISSN 0267-9477 R&D Projects: GA MŠk LD14115; GA MŠk(CZ) LG13029 Institutional support: RVO:61388955 ; RVO:68378271 Keywords : time-resolved fluorescence * Fourier transform infra reds * Laser-induced breakdown spectroscopy Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.466, year: 2014

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,

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

Science.gov (United States)

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

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.

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.

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.

Time dependent and asymptotic neutron number probability distribution calculation using discrete Fourier transform

International Nuclear Information System (INIS)

Humbert, Ph.

2005-01-01

In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)

FTIR spectra of whey and casein hydrolysates in relation to their functional properties

NARCIS (Netherlands)

Ven, van der C.; Muresan, S.; Gruppen, H.; Bont, D.B.A.; Merck, K.B.; Voragen, A.G.J.

2002-01-01

Mid-infrared spectra of whey and casein hydrolysates were recorded using Fourier transform infrared (FTIR) spectroscopy. Multivariate data analysis techniques were used to investigate the capacity of FTIR spectra to classify hydrolysates and to study the ability of the spectra to predict bitterness,

High-resolution magnetic-domain imaging by Fourier transform holography at 21 nm wavelength

International Nuclear Information System (INIS)

Schaffert, Stefan; Pfau, Bastian; Günther, Christian M; Schneider, Michael; Korff Schmising, Clemens von; Eisebitt, Stefan; Geilhufe, Jan

2013-01-01

Exploiting x-ray magnetic circular dichroism at the L-edges of 3d transition metals, Fourier transform holography has become a standard technique to investigate magnetic samples with sub-100 nm spatial resolution. Here, magnetic imaging in the 21 nm wavelength regime using M-edge circular dichroism is demonstrated. Ultrafast pulses in this wavelength regime are increasingly available from both laser- and accelerator-driven soft x-ray sources. We explain the adaptations concerning sample preparation and data evaluation compared to conventional holography in the 1 nm wavelength range. We find the correction of the Fourier transform hologram to in-plane Fourier components to be critical for high-quality reconstruction and demonstrate 70 nm spatial resolution in magnetization imaging with this approach. (paper)

Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

International Nuclear Information System (INIS)

Dong Ping; Yang Ming; Cao Zhuoliang

2008-01-01

In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

All-optical signal processing of OTDM and OFDM signals based on time-domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen

2014-01-01

All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....

A transformada de Fourier em basic The Fourier transform (FFT in basic

Directory of Open Access Journals (Sweden)

Mauricio Gomes Constantino

2000-06-01

Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.

Spectroscopic analysis of bladder cancer tissues using Fourier transform infrared spectroscopy

Science.gov (United States)

Al-Muslet, Nafie A.; Ali, Essam E.

2012-03-01

Bladder cancer is one of the most common cancers in Africa. It takes several days to reach a diagnosis using histological examinations of specimens obtained by endoscope, which increases the medical expense. Recently, spectroscopic analysis of bladder cancer tissues has received considerable attention as a diagnosis technique due to its sensitivity to biochemical variations in the samples. This study investigated the use of Fourier transform infrared (FTIR) spectroscopy to analyze a number of bladder cancer tissues. Twenty-two samples were collected from 11 patients diagnosed with bladder cancer from different hospitals without any pretreatment. From each patient two samples were collected, one normal and another cancerous. FTIR spectrometer was used to differentiate between normal and cancerous bladder tissues via changes in spectra of these samples. The investigations detected obvious changes in the bands of proteins (1650, 1550 cm-1), lipids (2925, 2850 cm-1), and nucleic acid (1080, 1236 cm-1). The results show that FTIR spectroscopy is promising as a rapid, accurate, nondestructive, and easy to use alternative method for identification and diagnosis of bladder cancer tissues.

Thermoluminescence spectra measured with a Michelson interferometer

International Nuclear Information System (INIS)

Haschberger, P.

1991-01-01

A Michelson interferometer was redesigned to prove its capabilities in the measurement of short-lived, low-intensity thermoluminescence spectra. Interferograms are collected during heating up the thermoluminescent probe in a heater plate. A personal computer controls the data acquisition and processes the Fourier transform. As the results show, even a comparatively simple and limited setup leads to relevant and reproducible spectra. (author)

Symmetrized neutron transport equation and the fast Fourier transform method

International Nuclear Information System (INIS)

Sinh, N.Q.; Kisynski, J.; Mika, J.

1978-01-01

The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations

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

Science.gov (United States)

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

2016-04-01

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

On Analog of Fourier Transform in Interior of the Light Cone

Directory of Open Access Journals (Sweden)

Tatyana Shtepina

2014-01-01

Full Text Available We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.

Physiological response of Arundo donax to cadmium stress by Fourier transform infrared spectroscopy.

Science.gov (United States)

Yu, Shunhui; Sheng, Li; Zhang, Chunyan; Deng, Hongping

2018-06-05

The present paper deals with the physiological response of the changes in chemical contents of the root, stem and leaf of Arundo donax seedlings stressed by excess cadmium using Fourier transform infrared spectroscopy technique, cadmium accumulation in plant by atomic absorption spectroscopy were tested after different concentrations cadmium stress. The results showed that low cadmium concentrations (Fourier transform infrared spectroscopy technique for the non-invasive and rapid monitoring of the plants stressed with heavy metals, Arundo donax is suitable for phytoremediation of cadmium -contaminated wetland. Copyright © 2018 Elsevier B.V. All rights reserved.

The Fourier transform as a signature for chaos in nuclear energy levels

International Nuclear Information System (INIS)

Bybee, C.R.; Mitchell, G.E.; Shriner, J.F. Jr.

1996-01-01

The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)

The Fourier transform as a signature for chaos in nuclear energy levels

Energy Technology Data Exchange (ETDEWEB)

Bybee, C.R. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Mitchell, G.E. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Shriner, J.F. Jr. [Tennessee Technological Univ., Cookeville (United States)

1996-08-01

The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)

A singularity extraction technique for computation of antenna aperture fields from singular plane wave spectra

DEFF Research Database (Denmark)

Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel

2008-01-01

An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...

Analog fourier transform channelizer and OFDM receiver

OpenAIRE

2007-01-01

An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...

Directional short-time Fourier transform of distributions

Directory of Open Access Journals (Sweden)

Katerina Hadzi-Velkova Saneva

2016-04-01

Full Text Available Abstract In this paper we consider the directional short-time Fourier transform (DSTFT that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013. We analyze the DSTFT and its transpose on test function spaces S ( R n $\\mathcal {S}(\\mathbb {R}^{n}$ and S ( Y 2 n $\\mathcal {S}(\\mathbb {Y}^{2n}$ , respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.

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.

Early detection of rogue waves by the wavelet transforms

International Nuclear Information System (INIS)

Bayındır, Cihan

2016-01-01

Highlights: • The advantages of wavelet analysis over the Fourier analysis for the early detection of rogue waves are discussed. • The triangular wavelet spectra can be detected at early stages of the development of rogue waves. • The wavelet analysis is capable of detecting not only the emergence but also the location of a rogue wave. • Wavelet analysis is also capable of predicting the characteristic distances between successive rogue waves. - Abstract: We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the development of rogue waves in a chaotic wave field. Compared to the Fourier spectra, the wavelet spectra are capable of detecting not only the emergence of a rogue wave but also its possible spatial (or temporal) location. Due to this fact, wavelet transform is also capable of predicting the characteristic distances between successive rogue waves. Therefore multiple simultaneous breaking of the successive rogue waves on ships or on the offshore structures can be predicted and avoided by smart designs and operations.

