Application of fourier-transform infrared (ft-ir) spectroscopy for determination of total phenolics of freeze dried lemon juices

International Nuclear Information System (INIS)

Sherazi, S.T.H.; Bhutto, A.A.; Mehesar, S.A.

2017-01-01

A cost effective and environmentally safe analytical method for rapid assessment of total phenolic content (TPC) in freeze dried lemon juice samples was developed using transmission Fourier-transform infrared spectroscopy (FT-IR) in conjunction with chemometric techniques. Two types of calibrations i.e. simple Beer's law and partial least square (PLS) were applied to investigate most accurate calibration model based on region from1420 to 1330 cm-1. The better analytical performance was obtained by PLS technique coefficient of determination (R2), root mean square error of calibration (RMSEC) with the value of 0.999 and 0.00864, respectively. The results of TPC in freeze dried lemon juice samples obtained by transmission FT-IR were compared with TPC observed by Folin-Ciocalteu (FC) assay and found to be comparable. Outcomes of the present study indicate that transmission FT-IR spectroscopic approach could be used as an alternative approach in place of Folin-Ciocalteu (FC) assay which is expensive and time-consuming conventional chemical methods for determination of the total phenolic content of lemon fruits. (author)

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

Science.gov (United States)

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

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

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.

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....

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,...

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)

Fourier Transform Infrared Spectroscopy (FT-IR) and Simple Algorithm Analysis for Rapid and Non-Destructive Assessment of Developmental Cotton Fibers.

Science.gov (United States)

Liu, Yongliang; Kim, Hee-Jin

2017-06-22

With cotton fiber growth or maturation, cellulose content in cotton fibers markedly increases. Traditional chemical methods have been developed to determine cellulose content, but it is time-consuming and labor-intensive, mostly owing to the slow hydrolysis process of fiber cellulose components. As one approach, the attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy technique has also been utilized to monitor cotton cellulose formation, by implementing various spectral interpretation strategies of both multivariate principal component analysis (PCA) and 1-, 2- or 3-band/-variable intensity or intensity ratios. The main objective of this study was to compare the correlations between cellulose content determined by chemical analysis and ATR FT-IR spectral indices acquired by the reported procedures, among developmental Texas Marker-1 (TM-1) and immature fiber ( im ) mutant cotton fibers. It was observed that the R value, CI IR , and the integrated intensity of the 895 cm -1 band exhibited strong and linear relationships with cellulose content. The results have demonstrated the suitability and utility of ATR FT-IR spectroscopy, combined with a simple algorithm analysis, in assessing cotton fiber cellulose content, maturity, and crystallinity in a manner which is rapid, routine, and non-destructive.

Comparative investigation of Fourier transform infrared (FT-IR) spectroscopy and X-ray diffraction (XRD) in the determination of cotton fiber crystallinity.

Science.gov (United States)

Liu, Yongliang; Thibodeaux, Devron; Gamble, Gary; Bauer, Philip; VanDerveer, Don

2012-08-01

Despite considerable efforts in developing curve-fitting protocols to evaluate the crystallinity index (CI) from X-ray diffraction (XRD) measurements, in its present state XRD can only provide a qualitative or semi-quantitative assessment of the amounts of crystalline or amorphous fraction in a sample. The greatest barrier to establishing quantitative XRD is the lack of appropriate cellulose standards, which are needed to calibrate the XRD measurements. In practice, samples with known CI are very difficult to prepare or determine. In a previous study, we reported the development of a simple algorithm for determining fiber crystallinity information from Fourier transform infrared (FT-IR) spectroscopy. Hence, in this study we not only compared the fiber crystallinity information between FT-IR and XRD measurements, by developing a simple XRD algorithm in place of a time-consuming and subjective curve-fitting process, but we also suggested a direct way of determining cotton cellulose CI by calibrating XRD with the use of CI(IR) as references.

Chemical profiling and adulteration screening of Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation infrared (2D-IR) spectroscopy

Science.gov (United States)

Qu, Lei; Chen, Jian-bo; Zhang, Gui-Jun; Sun, Su-qin; Zheng, Jing

2017-03-01

As a kind of expensive perfume and valuable herb, Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy is employed to establish a simple and quick method for the adulteration screening of ALR. First, the principal chemical constituents of ALR are characterized by FT-IR spectroscopy at room temperature and two-dimensional correlation infrared (2D-IR) spectroscopy with thermal perturbation. Besides the common cellulose and lignin compounds, a certain amount of resin is the characteristic constituent of ALR. Synchronous and asynchronous 2D-IR spectra indicate that the resin (an unstable secondary metabolite) is more sensitive than cellulose and lignin (stable structural constituents) to the thermal perturbation. Using a certified ALR sample as the reference, the infrared spectral correlation threshold is determined by 30 authentic samples and 6 adulterated samples. The spectral correlation coefficient of an authentic ALR sample to the standard reference should be not less than 0.9886 (p = 0.01). Three commercial adulterated ALR samples are identified by the correlation threshold. Further interpretation of the infrared spectra of the adulterated samples indicates the common adulterating methods - counterfeiting with other kind of wood, adding ingredient such as sand to increase the weight, and adding the cheap resin such as rosin to increase the content of resin compounds. Results of this research prove that FT-IR spectroscopy can be used as a simple and accurate quality control method of ALR.

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

Optical Determination of Lead Chrome Green in Green Tea by Fourier Transform Infrared (FT-IR Transmission Spectroscopy.

Directory of Open Access Journals (Sweden)

Xiaoli Li

Full Text Available The potential of Fourier transform infrared (FT-IR transmission spectroscopy for determination of lead chrome green in green tea was investigated based on chemometric methods. Firstly, the qualitative analysis of lead chrome green in tea was performed based on partial least squares discriminant analysis (PLS-DA, and the correct rate of classification was 100%. And then, a hybrid method of interval partial least squares (iPLS regression and successive projections algorithm (SPA was proposed to select characteristic wavenumbers for the quantitative analysis of lead chrome green in green tea, and 19 wavenumbers were obtained finally. Among these wavenumbers, 1384 (C = C, 1456, 1438, 1419(C = N, and 1506 (CNH cm-1 were the characteristic wavenumbers of lead chrome green. Then, these 19 wavenumbers were used to build determination models. The best model was achieved by least squares support vector machine (LS-SVMalgorithm with high coefficient of determination and low root-mean square error of prediction set (R2p = 0.864 and RMSEP = 0.291. All these results indicated the feasibility of IR spectra for detecting lead chrome green in green tea.

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

Science.gov (United States)

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

2012-06-01

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

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

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

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

Science.gov (United States)

Debnath, Lokenath

2012-01-01

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

Chemical profiling and adulteration screening of Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation infrared (2D-IR) spectroscopy.

Science.gov (United States)

Qu, Lei; Chen, Jian-Bo; Zhang, Gui-Jun; Sun, Su-Qin; Zheng, Jing

2017-03-05

As a kind of expensive perfume and valuable herb, Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy is employed to establish a simple and quick method for the adulteration screening of ALR. First, the principal chemical constituents of ALR are characterized by FT-IR spectroscopy at room temperature and two-dimensional correlation infrared (2D-IR) spectroscopy with thermal perturbation. Besides the common cellulose and lignin compounds, a certain amount of resin is the characteristic constituent of ALR. Synchronous and asynchronous 2D-IR spectra indicate that the resin (an unstable secondary metabolite) is more sensitive than cellulose and lignin (stable structural constituents) to the thermal perturbation. Using a certified ALR sample as the reference, the infrared spectral correlation threshold is determined by 30 authentic samples and 6 adulterated samples. The spectral correlation coefficient of an authentic ALR sample to the standard reference should be not less than 0.9886 (p=0.01). Three commercial adulterated ALR samples are identified by the correlation threshold. Further interpretation of the infrared spectra of the adulterated samples indicates the common adulterating methods - counterfeiting with other kind of wood, adding ingredient such as sand to increase the weight, and adding the cheap resin such as rosin to increase the content of resin compounds. Results of this research prove that FT-IR spectroscopy can be used as a simple and accurate quality control method of ALR. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Application of Fourier-transform infrared (FT-IR) spectroscopy for simple and easy determination of chylomicron-triglyceride and very low density lipoprotein-triglyceride.