Early detection of rogue waves by the wavelet transforms

Energy Technology Data Exchange (ETDEWEB)

Bayındır, Cihan, E-mail: cihan.bayindir@isikun.edu.tr

2016-01-08

Highlights: • The advantages of wavelet analysis over the Fourier analysis for the early detection of rogue waves are discussed. • The triangular wavelet spectra can be detected at early stages of the development of rogue waves. • The wavelet analysis is capable of detecting not only the emergence but also the location of a rogue wave. • Wavelet analysis is also capable of predicting the characteristic distances between successive rogue waves. - Abstract: We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the development of rogue waves in a chaotic wave field. Compared to the Fourier spectra, the wavelet spectra are capable of detecting not only the emergence of a rogue wave but also its possible spatial (or temporal) location. Due to this fact, wavelet transform is also capable of predicting the characteristic distances between successive rogue waves. Therefore multiple simultaneous breaking of the successive rogue waves on ships or on the offshore structures can be predicted and avoided by smart designs and operations.

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.

On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity

OpenAIRE

Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.

2008-01-01

It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Palushani, Evarist; Richter, T.; Ludwig, R.

2012-01-01

We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....

Products of multiple Fourier series with application to the multiblade transformation

Science.gov (United States)

Kunz, D. L.

1981-01-01

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

Spectrogram analysis of selected tremor signals using short-time Fourier transform and continuous wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Bartosch, T. [Erlanger-Nuernberg Univ., Erlanger (Germany). Lehrstul fuer Nachrichtentechnik I; Seidl, D. [Seismologisches Zentralobservatorium Graefenberg, Erlanegen (Greece). Bundesanstalt fuer Geiwissenschaften und Rohstoffe

1999-06-01

Among a variety of spectrogram methods short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were selected to analyse transients in non-stationary signals. Depending on the properties of the tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli (Italy).

Numerical computation of the discrete Fourier transform and its applications in the statistic processing of experimental data

International Nuclear Information System (INIS)

Marinescu, D.C.; Radulescu, T.G.

1977-06-01

The Integral Fourier Transform has a large range of applications in such areas as communication theory, circuit theory, physics, etc. In order to perform discrete Fourier Transform the Finite Fourier Transform is defined; it operates upon N samples of a uniformely sampled continuous function. All the properties known in the continuous case can be found in the discrete case also. The first part of the paper presents the relationship between the Finite Fourier Transform and the Integral one. The computing of a Finite Fourier Transform is a problem in itself since in order to transform a set of N data we have to perform N 2 ''operations'' if the transformation relations are used directly. An algorithm known as the Fast Fourier Transform (FFT) reduces this figure from N 2 to a more reasonable Nlog 2 N, when N is a power of two. The original Cooley and Tuckey algorithm for FFT can be further improved when higher basis are used. The price to be paid in this case is the increase in complexity of such algorithms. The recurrence relations and a comparation among such algorithms are presented. The key point in understanding the application of FFT resides in the convolution theorem which states that the convolution (an N 2 type procedure) of the primitive functions is equivalent to the ordinar multiplication of their transforms. Since filtering is actually a convolution process we present several procedures to perform digital filtering by means of FFT. The best is the one using the segmentation of records and the transformation of pairs of records. In the digital processing of signals, besides digital filtering a special attention is paid to the estimation of various statistical characteristics of a signal as: autocorrelation and correlation functions, periodiograms, density power sepctrum, etc. We give several algorithms for the consistent and unbiased estimation of such functions, by means of FFT. (author)

How to use the Fast Fourier Transform in Large Finite Fields

OpenAIRE

Petersen, Petur Birgir

2011-01-01

The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.

Baseline correction combined partial least squares algorithm and its application in on-line Fourier transform infrared quantitative analysis.

Science.gov (United States)

Peng, Jiangtao; Peng, Silong; Xie, Qiong; Wei, Jiping

2011-04-01

In order to eliminate the lower order polynomial interferences, a new quantitative calibration algorithm "Baseline Correction Combined Partial Least Squares (BCC-PLS)", which combines baseline correction and conventional PLS, is proposed. By embedding baseline correction constraints into PLS weights selection, the proposed calibration algorithm overcomes the uncertainty in baseline correction and can meet the requirement of on-line attenuated total reflectance Fourier transform infrared (ATR-FTIR) quantitative analysis. The effectiveness of the algorithm is evaluated by the analysis of glucose and marzipan ATR-FTIR spectra. BCC-PLS algorithm shows improved prediction performance over PLS. The root mean square error of cross-validation (RMSECV) on marzipan spectra for the prediction of the moisture is found to be 0.53%, w/w (range 7-19%). The sugar content is predicted with a RMSECV of 2.04%, w/w (range 33-68%). Copyright © 2011 Elsevier B.V. All rights reserved.

Fourier transform infrared spectroscopy combined with chemometrics for discrimination of Curcuma longa, Curcuma xanthorrhiza and Zingiber cassumunar.

Science.gov (United States)

Rohaeti, Eti; Rafi, Mohamad; Syafitri, Utami Dyah; Heryanto, Rudi

2015-02-25

Turmeric (Curcuma longa), java turmeric (Curcuma xanthorrhiza) and cassumunar ginger (Zingiber cassumunar) are widely used in traditional Indonesian medicines (jamu). They have similar color for their rhizome and possess some similar uses, so it is possible to substitute one for the other. The identification and discrimination of these closely-related plants is a crucial task to ensure the quality of the raw materials. Therefore, an analytical method which is rapid, simple and accurate for discriminating these species using Fourier transform infrared spectroscopy (FTIR) combined with some chemometrics methods was developed. FTIR spectra were acquired in the mid-IR region (4000-400 cm(-1)). Standard normal variate, first and second order derivative spectra were compared for the spectral data. Principal component analysis (PCA) and canonical variate analysis (CVA) were used for the classification of the three species. Samples could be discriminated by visual analysis of the FTIR spectra by using their marker bands. Discrimination of the three species was also possible through the combination of the pre-processed FTIR spectra with PCA and CVA, in which CVA gave clearer discrimination. Subsequently, the developed method could be used for the identification and discrimination of the three closely-related plant species. Copyright © 2014 Elsevier B.V. All rights reserved.

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

Science.gov (United States)

Moon, F. C.

1973-01-01

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

Experimental demonstrations of the properties of Fourier transforms using diffraction phenomena

International Nuclear Information System (INIS)

Bazin, M.J.; Lucie, P.H.; Oliveira, S.M.M. de.

1984-01-01

The standard mathematical properties of Fourier transforms and the experimental characteristics of diffraction phenomena are systematically brought together. An experimental realization of a particular case of the convolution theorem is displayed in details. (Author) [pt

Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

Energy Technology Data Exchange (ETDEWEB)

Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-07-19

This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performing a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.

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...

On Fourier re-expansions

OpenAIRE

Liflyand, E.

2012-01-01

We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.

All-optical signal processing of OTDM and OFDM signals based on time-domain optical fourier transformation

DEFF Research Database (Denmark)

Galili, Michael; Guan, Pengyu; Lillieholm, Mads

2017-01-01

In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed.......In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed....