Science.gov (United States)

Sato, Kenichi; Seimiya, Masanori; Kodera, Yoshio; Kitamura, Akihide; Nomura, Fumio

2010-02-01

Fourier-transform infrared (FT-IR) spectroscopy is a simple and reagent-free physicochemical analysis method, and is a potential alternative to more time-consuming and labor-intensive procedures. In this study, we aimed to use FT-IR spectroscopy to determine serum concentrations of chylomicron-triglyceride (TG) and very low density lipoprotein (VLDL)-TG. We analyzed a chylomicron fraction and VLDL fraction, which had been obtained by ultracentrifugation, to search for wavelengths to designate to each fraction. Then, partial least square (PLS) calibrations were developed using a training set of samples, for which TG concentrations had been determined by conventional procedures. Validation was conducted with another set of samples using the PLS model to predict serum TG concentrations on the basis of the samples' IR spectra. We analyzed a total of 150 samples. Serum concentrations of chylomicron-TG and VLDL-TG estimated by FT-IR spectroscopy agreed well with those obtained by the reference method (r=0.97 for both lipoprotein fractions). FT-IR spectrometric analysis required 15mul of serum and was completed within 1min. Serum chylomicron-TG and VLDL-TG concentrations can be determined with FT-IR spectroscopy. This rapid and simple test may have a great impact on the management of patients with dyslipidemia. Copyright 2009. Published by Elsevier B.V.

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)

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

Science.gov (United States)

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

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.

Modeling Microalgal Biosediment Formation Based on Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Monitoring.

Science.gov (United States)

Ogburn, Zachary L; Vogt, Frank

2018-03-01

With increasing amounts of anthropogenic pollutants being released into ecosystems, it becomes ever more important to understand their fate and interactions with living organisms. Microalgae play an important ecological role as they are ubiquitous in marine environments and sequester inorganic pollutants which they transform into organic biomass. Of particular interest in this study is their role as a sink for atmospheric CO 2 , a greenhouse gas, and nitrate, one cause of harmful algal blooms. Novel chemometric hard-modeling methodologies have been developed for interpreting phytoplankton's chemical and physiological adaptations to changes in their growing environment. These methodologies will facilitate investigations of environmental impacts of anthropogenic pollutants on chemical and physiological properties of marine microalgae (here: Nannochloropsis oculata). It has been demonstrated that attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy can gain insights into both and this study only focuses on the latter. From time-series of spectra, the rate of microalgal biomass settling on top of a horizontal ATR element is derived which reflects several of phytoplankton's physiological parameters such as growth rate, cell concentrations, cell size, and buoyancy. In order to assess environmental impacts on such parameters, microalgae cultures were grown under 25 different chemical scenarios covering 200-600 ppm atmospheric CO 2 and 0.35-0.75 mM dissolved NO 3 - . After recording time-series of ATR FT-IR spectra, a multivariate curve resolution-alternating least squares (MCR-ALS) algorithm extracted spectroscopic and time profiles from each data set. From the time profiles, it was found that in the considered concentration ranges only NO 3 - has an impact on the cells' physiological properties. In particular, the cultures' growth rate has been influenced by the ambient chemical conditions. Thus, the presented spectroscopic�

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…

On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

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

ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.

Science.gov (United States)

Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...

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

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

Forensic Drug Identification, Confirmation, and Quantification Using Fully Integrated Gas Chromatography with Fourier Transform Infrared and Mass Spectrometric Detection (GC-FT-IR-MS).

Science.gov (United States)

Lanzarotta, Adam; Lorenz, Lisa; Voelker, Sarah; Falconer, Travis M; Batson, JaCinta S

2018-05-01

This manuscript is a continuation of a recent study that described the use of fully integrated gas chromatography with direct deposition Fourier transform infrared detection and mass spectrometric detection (GC-FT-IR-MS) to identify and confirm the presence of sibutramine and AB-FUBINACA. The purpose of the current study was to employ the GC-FT-IR portion of the same instrument to quantify these compounds, thereby demonstrating the ability to identify, confirm, and quantify drug substances using a single GC-FT-IR-MS unit. The performance of the instrument was evaluated by comparing quantitative analytical figures of merit to those measured using an established, widely employed method for quantifying drug substances, high performance liquid chromatography with ultraviolet detection (HPLC-UV). The results demonstrated that GC-FT-IR was outperformed by HPLC-UV with regard to sensitivity, precision, and linear dynamic range (LDR). However, sibutramine and AB-FUBINACA concentrations measured using GC-FT-IR were not significantly different at the 95% confidence interval compared to those measured using HPLC-UV, which demonstrates promise for using GC-FT-IR as a semi-quantitative tool at the very least. The most significant advantage of GC-FT-IR compared to HPLC-UV is selectivity; a higher level of confidence regarding the identity of the analyte being quantified is achieved using GC-FT-IR. Additional advantages of using a single GC-FT-IR-MS instrument for identification, confirmation, and quantification are efficiency, increased sample throughput, decreased consumption of laboratory resources (solvents, chemicals, consumables, etc.), and thus cost.

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

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.

Differentiation between probiotic and wild-type Bacillus cereus isolates by antibiotic susceptibility test and Fourier transform infrared spectroscopy (FT-IR).

Science.gov (United States)

Mietke, Henriette; Beer, W; Schleif, Julia; Schabert, G; Reissbrodt, R

2010-05-30

Animal feed often contains probiotic Bacillus strains used as feed additives. Spores of the non-pathogenic B. cereus var. toyoi (product name Toyocerin) are used. Distinguishing between toxic wild-type Bacillus cereus strains and this probiotic strain is essential for evaluating the quality and risk of feed. Bacillus cereus CIP 5832 (product name Paciflor was used as probiotic strain until 2001. The properties of the two probiotic strains are quite similar. Differentiating between probiotic strains and wild-type B. cereus strains is not easy. ss-lactam antibiotics such as penicillin and cefamandole exhibit an inhibition zone in the agar diffusion test of probiotic B. cereus strains which are not seen for wild-type strains. Therefore, performing the agar diffusion test first may make sense before FT-IR testing. When randomly checking these strains by Fourier transform infrared spectroscopy (FT-IR), the probiotic B. cereus strains were separated from wild-type B. cereus/B. thuringiensis/B. mycoides/B. weihenstephanensis strains by means of hierarchical cluster analysis. The discriminatory information was contained in the spectral windows 3000-2800 cm(-1) ("fatty acid region"), 1200-900 cm(-1) ("carbohydrate region") and 900-700 cm(-1) ("fingerprint region"). It is concluded that FT-IR spectroscopy can be used for the rapid quality control and risk analysis of animal feed containing probiotic B. cereus strains. (c) 2010 Elsevier B.V. All rights reserved.

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...

Raman and Fourier Transform Infrared (FT-IR) Mineral to Matrix Ratios Correlate with Physical Chemical Properties of Model Compounds and Native Bone Tissue.

Science.gov (United States)

Taylor, Erik A; Lloyd, Ashley A; Salazar-Lara, Carolina; Donnelly, Eve

2017-10-01

Raman and Fourier transform infrared (FT-IR) spectroscopic imaging techniques can be used to characterize bone composition. In this study, our objective was to validate the Raman mineral:matrix ratios (ν 1 PO 4 :amide III, ν 1 PO 4 :amide I, ν 1 PO 4 :Proline + hydroxyproline, ν 1 PO 4 :Phenylalanine, ν 1 PO 4 :δ CH 2 peak area ratios) by correlating them to ash fraction and the IR mineral:matrix ratio (ν 3 PO 4 :amide I peak area ratio) in chemical standards and native bone tissue. Chemical standards consisting of varying ratios of synthetic hydroxyapatite (HA) and collagen, as well as bone tissue from humans, sheep, and mice, were characterized with confocal Raman spectroscopy and FT-IR spectroscopy and gravimetric analysis. Raman and IR mineral:matrix ratio values from chemical standards increased reciprocally with ash fraction (Raman ν 1 PO 4 /Amide III: P Raman ν 1 PO 4 /Amide I: P Raman ν 1 PO 4 /Proline + Hydroxyproline: P Raman ν 1 PO 4 /Phenylalanine: P Raman ν 1 PO 4 /δ CH 2 : P Raman and IR mineral:matrix ratio values were strongly correlated ( P Raman mineral:matrix bone composition parameter correlates strongly to ash fraction and to its IR counterpart. Finally, the mineral:matrix ratio values of the native bone tissue are similar to those of both chemical standards and theoretical values, confirming the biological relevance of the chemical standards and the characterization techniques.

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

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

Forensic Hair Differentiation Using Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Spectroscopy.

Science.gov (United States)

Manheim, Jeremy; Doty, Kyle C; McLaughlin, Gregory; Lednev, Igor K

2016-07-01

Hair and fibers are common forms of trace evidence found at crime scenes. The current methodology of microscopic examination of potential hair evidence is absent of statistical measures of performance, and examiner results for identification can be subjective. Here, attenuated total reflection (ATR) Fourier transform-infrared (FT-IR) spectroscopy was used to analyze synthetic fibers and natural hairs of human, cat, and dog origin. Chemometric analysis was used to differentiate hair spectra from the three different species, and to predict unknown hairs to their proper species class, with a high degree of certainty. A species-specific partial least squares discriminant analysis (PLSDA) model was constructed to discriminate human hair from cat and dog hairs. This model was successful in distinguishing between the three classes and, more importantly, all human samples were correctly predicted as human. An external validation resulted in zero false positive and false negative assignments for the human class. From a forensic perspective, this technique would be complementary to microscopic hair examination, and in no way replace it. As such, this methodology is able to provide a statistical measure of confidence to the identification of a sample of human, cat, and dog hair, which was called for in the 2009 National Academy of Sciences report. More importantly, this approach is non-destructive, rapid, can provide reliable results, and requires no sample preparation, making it of ample importance to the field of forensic science. © The Author(s) 2016.

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)

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.

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.

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

Science.gov (United States)

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

Multivariate Calibration and Model Integrity for Wood Chemistry Using Fourier Transform Infrared Spectroscopy

OpenAIRE

Zhou, Chengfeng; Jiang, Wei; Cheng, Qingzheng; Via, Brian K.

2015-01-01

This research addressed a rapid method to monitor hardwood chemical composition by applying Fourier transform infrared (FT-IR) spectroscopy, with particular interest in model performance for interpretation and prediction. Partial least squares (PLS) and principal components regression (PCR) were chosen as the primary models for comparison. Standard laboratory chemistry methods were employed on a mixed genus/species hardwood sample set to collect the original data. PLS was found to provide bet...

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)

Rainbow Fourier Transform

Science.gov (United States)

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

2012-01-01

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

Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

Serov, Valery

2017-01-01

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

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

International Nuclear Information System (INIS)

Canet, D.

1988-01-01

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

Comparison of Fiber Optic and Conduit Attenuated Total Reflection (ATR) Fourier Transform Infrared (FT-IR) Setup for In-Line Fermentation Monitoring.

Science.gov (United States)

Koch, Cosima; Posch, Andreas E; Herwig, Christoph; Lendl, Bernhard

2016-12-01

The performance of a fiber optic and an optical conduit in-line attenuated total reflection mid-infrared (IR) probe during in situ monitoring of Penicillium chrysogenum fermentation were compared. The fiber optic probe was connected to a sealed, portable, Fourier transform infrared (FT-IR) process spectrometer via a plug-and-play interface. The optical conduit, on the other hand, was connected to a FT-IR process spectrometer via a knuckled probe with mirrors that had to be adjusted prior to each fermentation, which were purged with dry air. Penicillin V (PenV) and its precursor phenoxyacetic acid (POX) concentrations were determined by online high-performance liquid chromatography and the obtained concentrations were used as reference to build partial least squares regression models. Cross-validated root-mean-square errors of prediction were found to be 0.2 g L -1 (POX) and 0.19 g L -1 (PenV) for the fiber optic setup and 0.17 g L -1 (both POX and PenV) for the conduit setup. Higher noise-levels and spectrum-to-spectrum variations of the fiber optic setup lead to higher noise of estimated (i.e., unknown) POX and PenV concentrations than was found for the conduit setup. It seems that trade-off has to be made between ease of handling (fiber optic setup) and measurement accuracy (optical conduit setup) when choosing one of these systems for bioprocess monitoring. © The Author(s) 2016.

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.

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

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.

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

Science.gov (United States)

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

Characterization by Fourier transform infrared spectroscopy (FT-IR) and 2D IR correlation spectroscopy of a carbosilane dendrimer with peripheral ammonium groups

Energy Technology Data Exchange (ETDEWEB)

Popescu, Maria-Cristina, E-mail: cpopescu@icmpp.ro [' Petru Poni' Institute of Macromolecular Chemistry (Romania); Gomez, Rafael; Mata, Fco Javier de la; Rasines, Beatriz [Universidad de Alcala, Departamento de Quimica Inorganica (Spain); Simionescu, Bogdan C. [' Petru Poni' Institute of Macromolecular Chemistry (Romania)

2013-06-15

Fourier transform infrared spectroscopy and 2D correlation spectroscopy were used to study the microstructural changes occurring on heating of a new carbosilane dendrimer with peripheral ammonium groups. Temperature-dependent spectral variations in the 3,010-2,710, 1,530-1,170, and 1,170-625 cm{sup -1} regions were monitored during the heating process. The dependence, on temperature, of integral absorptions and position of spectral bands was established and the spectral modifications associated with molecular conformation rearrangements, allowing molecular shape changes, were found. Before 180 Degree-Sign C, the studied carbosilane dendrimer proved to be stable, while at higher temperatures it oxidizes and Si-O groups appear. 2D IR correlation spectroscopy gives new information about the effect of temperature on the structure and dynamics of the system. Synchronous and asynchronous spectra indicate that, at low temperature, conformational changes of CH{sub 3} and CH{sub 3}-N{sup +} groups take place first. With increasing temperature, the intensity variation of the CH{sub 2}, C-N, Si-C and C-C groups from the dendritic core is faster than that of the terminal units. This indicates that, with increasing temperature, the segments of the dendritic core obtain enough energy to change their conformation more easily as compared to the terminal units, due to their internal flexibility.

Characterization by Fourier transform infrared spectroscopy (FT-IR) and 2D IR correlation spectroscopy of a carbosilane dendrimer with peripheral ammonium groups

International Nuclear Information System (INIS)

Popescu, Maria-Cristina; Gómez, Rafael; Mata, Fco Javier de la; Rasines, Beatriz; Simionescu, Bogdan C.

2013-01-01

Fourier transform infrared spectroscopy and 2D correlation spectroscopy were used to study the microstructural changes occurring on heating of a new carbosilane dendrimer with peripheral ammonium groups. Temperature-dependent spectral variations in the 3,010–2,710, 1,530–1,170, and 1,170–625 cm −1 regions were monitored during the heating process. The dependence, on temperature, of integral absorptions and position of spectral bands was established and the spectral modifications associated with molecular conformation rearrangements, allowing molecular shape changes, were found. Before 180 °C, the studied carbosilane dendrimer proved to be stable, while at higher temperatures it oxidizes and Si–O groups appear. 2D IR correlation spectroscopy gives new information about the effect of temperature on the structure and dynamics of the system. Synchronous and asynchronous spectra indicate that, at low temperature, conformational changes of CH 3 and CH 3 –N + groups take place first. With increasing temperature, the intensity variation of the CH 2 , C–N, Si–C and C–C groups from the dendritic core is faster than that of the terminal units. This indicates that, with increasing temperature, the segments of the dendritic core obtain enough energy to change their conformation more easily as compared to the terminal units, due to their internal flexibility.

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

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)

The relationship between shock response spectrum and fast Fourier transform

International Nuclear Information System (INIS)

Zola, Maurizio

2001-01-01

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

Investigation of the Cross-Section Stratifications of Icons Using Micro-Raman and Micro-Fourier Transform Infrared (FT-IR) Spectroscopy.

Science.gov (United States)

Lazidou, Dimitra; Lampakis, Dimitrios; Karapanagiotis, Ioannis; Panayiotou, Costas

2018-01-01

The cross-section stratifications of samples, which were removed from six icons, are studied using optical microscopy, micro-Raman spectroscopy, and micro-Fourier transform infrared (FT-IR) spectroscopy. The icons, dated from the 14th to 19th centuries, are prominent examples of Byzantine painting art and are attributed to different artistic workshops of ​​northern Greece. The following materials are identified in the cross-sections of the icon samples using micro-Raman spectroscopy: anhydrite; calcite; carbon black; chrome yellow; cinnabar; gypsum; lead white; minium; orpiment; Prussian blue; red ochre; yellow ochre; and a paint of organic origin which can be either indigo ( Indigofera tinctoria L. and others) or woad ( Isatis tinctoria L.). The same samples are investigated using micro-FT-IR which leads to the following identifications: calcite; calcium oxalates; chrome yellow; gypsum; kaolinite; lead carboxylates; lead sulfate (or quartz); lead white; oil; protein; Prussian blue; saponified oil; shellac; silica; and tree resin. The study of the cross-sections of the icon samples reveals the combinations of the aforementioned inorganic and organic materials. Although the icons span over a long period of six centuries, the same stratification comprising gypsum ground layer, paint layers prepared by modified "egg tempera" techniques (proteinaceous materials mixed with oil and resins), and varnish layer is revealed in the investigated samples. Moreover, the presence of three layers of varnishes, one at the top and other two as intermediate layers, in the cross-section analysis of a sample from Virgin and Child provide evidence of later interventions.