Subwavelength Fourier-transform imaging without a lens or a beamsplitter

International Nuclear Information System (INIS)

Liu Rui-Feng; Yuan Xin-Xing; Fang Yi-Zhen; Zhang Pei; Zhou Yu; Gao Hong; Li Fu-Li

2014-01-01

The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device (CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments. Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Analysis by Fourier Transform Infrared (FTIR) of the gamma radiation effect on epoxy resin, used as solidification agent of radioactive wastes

International Nuclear Information System (INIS)

Liu, C.H.; Riella, H.G.; Guedes, S.M.L.

1995-01-01

The effects of gamma radiation on Epoxy resin, used as solidification agent of radioactive wastes, were studied by Fourier Transform Infrared (FTIR). The spectra showed no significant modifications on Epoxy resin functional groups (irradiated with dose from 0 to 1 MGy). Up to 1 MGy Epoxy resin did not oxidize, confirming the Epoxy good radiation strength. The presence of aromatic chain and amine group, mainly tertiary amine, give good radiolytic stability to the Epoxy, increasing the interest to use this material in nuclear facilities. (author). 3 refs, 2 figs

Description of the electron-hydrogen collision by the Coulomb Fourier transform method

International Nuclear Information System (INIS)

Levin, S.B.

2005-01-01

A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals

Fourier transform distribution function of relaxation times; application and limitations

NARCIS (Netherlands)

Boukamp, Bernard A.

2015-01-01

A simple Fourier transform (FT) method is presented for obtaining a Distribution Function of Relaxation Times (DFRT) for electrochemical impedance spectroscopy (EIS) data. By using a special data extension procedure the FT is performed over the range from -∞ ≤ lnω ≤ + ∞. The integration procedure is

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2007-01-01

A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

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

Science.gov (United States)

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

2011-02-10

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

New Atomic Data for Doubly Ionized Iron Group Atoms by High Resolution UV Fourier Transform Spectroscopy

Science.gov (United States)

Smith, Peter L.; Pickering, Juliet C.; Thorne, A. P.

2002-01-01

Currently available laboratory spectroscopic data of doubly ionized iron-group element were obtained about 50 years ago using spectrographs of modest dispersion, photographic plates, and eye estimates of intensities. The accuracy of the older wavelength data is about 10 mAngstroms at best, whereas wavelengths are now needed to an accuracy of 1 part in 10(exp 6) to 10(exp 7) (0.2 to 2 mAngstroms at 2000 Angstroms). The Fourier transform (FT) spectroscopy group at Imperial College, London, and collaborators at the Harvard College Observatory have used a unique VUV FT spectrometer in a program focussed on improving knowledge of spectra of many neutral and singly and doubly ionized, astrophysically important, iron group elements. Spectra of Fe II and Fe III have been recorded at UV and VUV wavelengths with signal-to-noise ratios of several hundred for the stronger lines. Wavelengths and energy levels for Fe III are an order of magnitude more accurate than previous work; analysis is close to completion. f-values for Fe II have been published.

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

Science.gov (United States)

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

2015-12-01

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

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.

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

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia.

Science.gov (United States)

Samsir, Sri A'jilah; Bunawan, Hamidun; Yen, Choong Chee; Noor, Normah Mohd

2016-09-01

In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600-3100 cm(-) (1) in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA) of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (South) were clustered together in one group while samples from Perak, Kedah, Penang, Selangor, Kelantan, and Terengganu (North and East Coast) were in another clustered group.

Tabletop single-shot extreme ultraviolet Fourier transform holography of an extended object.

Science.gov (United States)

Malm, Erik B; Monserud, Nils C; Brown, Christopher G; Wachulak, Przemyslaw W; Xu, Huiwen; Balakrishnan, Ganesh; Chao, Weilun; Anderson, Erik; Marconi, Mario C

2013-04-22

We demonstrate single and multi-shot Fourier transform holography with the use of a tabletop extreme ultraviolet laser. The reference wave was produced by a Fresnel zone plate with a central opening that allowed the incident beam to illuminate the sample directly. The high reference wave intensity allows for larger objects to be imaged compared to mask-based lensless Fourier transform holography techniques. We obtain a spatial resolution of 169 nm from a single laser pulse and a resolution of 128 nm from an accumulation of 20 laser pulses for an object ~11x11μm(2) in size. This experiment utilized a tabletop extreme ultraviolet laser that produces a highly coherent ~1.2 ns laser pulse at 46.9 nm wavelength.

Fourier transform-infrared spectroscopy as a diagnostic tool for mosquito coil smoke inhalation toxicity in Swiss Albino mice

Science.gov (United States)

Anusha, Chidambaram; Sankar, Renu; Varunkumar, Krishnamoorthy; Sivasindhuja, Gnanasambantham; Ravikumar, Vilwanathan

2017-12-01

The goal of this study is to establish Fourier transform-infrared (FTIR) spectroscopy as a diagnostic tool for allethrin-based mosquito coil smoke inhalation induced toxicity in mice. Primarily, we confirmed mosquito coil smoke inhalation toxicity in mice via reduced the body, organ weight and major vital organ tissue morphological structure changes. Furthermore, FTIR spectra was collected from control and mosquito coil smoke inhalation (8 h per day for 30 days) mice various tissues like liver, kidney, lung, heart and brain, to investigate the functional groups and their corresponding biochemical content variations. The FTIR spectra result shown major bio macromolecules such as protein and lipid functional peaks were shifted (decreased) in the mosquito coil smoke inhalation group as compared to control. The drastic peak shift was noticed in the liver, kidney followed by lung and brain. It is therefore concluded that the FTIR spectroscopy can be a successful detection tool in mosquito coil smoke inhalation toxicity.

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.

Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles

International Nuclear Information System (INIS)

Alt, E.O.; Levin, S.B.; Yakovlev, S.L.

2004-01-01

A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the 'Coulomb representation'. Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable

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

Science.gov (United States)

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

2012-08-30

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

Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

KAUST Repository

Lin, Sian-Jheng

2016-09-13

In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.

Fourier Transform Near Infrared Microspectroscopy, Infrared Chemical Imaging, High-Resolution Nuclear Magnetic Resonance and Fluorescence Microspectroscopy Detection of Single Cancer Cells and Single Viral Particles

CERN Document Server

Baianu,I C; Hofmann, N E; Korban, S S; Lozano, P; You, T

2004-01-01

Single Cancer Cells from Human tumors are being detected and imaged by Fourier Transform Infrared (FT-IR), Fourier Transform Near Infrared (FT-NIR)Hyperspectral Imaging and Fluorescence Correlation Microspectroscopy. The first FT-NIR chemical, microscopic images of biological systems approaching one micron resolution are here reported. Chemical images obtained by FT-NIR and FT-IR Microspectroscopy are also presented for oil in soybean seeds and somatic embryos under physiological conditions. FT-NIR spectra of oil and proteins were obtained for volumes as small as two cubic microns. Related, HR-NMR analyses of oil contents in somatic embryos as well as 99% accurate calibrations are also presented here with nanoliter precision. Such high-resolution, 400 MHz H-1 NMR analyses allowed the selection of mutagenized embryos with higher oil content (e.g. >~20%) compared to the average levels in non-mutagenized control embryos. Moreover, developmental changes in single soybean seeds and/or somatic embryos may be monito...

Identification of Spectral Regions for Quantification of Red Wine Tannins with Fourier Transform Mid-Infrared Spectroscopy

DEFF Research Database (Denmark)

Jensen, Jacob Skibsted; Egebo, Max; Meyer, Anne S.

2008-01-01

Accomplishment of fast tannin measurements is receiving increased interest as tannins are important for the mouthfeel and color properties of red wines. Fourier transform mid-infrared spectroscopy allows fast measurement of different wine components, but quantification of tannins is difficult due...... to interferences from spectral responses of other wine components. Four different variable selection tools were investigated for the identification of the most important spectral regions which would allow quantification of tannins from the spectra using partial least-squares regression. The study included...... to be particularly important for tannin quantification. The spectral regions identified from the variable selection methods were used to develop calibration models. All four variable selection methods identified regions that allowed an improved quantitative prediction of tannins (RMSEP = 69−79 mg of CE/L; r = 0...

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.)

Characterization of polyesters by matrix-assisted laser desorption/ionization and Fourier transform mass spectrometry.

Science.gov (United States)

Mize, Todd H; Simonsick, William J; Amster, I Jonathan

2003-01-01

Two homopolyesters, poly(neopentyl glycol-alt-isophthalic acid) and poly(hexanediol-alt-azelaic acid), and two copolyesters, poly(dipropoxylated bisphenol-A-alt-(isophthalic acid-co-adipic acid)) and poly(neopentyl glycol-alt-(adipic acid-co-isophthalic acid)) were analyzed by internal source matrix assisted laser desorption/ionization Fourier transform mass spectrometry (MALDI-FTMS). The high resolution and high mass accuracy provided by FTMS greatly facilitate the characterization of the polyester and copolyester samples. Isobaric resolution allows the ion abundances of overlapping isotopic envelopes to be assessed. Repeat units were confirmed and end functionality assigned. Single shot mass spectra of the entire polymeric distribution demonstrate that the dynamic range of this internal MALDI source instrument and the analyzer cell exceeds performance of those previously reported for higher field instruments. Corrections of space charge mass shift effects are demonstrated for the analytes using an external calibrant and (subsequent to confirmation of structure) via internal calibration which removes ambiguity due to space charge differences in calibrant and analyte spectra. Capillary gel permeation chromatography was used to prepare low polydispersity samples from a high polydispersity polyester, improving the measurement of molecular weight distribution two-fold while retaining the benefits of high resolution mass spectrometry for elucidation of oligomer identity.

Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

Science.gov (United States)

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

2010-01-01

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

Application of fast Fourier transform in thermo-magnetic convection analysis

International Nuclear Information System (INIS)

Pyrda, L

2014-01-01

Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·10 5 and 1.86·10 6 with thermo-magnetic Rayleigh numbers up to 1.8·10 8 and 4.5·10 8 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.

Teaching stable two-mirror resonators through the fractional Fourier transform

International Nuclear Information System (INIS)

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

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.

Magneto-sensor circuit efficiency incremented by Fourier-transformation

KAUST Repository

Talukdar, Abdul Hafiz Ibne; Useinov, Arthur; Hussain, Muhammad Mustafa

2011-01-01

In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.

Magneto-sensor circuit efficiency incremented by Fourier-transformation

KAUST Repository

Talukdar, Abdul Hafiz Ibne

2011-10-01

In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

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

2013-01-01

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

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

Science.gov (United States)

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

Solving singular convolution equations using the inverse fast Fourier transform

Czech Academy of Sciences Publication Activity Database

Krajník, E.; Montesinos, V.; Zizler, P.; Zizler, Václav

2012-01-01

Roč. 57, č. 5 (2012), s. 543-550 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular convolution equations * fast Fourier transform * tempered distribution Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/m8437t3563214048/

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

Application of fast Fourier transform cross-correlation and mass spectrometry data for accurate alignment of chromatograms.

Science.gov (United States)

Zheng, Yi-Bao; Zhang, Zhi-Min; Liang, Yi-Zeng; Zhan, De-Jian; Huang, Jian-Hua; Yun, Yong-Huan; Xie, Hua-Lin

2013-04-19

Chromatography has been established as one of the most important analytical methods in the modern analytical laboratory. However, preprocessing of the chromatograms, especially peak alignment, is usually a time-consuming task prior to extracting useful information from the datasets because of the small unavoidable differences in the experimental conditions caused by minor changes and drift. Most of the alignment algorithms are performed on reduced datasets using only the detected peaks in the chromatograms, which means a loss of data and introduces the problem of extraction of peak data from the chromatographic profiles. These disadvantages can be overcome by using the full chromatographic information that is generated from hyphenated chromatographic instruments. A new alignment algorithm called CAMS (Chromatogram Alignment via Mass Spectra) is present here to correct the retention time shifts among chromatograms accurately and rapidly. In this report, peaks of each chromatogram were detected based on Continuous Wavelet Transform (CWT) with Haar wavelet and were aligned against the reference chromatogram via the correlation of mass spectra. The aligning procedure was accelerated by Fast Fourier Transform cross correlation (FFT cross correlation). This approach has been compared with several well-known alignment methods on real chromatographic datasets, which demonstrates that CAMS can preserve the shape of peaks and achieve a high quality alignment result. Furthermore, the CAMS method was implemented in the Matlab language and available as an open source package at http://www.github.com/matchcoder/CAMS. Copyright © 2013. Published by Elsevier B.V.

Valuation of European Call Option via Inverse Fourier Transform

Directory of Open Access Journals (Sweden)

Rubenis Oskars

2017-12-01

Full Text Available Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.

Efficient estimation of burst-mode LDA power spectra

DEFF Research Database (Denmark)

Velte, Clara Marika; George, William K

2010-01-01

the velocity bias effects. Residence time weighting should also be used to compute velocity spectra. The residence time-weighted direct Fourier transform can, however, be computationally heavy, especially for the large data sets needed to eliminate finite time window effects and given the increased...

Noise figure of amplified dispersive Fourier transformation

International Nuclear Information System (INIS)

Goda, Keisuke; Jalali, Bahram

2010-01-01

Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.

Functional Fourier transforms and the loop equation

International Nuclear Information System (INIS)

Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.

1986-01-01

The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables

A high-resolution Fourier Transform Spectrometer for planetary spectroscopy

Science.gov (United States)

Cruikshank, D. P.; Sinton, W. M.

1973-01-01

The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.

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.

Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer

Energy Technology Data Exchange (ETDEWEB)

Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

1993-10-01

We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

Science.gov (United States)

Singh, Iqbal

2008-01-01

To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

Correcting attenuated total reflection-fourier transform infrared spectra for water vapor and carbon dioxide

DEFF Research Database (Denmark)

Bruun, Susanne Wrang; Kohler, Achim; Adt, Isabelle

2006-01-01

an absorption band from either water vapor or CO(2). From two calibration data sets, gas model spectra were estimated in each of the four spectral regions, and these model spectra were applied for correction of gas absorptions in two independent test sets (spectra of aqueous solutions and a yeast biofilm (C...... of the growing yeast biofilm, the gas correction revealed otherwise hidden variations of relevance for modeling the growth dynamics. As the presented method improved the interpretation of the principle component analysis (PCA) models, it has proven to be a valuable tool for filtering atmospheric variation in ATR...