Supercritical Fluid Chromatography/Fourier Transform Infrared Spectroscopy Of Food Components

Science.gov (United States)

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

1989-12-01

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

CO 2 Capture Capacity and Swelling Measurements of Liquid-like Nanoparticle Organic Hybrid Materials via Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy

KAUST Repository

Park, Youngjune; Shin, Dolly; Jang, Young Nam; Park, Ah-Hyung Alissa

2012-01-01

attenuated total reflectance (ATR) Fourier transform infrared (FT-IR) spectroscopy. Simultaneous measurements of CO 2 capture capacity and swelling behaviors of polyetheramine (Jeffamine M-2070) and its corresponding NOHMs (NOHM-I-PE2070) were reported

Analysis of cigarette smoke by Fourier transform infrared spectrometry

Energy Technology Data Exchange (ETDEWEB)

Maddox, W.L. (Oak Ridge National Lab., TN); Mamantov, G.

1977-02-01

The application of Fourier transform infrared spectrometry (FT-IR) to the quantitative determination of several components in the gas phase of whole, dilute tobacco smoke was demonstrated. The 18-cm absorption cell was part of a cigarette smoking system similar to the intermittent inhalation exposure devices used in smoking and health research with rodents. Concentrations were measured for carbon monoxide, carbon dioxide, methane, ethylene, and methanol in 7 to 22% smoke. The precision of a measurement in 22% smoke ranged from 3% for carbon dioxide to 34% for ethylene. Absorbances measured for isoprene and hydrogen cyanide followed expected concentrations in different cigarette smokes. It was shown that the concentrations of these components remain constant during a 30-s hold-up following each puff on the cigarettes.

Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

OpenAIRE

Jelle, Bjørn Petter; Hovde, Per Jostein

2012-01-01

Material characterization may be carried out by the attenuated total reflectance (ATR) Fourier transform infrared (FTIR) radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for exa...

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

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.

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 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",…

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

Analysis of tokamak plasma confinement modes using the fast Fourier transformation

International Nuclear Information System (INIS)

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

2016-01-01

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

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

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.

Advanced multivariate data evaluation for Fourier transform infrared spectroscopy

International Nuclear Information System (INIS)

Diewok, J.

2002-12-01

The objective of the presented dissertation was the evaluation, application and further development of advanced multivariate data evaluation methods for qualitative and quantitative Fourier transform infrared (FT-IR) measurements, especially of aqueous samples. The focus was set on 'evolving systems'; i.e. chemical systems that change gradually with a master variable, such as pH, reaction time, elution time, etc. and that are increasingly encountered in analytical chemistry. FT-IR measurements on such systems yield 2-way and 3-way data sets, i.e. data matrices and cubes. The chemometric methods used were soft-modeling techniques, like multivariate curve resolution - alternating least squares (MCR-ALS) or principal component analysis (PCA), hard modeling of equilibrium systems and two-dimensional correlation spectroscopy (2D-CoS). The research results are presented in six publications and comprise: A new combination of FT-IR flow titrations and second-order calibration by MCR-ALS for the quantitative analysis of mixture samples of organic acids and sugars. A novel combination of MCR-ALS with a hard-modeled equilibrium constraint for second-order quantitation in pH-modulated samples where analytes and interferences show very similar acid-base behavior. A detailed study in which MCR-ALS and 2D-CoS are directly compared for the first time. From the analysis of simulated and experimental acid-base equilibrium systems, the performance and interpretability of the two methods is evaluated. Investigation of the binding process of vancomycin, an important antibiotic, to a cell wall analogue tripeptide by time-resolved FT-IR spectroscopy and detailed chemometric evaluation. Determination of red wine constituents by liquid chromatography with FT-IR detection and MCR-ALS for resolution of overlapped peaks. Classification of red wine cultivars from FT-IR spectroscopy of phenolic wine extracts with hierarchical clustering and soft independent modeling of class analogy (SIMCA

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....

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

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

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.

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

Using Fourier transform IR spectroscopy to analyze biological materials

Science.gov (United States)

Baker, Matthew J; Trevisan, Júlio; Bassan, Paul; Bhargava, Rohit; Butler, Holly J; Dorling, Konrad M; Fielden, Peter R; Fogarty, Simon W; Fullwood, Nigel J; Heys, Kelly A; Hughes, Caryn; Lasch, Peter; Martin-Hirsch, Pierre L; Obinaju, Blessing; Sockalingum, Ganesh D; Sulé-Suso, Josep; Strong, Rebecca J; Walsh, Michael J; Wood, Bayden R; Gardner, Peter; Martin, Francis L

2015-01-01

IR spectroscopy is an excellent method for biological analyses. It enables the nonperturbative, label-free extraction of biochemical information and images toward diagnosis and the assessment of cell functionality. Although not strictly microscopy in the conventional sense, it allows the construction of images of tissue or cell architecture by the passing of spectral data through a variety of computational algorithms. Because such images are constructed from fingerprint spectra, the notion is that they can be an objective reflection of the underlying health status of the analyzed sample. One of the major difficulties in the field has been determining a consensus on spectral pre-processing and data analysis. This manuscript brings together as coauthors some of the leaders in this field to allow the standardization of methods and procedures for adapting a multistage approach to a methodology that can be applied to a variety of cell biological questions or used within a clinical setting for disease screening or diagnosis. We describe a protocol for collecting IR spectra and images from biological samples (e.g., fixed cytology and tissue sections, live cells or biofluids) that assesses the instrumental options available, appropriate sample preparation, different sampling modes as well as important advances in spectral data acquisition. After acquisition, data processing consists of a sequence of steps including quality control, spectral pre-processing, feature extraction and classification of the supervised or unsupervised type. A typical experiment can be completed and analyzed within hours. Example results are presented on the use of IR spectra combined with multivariate data processing. PMID:24992094

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

Science.gov (United States)

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

Multivariate analysis of attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopic data to confirm phase partitioning in methacrylate-based dentin adhesive.

Science.gov (United States)

Ye, Qiang; Parthasarathy, Ranganathan; Abedin, Farhana; Laurence, Jennifer S; Misra, Anil; Spencer, Paulette

2013-12-01

Water is ubiquitous in the mouths of healthy individuals and is a major interfering factor in the development of a durable seal between the tooth and composite restoration. Water leads to the formation of a variety of defects in dentin adhesives; these defects undermine the tooth-composite bond. Our group recently analyzed phase partitioning of dentin adhesives using high-performance liquid chromatography (HPLC). The concentration measurements provided by HPLC offered a more thorough representation of current adhesive performance and elucidated directions to be taken for further improvement. The sample preparation and instrument analysis using HPLC are, however, time-consuming and labor-intensive. The objective of this work was to develop a methodology for rapid, reliable, and accurate quantitative analysis of near-equilibrium phase partitioning in adhesives exposed to conditions simulating the wet oral environment. Analysis by Fourier transform infrared (FT-IR) spectroscopy in combination with multivariate statistical methods, including partial least squares (PLS) regression and principal component regression (PCR), were used for multivariate calibration to quantify the compositions in separated phases. Excellent predictions were achieved when either the hydrophobic-rich phase or the hydrophilic-rich phase mixtures were analyzed. These results indicate that FT-IR spectroscopy has excellent potential as a rapid method of detection and quantification of dentin adhesives that experience phase separation under conditions that simulate the wet oral environment.

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

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 ...

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

Ferraro, John R

1985-01-01

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

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)

Quantitative gas analysis with FT-IR

DEFF Research Database (Denmark)

Bak, J.; Larsen, A.

1995-01-01

Calibration spectra of CO in the 2.38-5100 ppm concentration range (22 spectra) have been measured with a spectral resolution of 4 cm(-1), in the mid-IR (2186-2001 cm(-1)) region, with a Fourier transform infrared (FT-IR) instrument. The multivariate calibration method partial least-squares (PLS1...

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

Science.gov (United States)

Thomas L. Eberhardt

2009-01-01

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

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.

Fourier transform IR studies on the interaction of selected chemicals with isolated cuticles

International Nuclear Information System (INIS)

Luque, P.; Ramirez, F.J.; Heredia, A.; Bukovac, M.J.