Combining Fourier phase encoding and broadband inversion toward J-edited spectra

Science.gov (United States)

Lin, Yulan; Guan, Quanshuai; Su, Jianwei; Chen, Zhong

2018-06-01

Nuclear magnetic resonance (NMR) spectra are often utilized for gathering accurate information relevant to molecular structures and composition assignments. In this study, we develop a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks, and combine it with a pure shift experiments (PSYCHE) based J-modulated scheme, providing simple 2D J-edited spectra for accurate measurement of scalar coupling networks. Chemical shifts and J coupling constants of protons coupled to the specific protons are demonstrated along the F2 and F1 dimensions, respectively. Polychromatic pulses by Fourier phase encoding were performed to simultaneously detect several coupling networks. Proton-proton scalar couplings are chosen by a polychromatic pulse and a PSYCHE element. Axis peaks and unwanted couplings are complete eradicated by incorporating a selective COSY block as a preparation period. The theoretical principles and the signal processing procedure are laid out, and experimental observations are rationalized on the basis of theoretical analyses.

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

Science.gov (United States)

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

Improved method of generating bit reversed numbers for calculating fast fourier transform

Digital Repository Service at National Institute of Oceanography (India)

Suresh, T.

Fast Fourier Transform (FFT) is an important tool required for signal processing in defence applications. This paper reports an improved method for generating bit reversed numbers needed in calculating FFT using radix-2. The refined algorithm takes...

Spectrogram analysis of selected tremor signals using short-time Fourier transform and continuous wavelet transform

Directory of Open Access Journals (Sweden)

D. Seidl

1999-06-01

Full Text Available Among a variety of spectrogram methods Short-Time Fourier Transform (STFT and Continuous Wavelet Transform (CWT were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.

The discrete Fourier transform theory, algorithms and applications

CERN Document Server

Sundaraajan, D

2001-01-01

This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and

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

Science.gov (United States)

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

2014-01-10

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

Simple example of track finding by Fourier transform and possibilities for vector or optical processors

International Nuclear Information System (INIS)

Underwood, D.

1986-01-01

Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs

All-optical WDM Regeneration of DPSK Signals using Optical Fourier Transformation and Phase Sensitive Amplification

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian

2015-01-01

We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Directory of Open Access Journals (Sweden)

Salman Ahmad

2014-06-01

Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

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

Directory of Open Access Journals (Sweden)

Pablo Soto-Quiros

2015-01-01

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

Fourier transform Raman spectroscopic characterisation of cells of the plant-associated soil bacterium Azospirillum brasilense Sp7

Science.gov (United States)

Kamnev, A. A.; Tarantilis, P. A.; Antonyuk, L. P.; Bespalova, L. A.; Polissiou, M. G.; Colina, M.; Gardiner, P. H. E.; Ignatov, V. V.

2001-05-01

Structural and compositional features of bacterial cell samples and of lipopolysaccharide-protein complex isolated from the cell surface of the plant-growth-promoting rhizobacterium Azospirillum brasilense (wild-type strain Sp7) were characterised using Fourier transform (FT) Raman spectroscopy. The structural spectroscopic information obtained is analysed and considered together with analytical data on the content of metal cations (Co 2+, Cu 2+ and Zn 2+) in the bacterial cells grown in a standard medium as well as in the presence of each of the cations (0.2 mM). The latter, being taken up by bacterial cells from the culture medium in significant amounts, were shown to induce certain metabolic changes in the bacterium revealed in FT-Raman spectra, which is discussed from the viewpoint of bacterial response to environmental stresses.

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

Science.gov (United States)

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

2017-05-01

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

Study of tissue engineered bone nodules by Fourier transform infrared spectroscopy.

Science.gov (United States)

Aydin, Halil Murat; Hu, Bin; Suso, Josep Sulé; El Haj, Alicia; Yang, Ying

2011-02-21

The key criteria for assessing the success of bone tissue engineering are the quality and quantity of the produced minerals within the cultured constructs. The accumulation of calcium ions and inorganic phosphates in culture medium serves as nucleating agents for the formation of hydroxyapatite, which is the main inorganic component of bone. Bone nodule formation is one of the hallmarks of mineralization in such cell cultures. In this study, we developed a new two-step procedure to accelerate bone formation in which mouse bone cell aggregates were produced first on various chemically treated non-adhesive substrates. After this step, the bone cells' growth and mineralization were followed in conventional culture plates. The number and size of cell aggregates were studied with light microscopy. The minerals' formation in the form of nodules produced by the cell aggregates and the bone crystal quality were studied with Fourier Transform Infrared (FTIR) spectroscopy. The FTIR spectra of the ash specimens (mineral phase only) from thermal gravimetric analysis (TGA) provided valuable information of the quality of the minerals. The υ(4) PO(4) region (550-650 cm(-1)), which reveals apatitic and non-apatitic HPO(4) or PO(4) environments, and phosphate region (910-1180 cm(-1)) were examined for the minerals produced in the form of nodules. The peak position and intensity of the spectra demonstrate that the quality of the bone produced by cell aggregates, especially from the bigger ones, which were formed on Plunoric treated substrates, exhibit a composition more similar to that of native bone. This work establishes a new protocol for high quality bone formation and characterization, with the potential to be applied to bone tissue engineering.

An OTDM-To-WDM Converter Using Optical Fourier Transformation

OpenAIRE

Khin Su Myat Min; Zaw Myo Lwin; Hla Myo Tun

2015-01-01

We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements ar...

Fast Fourier transformation results from gamma-ray burst profiles

Science.gov (United States)

Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.

1992-01-01

Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.

Fast Fourier transformation in vibration analysis of physically active systems

International Nuclear Information System (INIS)

Hafeez, T.; Amir, M.; Farooq, U.; Day, P.

2003-01-01

Vibration of all physical systems may be expressed as the summation of an infinite number of sine and cosine terms known as Fourier series. The basic vibration analysis tool used is the frequency 'spectrum' (a graph of vibration where the amplitude of vibration is plotted against frequency). When a particular rotating component begins to fail, its vibration tends to increase. Spectra graphs are powerful diagnostic tool for detecting components' degradation. Spectra obtained with accelerometers located at the various locations on the components and their analysis in practice from rotating machines enable early detecting of incipient failure. Consequence of unexpected failure can be catastrophic and costly. This study provides basis to relate defective component by its constituent frequencies and then to the known discrete frequency of its 'signature' or 'thumbprint' to predict and verify the sustained dynamic behavior of machine designs harmful effects of forced vibration. The spectra for gearbox of a vane with teeth damaged fault are presented here which signified the importance of FFT analysis as diagnostic tool. This may be helpful to predictive maintenance of the machinery. (author)

Determination of Oxidized Phosphatidylcholines by Hydrophilic Interaction Liquid Chromatography Coupled to Fourier Transform Mass Spectrometry

Directory of Open Access Journals (Sweden)

Pia Sala

2015-04-01

Full Text Available A novel liquid chromatography-mass spectrometry (LC-MS approach for analysis of oxidized phosphatidylcholines by an Orbitrap Fourier Transform mass spectrometer in positive electrospray ionization (ESI coupled to hydrophilic interaction liquid chromatography (HILIC was developed. This method depends on three selectivity criteria for separation and identification: retention time, exact mass at a resolution of 100,000 and collision induced dissociation (CID fragment spectra in a linear ion trap. The process of chromatography development showed the best separation properties with a silica-based Kinetex column. This type of chromatography was able to separate all major lipid classes expected in mammalian samples, yielding increased sensitivity of oxidized phosphatidylcholines over reversed phase chromatography. Identification of molecular species was achieved by exact mass on intact molecular ions and CID tandem mass spectra containing characteristic fragments. Due to a lack of commercially available standards, method development was performed with copper induced oxidation products of palmitoyl-arachidonoyl-phosphatidylcholine, which resulted in a plethora of lipid species oxidized at the arachidonoyl moiety. Validation of the method was done with copper oxidized human low-density lipoprotein (LDL prepared by ultracentrifugation. In these LDL samples we could identify 46 oxidized molecular phosphatidylcholine species out of 99 possible candidates.

Quality assessment of pharmaceutical tablet samples using Fourier transform near infrared spectroscopy and multivariate analysis

Science.gov (United States)

Kandpal, Lalit Mohan; Tewari, Jagdish; Gopinathan, Nishanth; Stolee, Jessica; Strong, Rick; Boulas, Pierre; Cho, Byoung-Kwan

2017-09-01

Determination of the content uniformity, assessed by the amount of an active pharmaceutical ingredient (API), and hardness of pharmaceutical materials is important for achieving a high-quality formulation and to ensure the intended therapeutic effects of the end-product. In this work, Fourier transform near infrared (FT-NIR) spectroscopy was used to determine the content uniformity and hardness of a pharmaceutical mini-tablet and standard tablet samples. Tablet samples were scanned using an FT-NIR instrument and tablet spectra were collected at wavelengths of 1000-2500 nm. Furthermore, multivariate analysis was applied to extract the relationship between the FT-NIR spectra and the measured parameters. The results of FT-NIR spectroscopy for API and hardness prediction were as precise as the reference high-performance liquid chromatography and mechanical hardness tests. For the prediction of mini-tablet API content, the highest coefficient of determination for the prediction (R2p) was found to be 0.99 with a standard error of prediction (SEP) of 0.72 mg. Moreover, the standard tablet hardness measurement had a R2p value of 0.91 with an SEP of 0.25 kg. These results suggest that FT-NIR spectroscopy is an alternative and accurate nondestructive measurement tool for the detection of the chemical and physical properties of pharmaceutical samples.

Experimental demonstration of an OFDM receiver based on a silicon-nanophot onic discrete Fourier transform filter

DEFF Research Database (Denmark)

Da Ros, Francesco; Nolle, Markus; Meuer, C.

2014-01-01

We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit.......We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit....

Aliasless fresnel transform image reconstruction in phase scrambling fourier transform technique by data interpolation

International Nuclear Information System (INIS)

Yamada, Yoshifumi; Liu, Na; Ito, Satoshi

2006-01-01

The signal in the Fresnel transform technique corresponds to a blurred one of the spin density image. Because the amplitudes of adjacent sampled signals have a high interrelation, the signal amplitude at a point between sampled points can be estimated with a high degree of accuracy even if the sampling is so coarse as to generate aliasing in the reconstructed images. In this report, we describe a new aliasless image reconstruction technique in the phase scrambling Fourier transform (PSFT) imaging technique in which the PSFT signals are converted to Fresnel transform signals by multiplying them by a quadratic phase term and are then interpolated using polynomial expressions to generate fully encoded signals. Numerical simulation using MR images showed that almost completely aliasless images are reconstructed by this technique. Experiments using ultra-low-field PSFT MRI were conducted, and aliasless images were reconstructed from coarsely sampled PSFT signals. (author)

An algorithm for the basis of the finite Fourier transform

Science.gov (United States)

Santhanam, Thalanayar S.

1995-01-01

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

A fast Fourier transform program for the deconvolution of IN10 data

International Nuclear Information System (INIS)

Howells, W.S.

1981-04-01

A deconvolution program based on the Fast Fourier Transform technique is described and some examples are presented to help users run the programs and interpret the results. Instructions are given for running the program on the RAL IBM 360/195 computer. (author)

Multicomplementary operators via finite Fourier transform

International Nuclear Information System (INIS)

Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de

2005-01-01

A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail

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.

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

Science.gov (United States)

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

Fourier transform and mean quadratic variation of Bernoulli convolution on homogeneous Cantor set

Energy Technology Data Exchange (ETDEWEB)

Yu Zuguo E-mail: yuzg@hotmail.comz.yu

2004-07-01

For the Bernoulli convolution on homogeneous Cantor set, under some condition, it is proved that the mean quadratic variation and the average of Fourier transform of this measure are bounded above and below.

Live face detection based on the analysis of Fourier spectra

Science.gov (United States)

Li, Jiangwei; Wang, Yunhong; Tan, Tieniu; Jain, Anil K.

2004-08-01

Biometrics is a rapidly developing technology that is to identify a person based on his or her physiological or behavioral characteristics. To ensure the correction of authentication, the biometric system must be able to detect and reject the use of a copy of a biometric instead of the live biometric. This function is usually termed "liveness detection". This paper describes a new method for live face detection. Using structure and movement information of live face, an effective live face detection algorithm is presented. Compared to existing approaches, which concentrate on the measurement of 3D depth information, this method is based on the analysis of Fourier spectra of a single face image or face image sequences. Experimental results show that the proposed method has an encouraging performance.

Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses

Science.gov (United States)

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

2016-01-01

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

Vector Radix 2 × 2 Sliding Fast Fourier Transform

Directory of Open Access Journals (Sweden)

Keun-Yung Byun

2016-01-01

Full Text Available The two-dimensional (2D discrete Fourier transform (DFT in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT algorithm based on the vector radix (VR 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms

International Nuclear Information System (INIS)

Prakash, A; Lebensohn, R A

2009-01-01

In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations. Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version

Advances in hyperspectral remote sensing I: The visible Fourier transform hyperspectral imager

Directory of Open Access Journals (Sweden)

J. Bruce Rafert

2015-05-01

Full Text Available We discuss early hyperspectral research and development activities during the 1990s that led to the deployment of aircraft and satellite payloads whose heritage was based on the use of visible, spatially modulated, imaging Fourier transform spectrometers, beginning with early experiments at the Florida Institute of Technology, through successful launch and deployment of the Visible Fourier Transform Hyperspectral Imager on MightySat II.1 on 19 July 2000. In addition to a brief chronological overview, we also discuss several of the most interesting optical engineering challenges that were addressed over this timeframe, present some as-yet un-exploited features of field-widened (slit-less SMIFTS instruments, and present some images from ground-based, aircraft-based and satellite-based instruments that helped provide the impetus for the proliferation and development of entire new families of instruments and countless new applications for hyperspectral imaging.

Quadrature detection for the separation of the signals of positive and negative ions in fourier transform ion cyclotron resonance mass spectrometry

International Nuclear Information System (INIS)

Schweikhard, Lutz; Drader, Jared J.; Shi, Stone D.-H.; Hendrickson, Christopher L.; Marshall, Alan G.