1994-01-01

It is known that the plant cuticle represents the first barrier that must be overcome by any chemical reaching the plant surface from the atmosphere before entering the plant. Because of the importance of the cuticle as a barrier to penetration of a wide variety of compounds, its morphology, chemistry, and permeability have been extensively studied. However, only limited information is available on the nature of functional chemical groups present and their interaction and role during the penetration process. The usefulness of in situ Fourier transform infrared spectroscopy studies in identifying functional groups present in isolated cuticles is described and their relationships to the structure of the cuticular membrane are discussed. Applications of infrared spectroscopy on the presence and role of phenolics in the cuticle structure and during the cuticle development, nitrogen oxide binding to isolated cuticles, and the interactions between selected chemical probes during sorption by the cuticle are also described. (orig.)

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.

The Scope Of Fourier Transform Infrared (FTIR)

Science.gov (United States)

Hirschfeld, T.

1981-10-01

Three auarters of a century after its inception, a generation after its advantages were recognized, and a decade after its first commercialization, FT-IR dominates the growth of the IR market, and reigns alone over its high performance end. What lies ahead for FT-IR now? On one hand, the boundary between it and the classical scanning spectrometers is becoming fuzzy, as gratings attempt to use as much of FT-IR's computer technology as they can handle, and smaller FT systems invade the medium cost instrument range. On the other hand, technology advances in IR detectors, non-Fourier interference devices, and the often announced tunable laser are at long last getting set to make serious inroads in the field (although not necessarily in the manner most of us expected). However, the dominance of FT-IR as the leading edge of IR spectroscopy seems assured for a good many years. The evolution of FT-IR will be dominated by demands not yet fully satisfied such as rapid sample turnover, better quantitation, automated interpretation, higher GC-IR sensitivity, improved LC-IR, and, above all else, reliability and ease of use. These developments will be based on multiple small advances in hardware, large advances in the way systems are put together, and the traditional yearly revolutionary advances of the computer industry. The big question in the field will, however, still be whether our ambition and our skill can continue to keep up with the advances of our tools. It will be fun.

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

Identification of Quercus agrifolia (coast live oak resistant to the invasive pathogen Phytophthora ramorum in native stands using Fourier-transform infrared (FT-IR spectroscopy

Directory of Open Access Journals (Sweden)

Anna Olivia Conrad

2014-10-01

Full Text Available Over the last two decades coast live oak (CLO dominance in many California coastal ecosystems has been threatened by the alien invasive pathogen Phytophthora ramorum, the causal agent of sudden oak death. In spite of high infection and mortality rates in some areas, the presence of apparently resistant trees has been observed, including trees that become infected but recover over time. However, identifying resistant trees based on recovery alone can take many years. The objective of this study was to determine if Fourier-transform infrared (FT-IR spectroscopy, a chemical fingerprinting technique, can be used to identify CLO resistant to P. ramorum prior to infection. Soft independent modeling of class analogy identified spectral regions that differed between resistant and susceptible trees. Regions most useful for discrimination were associated with carbonyl group vibrations. Additionally, concentrations of two putative phenolic biomarkers of resistance were predicted using partial least squares regression; > 99% of the variation was explained by this analysis. This study demonstrates that chemical fingerprinting can be used to identify resistance in a natural population of forest trees prior to infection with a pathogen. FT-IR spectroscopy may be a useful approach for managing forests impacted by sudden oak death, as well as in other situations where emerging or existing forest pests and diseases are of concern.

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.

Automated Fast Screening Method for Cocaine Identification in Seized Drug Samples Using a Portable Fourier Transform Infrared (FT-IR) Instrument.

Science.gov (United States)

Mainali, Dipak; Seelenbinder, John

2016-05-01

Quick and presumptive identification of seized drug samples without destroying evidence is necessary for law enforcement officials to control the trafficking and abuse of drugs. This work reports an automated screening method to detect the presence of cocaine in seized samples using portable Fourier transform infrared (FT-IR) spectrometers. The method is based on the identification of well-defined characteristic vibrational frequencies related to the functional group of the cocaine molecule and is fully automated through the use of an expert system. Traditionally, analysts look for key functional group bands in the infrared spectra and characterization of the molecules present is dependent on user interpretation. This implies the need for user expertise, especially in samples that likely are mixtures. As such, this approach is biased and also not suitable for non-experts. The method proposed in this work uses the well-established "center of gravity" peak picking mathematical algorithm and combines it with the conditional reporting feature in MicroLab software to provide an automated method that can be successfully employed by users with varied experience levels. The method reports the confidence level of cocaine present only when a certain number of cocaine related peaks are identified by the automated method. Unlike library search and chemometric methods that are dependent on the library database or the training set samples used to build the calibration model, the proposed method is relatively independent of adulterants and diluents present in the seized mixture. This automated method in combination with a portable FT-IR spectrometer provides law enforcement officials, criminal investigators, or forensic experts a quick field-based prescreening capability for the presence of cocaine in seized drug samples. © The Author(s) 2016.

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

Spectrums Transform Operators in Bases of Fourier and Walsh Functions

Directory of Open Access Journals (Sweden)

V. V. Syuzev

2017-01-01

Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel

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

International Nuclear Information System (INIS)

Golubov, B I

1998-01-01

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

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

Directory of Open Access Journals (Sweden)

Zohreh Moghareh Abed

2010-01-01

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

Electro-optic imaging Fourier transform spectrometer

Science.gov (United States)

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

2009-01-01

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

Applications of FT-IR spectrophotometry in cancer diagnostics.

Science.gov (United States)

Bunaciu, Andrei A; Hoang, Vu Dang; Aboul-Enein, Hassan Y

2015-01-01

This review provides a brief background to the application of infrared spectroscopy, including Fourier transform-infrared spectroscopy, in biological fluids. It is not meant to be complete or exhaustive but to provide the reader with sufficient background for selected applications in cancer diagnostics. Fourier transform-infrared spectroscopy (FT-IR) is a fast and nondestructive analytical method. The infrared spectrum of a mixture serves as the basis to quantitate its constituents, and a number of common clinical chemistry tests have proven to be feasible using this approach. This review focuses on biomedical FT-IR applications, published in the period 2009-2013, used for early detection of cancer through qualitative and quantitative analysis.

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

Multivariate Calibration and Model Integrity for Wood Chemistry Using Fourier Transform Infrared Spectroscopy

Directory of Open Access Journals (Sweden)

Chengfeng Zhou

2015-01-01

Full Text Available This research addressed a rapid method to monitor hardwood chemical composition by applying Fourier transform infrared (FT-IR spectroscopy, with particular interest in model performance for interpretation and prediction. Partial least squares (PLS and principal components regression (PCR were chosen as the primary models for comparison. Standard laboratory chemistry methods were employed on a mixed genus/species hardwood sample set to collect the original data. PLS was found to provide better predictive capability while PCR exhibited a more precise estimate of loading peaks and suggests that PCR is better for model interpretation of key underlying functional groups. Specifically, when PCR was utilized, an error in peak loading of ±15 cm−1 from the true mean was quantified. Application of the first derivative appeared to assist in improving both PCR and PLS loading precision. Research results identified the wavenumbers important in the prediction of extractives, lignin, cellulose, and hemicellulose and further demonstrated the utility in FT-IR for rapid monitoring of wood chemistry.

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.

Fourier transform spectra of quantum dots

Science.gov (United States)

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

2010-05-01

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

Fourier-transform optical microsystems

Science.gov (United States)

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

1999-01-01

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

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 ...

Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) for Rapid Determination of Microbial Cell Lipid Content: Correlation with Gas Chromatography-Mass Spectrometry (GC-MS).

Science.gov (United States)

Millan-Oropeza, Aaron; Rebois, Rolando; David, Michelle; Moussa, Fathi; Dazzi, Alexandre; Bleton, Jean; Virolle, Marie-Joelle; Deniset-Besseau, Ariane

2017-10-01

There is a growing interest worldwide for the production of renewable oil without mobilizing agriculture lands; fast and reliable methods are needed to identify highly oleaginous microorganisms of potential industrial interest. The aim of this study was to demonstrate the relevance of attenuated total reflection (ATR) spectroscopy to achieve this goal. To do so, the total lipid content of lyophilized samples of five Streptomyces strains with varying lipid content was assessed with two classical quantitative but time-consuming methods, gas chromatography-mass spectrometry (GC-MS) and ATR Fourier transform infrared (ATR FT-IR) spectroscopy in transmission mode with KBr pellets and the fast ATR method, often questioned for its lack of reliability. A linear correlation between these three methods was demonstrated allowing the establishment of equations to convert ATR values expressed as CO/amide I ratio, into micrograms of lipid per milligram of biomass. The ATR method proved to be as reliable and quantitative as the classical GC-MS and FT-IR in transmission mode methods but faster and more reproducible than the latter since it involves far less manipulation for sample preparation than the two others. Attenuated total reflection could be regarded as an efficient fast screening method to identify natural or genetically modified oleaginous microorganisms by the scientific community working in the field of bio-lipids.