2002-01-01

Positive and negative ions may be confined simultaneously in a nested open cylindrical Malmberg-Penning trap. However, ion charge sign cannot be distinguished by conventional dipolar (linearly-polarized) detection with a single pair of opposed electrodes. Here, the signals from each of two orthogonal pairs of opposed detection electrodes are acquired simultaneously and stored as real and imaginary parts of mathematically complex data. Complex Fourier transformation yields separate spectra for positive and negative ions. For a fullerene sample, experimental quadrature detection yields C 60 + and C 60 - signals separated by ∼1440 u rather than by the mass of two electrons, ∼0.001 u in conventional dipolar detection

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

Science.gov (United States)

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

2015-03-01

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

Capillary supercritical fluid chromatography - Fourier transform infrared spectrometry

International Nuclear Information System (INIS)

Olesik, S.V.; French, S.B.; Movotny, M.

1984-01-01

One of the most demanding tasks asked of an analytical chemist today is to separate and identify the components of a nonvolatile complex mixture. An efficient separation technique combined with a universal detector that provides structural information, therefore, would be a great asset to analytical chemists. Capillary supercritical fluid chromatography (SFC) - Fourier transform infrared spectrometry (FTIR) shows great potential for being such a technique. SFC-FTIR shows great potential as a very powerful technique for separation and identification of thermally labile and nonvolatile compounds. Research is continuing in these labs to further optimize the technique. 2 refs

An OTDM-To-WDM Converter Using Optical Fourier Transformation

Directory of Open Access Journals (Sweden)

Khin Su Myat Min

2015-08-01

Full Text Available We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements are expressed.

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 Transform Infrared Absorption Spectroscopy for Quantitative Analysis of Gas Mixtures at Low Temperatures for Homeland Security Applications.

Science.gov (United States)

Meier, D C; Benkstein, K D; Hurst, W S; Chu, P M

2017-05-01

Performance standard specifications for point chemical vapor detectors are established in ASTM E 2885-13 and ASTM E 2933-13. The performance evaluation of the detectors requires the accurate delivery of known concentrations of the chemical target to the system under test. Referee methods enable the analyte test concentration and associated uncertainties in the analyte test concentration to be validated by independent analysis, which is especially important for reactive analytes. This work extends the capability of a previously demonstrated method for using Fourier transform infrared (FT-IR) absorption spectroscopy for quantitatively evaluating the composition of vapor streams containing hazardous materials at Acute Exposure Guideline Levels (AEGL) to include test conditions colder than laboratory ambient temperatures. The described method covers the use of primary reference spectra to establish analyte concentrations, the generation of secondary reference spectra suitable for measuring analyte concentrations under specified testing environments, and the use of additional reference spectra and spectral profile strategies to mitigate the uncertainties due to impurities and water condensation within the low-temperature (7 °C, -5 °C) test cell. Important benefits of this approach include verification of the test analyte concentration with characterized uncertainties by in situ measurements co-located with the detector under test, near-real-time feedback, and broad applicability to toxic industrial chemicals.

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

Science.gov (United States)

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

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

Time lens based optical fourier transformation for advanced processing of spectrally-efficient OFDM and N-WDM signals

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Morioka, Toshio

2016-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals.......We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals....

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

Science.gov (United States)

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

2013-12-01

typically achieve very high wavelength resolution, the intended application of our instrument (spectroscopic investigation of Europa's surface) places higher emphasis on the greater wavelength band sensitivity in the 2-12 μm range provided by a rotating refractor design. The instrument's embedded microcontroller is implemented on a flight-qualified VIRTEX-5 FPGA with the aim of sampling the instrument's detector and optical rotary encoder in order to construct an interferogram. Subsequent signal processing, including a Fast Fourier Transform (FFT), noise reduction/averaging, and spectral calibration techniques are applied in real-time to compose the sample spectrum. Deployment of an FPGA eliminates the instrument's need to share computing resources with the main spacecraft computer and takes advantage of the low power consumption and high-throughput hardware parallelism intrinsic to FPGA applications. This parallelism facilitates the high speed, low latency sampling/signal processing critical to instrument precision with minimal power consumption to achieve highly sensitive spectra within the constraints of available spacecraft resources. The instrument is characterized in simulated space-flight conditions and we demonstrate that this technology is capable of meeting the strict volume, sensitivity, and power consumption requirements for implementation in scientific space systems.

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.

Specification of the Fast Fourier Transform algorithm as a term rewriting system

NARCIS (Netherlands)

Rodenburg, P.H.; Hoekzema, D.J.

1987-01-01

We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of

Superexponentially damped Vlasov plasma oscillations in the Fourier transformed velocity space

International Nuclear Information System (INIS)

Sedlacek, Z.; Nocera, L.

2002-01-01

The Landau (exponentially) damped solutions of the Vlasov-Poisson equation Fourier transformed with respect to velocity are genuine eigenmodes corresponding to complex eigenvalues. In addition there exist solutions decaying faster than exponentially which exhibit no oscillatory behaviour. A new characterization is given of the initial conditions that give rise to these solutions together with a numerical demonstration

Fourier-transform ghost imaging with pure far-field correlated thermal light

International Nuclear Information System (INIS)

Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming

2007-01-01

Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed

Origin of multiple periodicities in the Fourier power spectra of the Plasmodium falciparum genome

Directory of Open Access Journals (Sweden)

Nunes Miriam CS

2011-12-01

Full Text Available Abstract Background Fourier transforms and their associated power spectra are used for detecting periodicities and protein-coding genes and is generally regarded as a well established technique. Many of the periodicities which have been found with this method are quite well understood such as the periodicity of 3 nt which is associated to codon usage. But what is the origin of the peculiar frequency multiples k/21 which were reported for a tiny section of chromosome 2 in P. falciparum? Are these present in other chromosomes and perhaps in related organisms? And how should we interpret fractional periodicities in genomes? Results We applied the binary indicator power spectrum to all chromosomes of P. falciparum, and found that the frequency overtones k/21 are present only in non-coding sections. We did not find such frequency overtones in any other related genomes. Furthermore, the frequency overtones were identified as artifacts of the way the genome is encoded into a numerical sequence, that is, they are frequency aliases. By choosing a different way to encode the sequence the overtones do not appear. In view of these results, we revisited early applications of this technique to proteins where frequency overtones were reported. Conclusions Some authors hinted recently at the possibility of mapping artifacts and frequency aliases in power spectra. However, in the case of P. falciparum the frequency aliases are particularly strong and can mask the 1/3 frequency which is used for gene detecting. This shows that albeit being a well known technique, with a long history of application in proteins, few researchers seem to be aware of the problems represented by frequency aliases.

Quantum Fourier transform, Heisenberg groups and quasi-probability distributions

International Nuclear Information System (INIS)

Patra, Manas K; Braunstein, Samuel L

2011-01-01

This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.

Instrumental concept and preliminary performances of SIFTI: static infrared fourier transform interferometer

Science.gov (United States)

Hébert, Philippe-Jean; Cansot, E.; Pierangelo, C.; Buil, C.; Bernard, F.; Loesel, J.; Trémas, T.; Perrin, L.; Courau, E.; Casteras, C.; Maussang, I.; Simeoni, D.