Application of Near-Infrared and Fourier Transform Infrared Spectroscopy in the Characterization of Ligand-Induced Conformation Changes in Folate Binding Protein Purified from Bovine Milk

DEFF Research Database (Denmark)

Bruun, Susanne Wrang; Holm, Jan; Hansen, Steen Ingemann

2006-01-01

Fourier transform infrared (FT-IR) and near-infrared (NIR) spectroscopy have been applied to detect structural alterations in folate binding protein (FBP) induced by ligation in different buffer types. The amide I region pointed to a beta-sheet to alpha-helix transition upon ligation in acetate...

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...

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.

Application of attenuated total reflectance Fourier transform infrared spectroscopy for determination of cefixime in oral pharmaceutical formulations.

Science.gov (United States)

Kandhro, Aftab A; Laghari, Abdul Hafeez; Mahesar, Sarfaraz A; Saleem, Rubina; Nelofar, Aisha; Khan, Salman Tariq; Sherazi, S T H

2013-11-01

A quick and reliable analytical method for the quantitative assessment of cefixime in orally administered pharmaceutical formulations is developed by using diamond cell attenuated total reflectance (ATR) Fourier transform infrared (FT-IR) spectroscopy as an easy procedure for quality control laboratories. The standards for calibration were prepared in aqueous medium ranging from 350 to 6000mg/kg. The calibration model was developed based on partial least square (PLS) using finger print region of FT-IR spectrum in the range from 1485 to 887cm(-1). Excellent coefficient of determination (R(2)) was achieved as high as 0.99976 with root mean square error of 44.8 for calibration. The application of diamond cell (smart accessory) ATR FT-IR proves a reliable determination of cefixime in pharmaceutical formulations to assess the quality of the final product. Copyright © 2013 Elsevier B.V. All rights reserved.

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.

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)

Decay of the Fourier transform analytic and geometric aspects

CERN Document Server

Iosevich, Alex

2014-01-01

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

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

DEFF Research Database (Denmark)

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

2008-01-01

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

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

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-02-05

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

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)

Two-dimensional fourier transform spectrometer

Science.gov (United States)

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

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

The applicability of Fourier transform infrared (FT-IR) spectroscopy in waste management

International Nuclear Information System (INIS)

Smidt, Ena; Meissl, Katharina

2007-01-01

State and stability or reactivity of waste materials are important properties that must be determined to obtain information about the future behavior and the emission potential of the materials. Different chemical and biological parameters are used to describe the stage of organic matter in waste materials. Fourier transform infrared spectroscopy provides information about the chemistry of waste materials in a general way. Several indicator bands that are referred to functional groups represent components or metabolic products. Their presence and intensity or their absence shed light on the phase of degradation or stabilization. The rapid assessment of the stage of organic matter decomposition is a very important field of application. Therefore, infrared spectroscopy is an appropriate tool for process and quality control, for the assessment of abandoned landfills and for checking of the successful landfill remediation. A wide range of applications are presented in this study for different waste materials. Progressing stages of a typical yard/kitchen waste composting process are shown. The fate of anaerobically 'stabilized' leftovers in a subsequent liquid aerobic process is revealed by spectroscopic characteristics. A compost that underwent the biological stabilization process is distinguished from a 'substrate' that comprises immature biogenic waste mixed with mineral compounds. Infrared spectra of freeze-dried leachate from untreated and aerated landfill material prove the effect of the aerobic treatment during 10 weeks in laboratory-scale experiments

Broadly tunable picosecond ir source

International Nuclear Information System (INIS)

Campillo, A.J.; Hyer, R.C.; Shapiro, S.L.

1979-01-01

A completely grating tuned (1.9 to 2.4 μm) picosecond traveling wave IR generator capable of controlled spectral bandwidth operation down to the Fourier Transform limit is reported. Subsequent down conversion in CdSe extends tuning to 10 to 20 μm

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.

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

Advances in data processing for open-path Fourier transform infrared spectrometry of greenhouse gases.

Science.gov (United States)

Shao, Limin; Griffiths, Peter R; Leytem, April B

2010-10-01

The automated quantification of three greenhouse gases, ammonia, methane, and nitrous oxide, in the vicinity of a large dairy farm by open-path Fourier transform infrared (OP/FT-IR) spectrometry at intervals of 5 min is demonstrated. Spectral pretreatment, including the automated detection and correction of the effect of interrupting the infrared beam, is by a moving object, and the automated correction for the nonlinear detector response is applied to the measured interferograms. Two ways of obtaining quantitative data from OP/FT-IR data are described. The first, which is installed in a recently acquired commercial OP/FT-IR spectrometer, is based on classical least-squares (CLS) regression, and the second is based on partial least-squares (PLS) regression. It is shown that CLS regression only gives accurate results if the absorption features of the analytes are located in very short spectral intervals where lines due to atmospheric water vapor are absent or very weak; of the three analytes examined, only ammonia fell into this category. On the other hand, PLS regression works allowed what appeared to be accurate results to be obtained for all three analytes.

Assessment of genetically modified soybean crops and different cultivars by Fourier transform infrared spectroscopy and chemometric analysis

Directory of Open Access Journals (Sweden)

Glaucia Braz Alcantara

2010-06-01

Full Text Available This paper describes the potentiality of Fourier transform infrared (FT-IR spectroscopy associated to chemometric analysis for assessment of conventional and genetically modified soybean crops. Recently, genetically modified organisms have been queried about their influence on the environment and their safety as food/feed. In this regard, chemical investigations are ever more required. Thus three different soybean cultivars distributed in transgenic Roundup ReadyTM soybean and theirs conventional counterparts were directly investigated by FT-IR spectroscopy and chemometric analysis. The application of PCA and KNN methods permitted the discrimination and classification of the genetically modified samples from conventional ones when they were separately analysed. The analyses showed the chemical variation according to genetic modification. Furthermore, this methodology was efficient for cultivar grouping and highlights cultivar dependence for discrimination between transgenic and non-transgenic samples. According to this study, FT-IR and chemometrics could be used as a quick, easy and low cost tool to assess the chemical composition variation in genetically modified organisms.

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...

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

Reduction and coding of synthetic aperture radar data with Fourier transforms

Science.gov (United States)

Tilley, David G.

1995-01-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

Study on Senna alata and its different extracts by Fourier transform infrared spectroscopy and two-dimensional correlation infrared spectroscopy

Science.gov (United States)

Adiana, M. A.; Mazura, M. P.

2011-04-01

Senna alata L. commonly known as candle bush belongs to the family of Fabaceae and the plant has been reported to possess anti-inflammatory, analgesic, laxative and antiplatelet-aggregating activity. In order to develop a rapid and effective analysis method for studying integrally the main constituents in the medicinal materials and their extracts, discriminating the extracts from different extraction process, comparing the categories of chemical constituents in the different extracts and monitoring the qualities of medicinal materials, we applied Fourier transform infrared spectroscopy (FT-IR) associated with second derivative infrared spectroscopy and two-dimensional infrared correlation spectroscopy (2D-IR) to study the main constituents of S. alata and its different extracts (extracted by hexane, dichloromethane, ethyl acetate and methanol in turn). The findings indicated that FT-IR and 2D-IR can provide many holistic variation rules of chemical constituents. Use of the macroscopical fingerprint characters of FT-IR and 2D-IR spectrum can identify the main chemical constituents in medicinal materials and their extracts, but also compare the components differences among similar samples. In a conclusion, FT-IR spectroscopy combined with 2D correlation analysis provides a powerful method for the quality control of traditional medicines.

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.

Study on Europium-Doped Hydroxyapatite Nanoparticles by Fourier Transform Infrared Spectroscopy and Their Antimicrobial Properties

Directory of Open Access Journals (Sweden)

Simona-Liliana Iconaru

2013-01-01

Full Text Available Fourier transform infrared spectroscopy (FT-IR analysis was conducted on europium-doped hydroxyapatite, Ca10-xEux(PO46(OH2 nanocrystalline powders (Eu:HAp with 0≤xEu≤0.2. Antimicrobial studies were also performed for the first time on Eu:HAp. The antimicrobial properties of Eu:HAp nanoparticles with 0≤xEu≤0.2 on Gram-negative (E. coli ATCC 25922, Pseudomonas aeruginosa 1397 and Gram-positive (Staphylococcus aureus 0364, Enterococcus faecalis ATCC 29212 bacteria systems and a species of fungus (Candida albicans ATCC 10231 were reported. Our study demonstrates that the antimicrobial activity of Eu:HAp nanoparticles is dependent on the europium concentration.

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)

Real time observation of proteolysis with Fourier transform infrared (FT-IR) and UV-circular dichroism spectroscopy: Watching a protease eat a protein

Science.gov (United States)

Güler, Günnur; Džafić, Enela; Vorob'ev, Mikhail M.; Vogel, Vitali; Mäntele, Werner

2011-06-01

Fourier transform infrared (FT-IR)- and UV-circular dichroism (UV-CD) spectroscopy have been used to study real-time proteolytic digestion of β-lactoglobulin (β-LG) and β-casein (β-CN) by trypsin at various substrate/enzyme ratios in D 2O-buffer at 37 °C. Both techniques confirm that protein substrate looses its secondary structure upon conversion to the peptide fragments. This perturbation alters the backbone of the protein chain resulting in conformational changes and degrading of the intact protein. Precisely, the most significant spectral changes which arise from digestion take place in the amide I and amide II regions. The FT-IR spectra for the degraded β-LG show a decrease around 1634 cm -1, suggesting a decrease of β-sheet structure in the course of hydrolysis. Similarly, the intensity around the 1654 cm -1 band decreases for β-CN digested by trypsin, indicating a reduction in the α-helical part. On the other hand, the intensity around ˜1594 cm -1 and ˜1406 cm -1 increases upon enzymatic breakdown of both substrates, suggesting an increase in the antisymmetric and symmetric stretching modes of free carboxylates, respectively, as released digestion products. Observation of further H/D exchange in the course of digestion manifests the structural opening of the buried groups and accessibility to the core of the substrate. On the basis of the UV-CD spectra recorded for β-LG and β-CN digested by trypsin, the unordered structure increases concomitant with a decrease in the remaining structure, thus, revealing breakdown of the intact protein into smaller fragments. This model study in a closed reaction system may serve as a basis for the much more complex digestion processes in an open reaction system such as the stomach.

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

Internal respiratory surrogate in multislice 4D CT using a combination of Fourier transform and anatomical features

International Nuclear Information System (INIS)

Hui, Cheukkai; Suh, Yelin; Robertson, Daniel; Beddar, Sam; Pan, Tinsu; Das, Prajnan; Crane, Christopher H.

2015-01-01

Purpose: The purpose of this study was to develop a novel algorithm to create a robust internal respiratory signal (IRS) for retrospective sorting of four-dimensional (4D) computed tomography (CT) images. Methods: The proposed algorithm combines information from the Fourier transform of the CT images and from internal anatomical features to form the IRS. The algorithm first extracts potential respiratory signals from low-frequency components in the Fourier space and selected anatomical features in the image space. A clustering algorithm then constructs groups of potential respiratory signals with similar temporal oscillation patterns. The clustered group with the largest number of similar signals is chosen to form the final IRS. To evaluate the performance of the proposed algorithm, the IRS was computed and compared with the external respiratory signal from the real-time position management (RPM) system on 80 patients. Results: In 72 (90%) of the 4D CT data sets tested, the IRS computed by the authors’ proposed algorithm matched with the RPM signal based on their normalized cross correlation. For these data sets with matching respiratory signals, the average difference between the end inspiration times (Δt ins ) in the IRS and RPM signal was 0.11 s, and only 2.1% of Δt ins were more than 0.5 s apart. In the eight (10%) 4D CT data sets in which the IRS and the RPM signal did not match, the average Δt ins was 0.73 s in the nonmatching couch positions, and 35.4% of them had a Δt ins greater than 0.5 s. At couch positions in which IRS did not match the RPM signal, a correlation-based metric indicated poorer matching of neighboring couch positions in the RPM-sorted images. This implied that, when IRS did not match the RPM signal, the images sorted using the IRS showed fewer artifacts than the clinical images sorted using the RPM signal. Conclusions: The authors’ proposed algorithm can generate robust IRSs that can be used for retrospective sorting of 4D CT data

Internal respiratory surrogate in multislice 4D CT using a combination of Fourier transform and anatomical features

Energy Technology Data Exchange (ETDEWEB)

Hui, Cheukkai; Suh, Yelin [Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); Robertson, Daniel; Beddar, Sam, E-mail: abeddar@mdanderson.org [Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas 77030 and Department of Radiation Physics, The University of Texas Graduate School of Biomedical Sciences, Houston, Texas 77030 (United States); Pan, Tinsu [Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas 77030 and Department of Imaging Physics, The University of Texas Graduate School of Biomedical Sciences, Houston, Texas 77030 (United States); Das, Prajnan; Crane, Christopher H. [Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States)

2015-07-15

Purpose: The purpose of this study was to develop a novel algorithm to create a robust internal respiratory signal (IRS) for retrospective sorting of four-dimensional (4D) computed tomography (CT) images. Methods: The proposed algorithm combines information from the Fourier transform of the CT images and from internal anatomical features to form the IRS. The algorithm first extracts potential respiratory signals from low-frequency components in the Fourier space and selected anatomical features in the image space. A clustering algorithm then constructs groups of potential respiratory signals with similar temporal oscillation patterns. The clustered group with the largest number of similar signals is chosen to form the final IRS. To evaluate the performance of the proposed algorithm, the IRS was computed and compared with the external respiratory signal from the real-time position management (RPM) system on 80 patients. Results: In 72 (90%) of the 4D CT data sets tested, the IRS computed by the authors’ proposed algorithm matched with the RPM signal based on their normalized cross correlation. For these data sets with matching respiratory signals, the average difference between the end inspiration times (Δt{sub ins}) in the IRS and RPM signal was 0.11 s, and only 2.1% of Δt{sub ins} were more than 0.5 s apart. In the eight (10%) 4D CT data sets in which the IRS and the RPM signal did not match, the average Δt{sub ins} was 0.73 s in the nonmatching couch positions, and 35.4% of them had a Δt{sub ins} greater than 0.5 s. At couch positions in which IRS did not match the RPM signal, a correlation-based metric indicated poorer matching of neighboring couch positions in the RPM-sorted images. This implied that, when IRS did not match the RPM signal, the images sorted using the IRS showed fewer artifacts than the clinical images sorted using the RPM signal. Conclusions: The authors’ proposed algorithm can generate robust IRSs that can be used for retrospective

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.

Analysis of serum cortisol levels by Fourier Transform Infrared Spectroscopy for diagnosis of stress in athletes

Directory of Open Access Journals (Sweden)

Lia Campos Lemes

Full Text Available Abstract Introduction Fourier-transform infrared (FT-IR spectroscopy is a technique with great potential for body fluids analyses. The aim of this study was to examine the impact of session training on cortisol concentrations in rugby players by means of infrared analysis of serum. Methods Blood collections were performed pre, post and 24 hours after of rugby training sessions. Serum cortisol was analyzed by FT-IR spectroscopy and chemiluminescent immunoassay. Results There was a significant difference between the integrated area, in the region of 1180-1102 cm-1, of the spectra for pre, post and post 24 h serums. The cortisol concentration obtained by chemiluminescent immunoassay showed no significant difference between pre, post and post 24 h. Positive correlations were obtained between the techniques (r = 0.75, post (r = 0.83 and post 24 h (r = 0.73. Conclusion The results showed no increase in cortisol levels of the players after the training sessions, as well as positive correlations indicating that FT-IR spectroscopy have produced promising results for the analysis of serum for diagnosis of stress.

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...

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.

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

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

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)

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.

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.

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.

Femtosecond nonlinear spectroscopy at surfaces: Second-harmonic probing of hole burning at the Si(111)7x7 surface and Fourier-transform sum-frequency vibrational spectroscopy

International Nuclear Information System (INIS)

McGuire, John Andrew

2004-01-01

The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of ∼ 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm -1 occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach

Femtosecond nonlinear spectroscopy at surfaces: Second-harmonic probing of hole burning at the Si(111)7x7 surface and fourier-transform sum-frequency vibrational spectroscopy

Energy Technology Data Exchange (ETDEWEB)

McGuire, John Andrew [Univ. of California, Berkeley, CA (United States)

2004-11-24

The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of {approx} 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm^-1 occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach.