2017-11-01

The SIFTI (Static Infrared Fourier Transform Interferometer) instrument aims at supporting an important part in a mission for atmospheric pollution sounding from space, by providing high spectral resolution and high Signal to Noise Ratio spectra of the atmosphere. They will allow to resolve tropospheric profiles of ozone (03) and carbon monoxide (C0), especially down to the planetary boundary layer (PBL), an altitude region of very high interest, though poorly monitored to date, for air quality and pollution monitoring. The retrieved profile of ozone, resp. C0, will contain 5 to 7, resp. 2.5 to 4, independent pieces of information. The French space agency CNES (Centre National d'Etudes Spatiales) has proposed and is studying an instrument concept for SIFTI based on a static interferometer, where the needed optical path are generated by a pair of crossed staircase fixed mirrors (replacing the moving reflector of dynamic Fourier transform interferometers like IASI or MIPAS). With the SIFTI design, a very high spectral resolution ( 0.1 cm-1 apodised) is achieved in a very compact optical setup, allowing a large throughput, hence a high SNR. The measurements are performed in the 9.5 μm band for 03 and in the 4.6 μm band for C0. The science return of the sounder can be further increased if an "intelligent pointing" process is implemented. This consists in combining the TIR sounder with a companion TIR imager, providing information on the cloud coverage in the next observed scene. 0nboard, real-time analysis of the IR image is used to command the sounder staring mirror to cloud free areas, which will maximize the probability for probing down to the surface. After the first part of the phase A, the architecture of SIFTI was studied as a trade-off between performance and resource budget. We review the main architecture and functional choices, and their advantages. The preliminary instrument concept is then presented in its main aspects and in terms of main subsystem

USING FOURIER TRANSFORM INFRARED (FTIR TO CHARACTERIZE TSUNAMI DEPOSITS IN NEAR-SHORE AND COASTAL WATERS OF THAILAND

Directory of Open Access Journals (Sweden)

S. Pongpiachan

2013-01-01

Full Text Available Understanding the tsunami cycle requires a simple method for identification of tsunami backwash deposits. This study investigates Fourier transform infrared (FTIR spectroscopy followed by careful analysis of variance (ANOVA, Gaussian distribution, hierarchical cluster analysis (HCA and principal component analysis (PCA for the discrimination of typical marine sediments and tsunami backwash deposits. In order to test the suitability of FTIR spectra as innovative methods for classifications of tsunami deposits, typical marine sediments and terrestrial soils were classified into three zones, namely zone-1 (i.e. typical marine sediments, zone-2 (i.e. including tsunami backwash deposits and zone-3 (i.e. coastal terrestrial soils. HCA was performed to group the spectra according to their spectral similarity in a dendrogram and successfully separate FTIR spectra of all three sampling zones into two main clusters with five sub-clusters. The simplicifolious (i.e. single-leafed type of dendrogram was observed with the strong dissimilarity of terrestrial components in subcluster- 5. Graphical displays of PC1 vs PC2 highlight the prominent features of zone-1, which is explicitly different from those of zone-2 and zone-3. The acceptable discrimination of typical marine sediments and tsunami backwash deposits, even six years after the tsunami on Boxing Day 2004, dramatically demonstrates the potential of the method for the identification of paleotsunami.

Fourier transform infrared spectroscopy, a new method for rapid determination of total organic and inorganic carbon and biogenic silica concentration in lake sediments

DEFF Research Database (Denmark)

Rosén, Peter; Vogel, Hendrik; Cunningham, Laura

2010-01-01

We demonstrate the use of Fourier transform infrared spectroscopy (FTIRS) to make quantitative measures of total organic carbon (TOC), total inorganic carbon (TIC) and biogenic silica (BSi) concentrations in sediment. FTIRS is a fast and cost-effective technique and only small sediment samples...... varied between r = 0.84-0.99 for TOC, r = 0.85-0.99 for TIC, and r = 0.68-0.94 for BSi. Because FTIR spectra contain information on a large number of both inorganic and organic components, there is great potential for FTIRS to become an important tool in paleolimnology....

Analysis of Chuanxiong Rhizoma and its active components by Fourier transform infrared spectroscopy combined with two-dimensional correlation infrared spectroscopy.

Science.gov (United States)

Guo, Yizhen; Lv, Beiran; Wang, Jingjuan; Liu, Yang; Sun, Suqin; Xiao, Yao; Lu, Lina; Xiang, Li; Yang, Yanfang; Qu, Lei; Meng, Qinghong

2016-01-15

As complicated mixture systems, active components of Chuanxiong Rhizoma are very difficult to identify and discriminate. In this paper, the macroscopic IR fingerprint method including Fourier transform infrared spectroscopy (FT-IR), the second derivative infrared spectroscopy (SD-IR) and two-dimensional correlation infrared spectroscopy (2DCOS-IR), was applied to study and identify Chuanxiong raw materials and its different segmented production of HPD-100 macroporous resin. Chuanxiong Rhizoma is rich in sucrose. In the FT-IR spectra, water eluate is more similar to sucrose than the powder and the decoction. Their second derivative spectra amplified the differences and revealed the potentially characteristic IR absorption bands and combined with the correlation coefficient, concluding that 50% ethanol eluate had more ligustilide than other eluates. Finally, it can be found from 2DCOS-IR spectra that proteins were extracted by ethanol from Chuanxiong decoction by HPD-100 macroporous resin. It was demonstrated that the above three-step infrared spectroscopy could be applicable for quick, non-destructive and effective analysis and identification of very complicated and similar mixture systems of traditional Chinese medicines. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Principles of Fourier analysis

CERN Document Server

Howell, Kenneth B

2001-01-01

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...

Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses

Directory of Open Access Journals (Sweden)

Lucy Lim

2016-01-01

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

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

Science.gov (United States)

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

2012-04-20

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

Fourier transform infrared difference spectroscopy of bacteriorhodopsin and its photoproducts regenerated with deuterated tyrosine

International Nuclear Information System (INIS)

Dollinger, G.; Eisenstein, L.; Lin, S.L.; Nakanishi, K.; Termini, J.

1986-01-01

Fourier transform infrared (FTIR) difference spectroscopy has been used to detect the vibrational modes due to tyrosine residues in the protein that change in position or intensity between light-adapted bacteriorhodopsin (LA) and other species, namely, the K and M intermediates and dark-adapted bacteriorhodopsin (DA). To aid in the identification of the bands that change in these various species, the FTIR spectra of the free amino acids Tyr-d0, Tyr-d2 ( 2 H at positions ortho to OH), and Tyr-d4 ( 2 H at positions ortho and meta to OH) were measured in H 2 O and D 2 O at low and high pH. The characteristic frequencies of the Tyr species obtained in this manner were then used to identify the changes in protonation state of the tyrosine residues in the various bacteriorhodopsin species. The two diagnostically most useful bands were the approximately 1480-cm-1 band of Tyr(OH)-d2 and the approximately 1277-cm-1 band of Tyr(O-)-d0. Mainly by observing the appearance or disappearance of these bands in the difference spectra of pigments incorporating the tyrosine isotopes, it was possible to identify the following: in LA, one tyrosine and one tyrosinate; in the K intermediate, two tyrosines; in the M intermediate, one tyrosine and one tyrosinate; and in DA, two tyrosines. Since these residues were observed in the difference spectra K/LA, M/LA, and DA/LA, they represent the tyrosine or tyrosinate groups that most likely undergo changes in protonation state due to the conversions. These changes are most likely linked to the proton translocation process of bacteriorhodopsin

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

Science.gov (United States)

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

2017-06-01

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

Flat-top pulse generation by the optical Fourier transform technique for ultrahigh speed signal processing

DEFF Research Database (Denmark)

Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

2009-01-01

This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super-Gaussian sp......This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super...