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

Fourier transform of momentum distribution in vanadium

International Nuclear Information System (INIS)

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

1985-01-01

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

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

Science.gov (United States)

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

1974-01-01

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

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.

Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.

Science.gov (United States)

Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami

2016-09-01

Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications. © The Author(s) 2016.

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)

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.

Fiber-optic Fourier transform infrared spectroscopy for remote label-free sensing of medical device surface contamination

Science.gov (United States)

Hassan, Moinuddin; Tan, Xin; Welle, Elissa; Ilev, Ilko

2013-05-01

As a potential major source of biochemical contamination, medical device surfaces are of critical safety concerns in the clinical practice and public health. The development of innovative sensing methods for accurate and real-time detection of medical device surface contamination is essential to protect patients from high risk infection. In this paper, we demonstrate an alternative fiber-optic Fourier Transform Infrared (FTIR) spectroscopy based sensing approach for remote, non-contact, and label-free detection of biochemical contaminants in the mid-infrared (mid-IR) region. The sensing probe is designed using mid-IR hollow fibers and FTIR measurements are carried out in reflection mode. Bovine Serum Albumin (BSA) and bacterial endotoxin of different concentrations under thoroughly dry condition are used to evaluate the detection sensitivity. The devised system can identify ≤0.0025% (≤4 × 1011 molecules) BSA and 0.5% (0.5 EU/ml) endotoxin concentration. The developed sensing approach may be applied to detect various pathogens that pose public health threats.

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 ...

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

This paper presents the design and integration of an intelligent controller for CIRIS (Compositional InfraRed Interferometric Spectrometer) on a stand-alone field programmable gate array (FPGA) architecture. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. This design eliminates the need for periodically accelerating/decelerating mirrors inherent to canonical Michelson designs and allows for a compact and robust device that is intrinsically radiation-hard, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 μm) on planetary exploration missions. A traditional Michelson FTS passes a monochromatic light source (incident light from the sample) through a system of refractors/mirrors followed by a mirror moving linearly in the plane of the incident light. This process selectively blocks certain wavelengths and permits measurement of the sample's absorption rates as a function of the wavelengths blocked to produce an 'inteferogram.' This is subsequently processed using a Fourier transform to obtain the sample's spectrum and ascertain the sample's composition. With our prototype CIRIS instrument in development at Design and Prototype Inc. and NASA-JPL, we propose the use of a rotating refractor spinning at a constant velocity to variably phase shift incident light to the detector as an alternative to a linearly moving mirror. This design eliminates sensitivity to vibrations, minimizing path length and non-linear errors due to minor perturbations to the system, in addition to facilitating compact design critical to meeting the strict volume requirements of spacecraft. Further, this is done without sacrificing spectral resolution or throughput when compared to Michelson or diffractive designs. While Michelson designs

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

Chlorococcalean microalgae Ankistrodesmus convolutes biodiesel characterization with Fourier transform-infrared spectroscopy and gas chromatography mass spectroscopy techniques

Directory of Open Access Journals (Sweden)

Swati SONAWANE

2015-12-01

Full Text Available The Chlorococcalean microalgae Ankistrodesmus convolutes was found in fresh water Godawari reservoir, Ahmednagar district of Maharashtra State, India. Microalgae are modern biomass for the production of liquid biofuel due to its high solar cultivation efficiency. The collection, harvesting and drying processes were play vital role in converting algal biomass into energy liquid fuel. The oil extraction was the important step for the biodiesel synthesis. The fatty acid methyl ester (FAME synthesis was carried through base catalyzed transesterification method. The product was analyzed by using the hyphened techniques like Fourier Transform-Infrared spectroscopy (FT-IR and Gas Chromatography Mass Spectroscopy (GCMS. FT-IR Spectroscopy was results the ester as functional group of obtained product while the Gas Chromatography Mass Spectroscopy was results the six type of fatty acid methyl ester with different concentration. Ankistrodesmus convolutes biodiesel consist of 46.5% saturated and 49.14% unsaturated FAME.

Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Spectroscopy as an Analytical Method to Investigate the Secondary Structure of a Model Protein Embedded in Solid Lipid Matrices.

Science.gov (United States)

Zeeshan, Farrukh; Tabbassum, Misbah; Jorgensen, Lene; Medlicott, Natalie J

2018-02-01

Protein drugs may encounter conformational perturbations during the formulation processing of lipid-based solid dosage forms. In aqueous protein solutions, attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy can investigate these conformational changes following the subtraction of spectral interference of solvent with protein amide I bands. However, in solid dosage forms, the possible spectral contribution of lipid carriers to protein amide I band may be an obstacle to determine conformational alterations. The objective of this study was to develop an ATR FT-IR spectroscopic method for the analysis of protein secondary structure embedded in solid lipid matrices. Bovine serum albumin (BSA) was chosen as a model protein, while Precirol AT05 (glycerol palmitostearate, melting point 58 ℃) was employed as the model lipid matrix. Bovine serum albumin was incorporated into lipid using physical mixing, melting and mixing, or wet granulation mixing methods. Attenuated total reflection FT-IR spectroscopy and size exclusion chromatography (SEC) were performed for the analysis of BSA secondary structure and its dissolution in aqueous media, respectively. The results showed significant interference of Precirol ATO5 with BSA amide I band which was subtracted up to 90% w/w lipid content to analyze BSA secondary structure. In addition, ATR FT-IR spectroscopy also detected thermally denatured BSA solid alone and in the presence of lipid matrix indicating its suitability for the detection of denatured protein solids in lipid matrices. Despite being in the solid state, conformational changes occurred to BSA upon incorporation into solid lipid matrices. However, the extent of these conformational alterations was found to be dependent on the mixing method employed as indicated by area overlap calculations. For instance, the melting and mixing method imparted negligible effect on BSA secondary structure, whereas the wet granulation mixing method promoted

Characterization of Archaeological Sediments Using Fourier Transform Infrared (FT-IR) and Portable X-ray Fluorescence (pXRF): An Application to Formative Period Pyro-Industrial Sites in Pacific Coastal Southern Chiapas, Mexico.

Science.gov (United States)

Neff, Hector; Bigney, Scott J; Sakai, Sachiko; Burger, Paul R; Garfin, Timothy; George, Richard G; Culleton, Brendan J; Kennett, Douglas J

2016-01-01

Archaeological sediments from mounds within the mangrove zone of far-southern Pacific coastal Chiapas, Mexico, are characterized in order to test the hypothesis that specialized pyro-technological activities of the region's prehistoric inhabitants (salt and ceramic production) created the accumulations visible today. Fourier transform infrared spectroscopy (FT-IR) is used to characterize sediment mineralogy, while portable X-ray fluorescence (pXRF) is used to determine elemental concentrations. Elemental characterization of natural sediments by both instrumental neutron activation analysis (INAA) and pXRF also contribute to understanding of processes that created the archaeological deposits. Radiocarbon dates combined with typological analysis of ceramics indicate that pyro-industrial activity in the mangrove zone peaked during the Late Formative and Terminal Formative periods, when population and monumental activity on the coastal plain and piedmont were also at their peaks. © The Author(s) 2015.

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.

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)

[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.

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..

Detection of Gastric Cancer with Fourier Transform Infrared Spectroscopy and Support Vector Machine Classification

Directory of Open Access Journals (Sweden)

Qingbo Li

2013-01-01

Full Text Available Early diagnosis and early medical treatments are the keys to save the patients' lives and improve the living quality. Fourier transform infrared (FT-IR spectroscopy can distinguish malignant from normal tissues at the molecular level. In this paper, programs were made with pattern recognition method to classify unknown samples. Spectral data were pretreated by using smoothing and standard normal variate (SNV methods. Leave-one-out cross validation was used to evaluate the discrimination result of support vector machine (SVM method. A total of 54 gastric tissue samples were employed in this study, including 24 cases of normal tissue samples and 30 cases of cancerous tissue samples. The discrimination results of SVM method showed the sensitivity with 100%, specificity with 83.3%, and total discrimination accuracy with 92.2%.

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.

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...

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

An FT-Raman, FT-IR, and Quantum Chemical Investigation of Stanozolol and Oxandrolone

Directory of Open Access Journals (Sweden)

Tibebe Lemma

2017-12-01

Full Text Available We have studied the Fourier Transform Infrared (FT-IR and the Fourier transform Raman (FT-Raman spectra of stanozolol and oxandrolone, and we have performed quantum chemical calculations based on the density functional theory (DFT with a B3LYP/6-31G (d, p level of theory. The FT-IR and FT-Raman spectra were collected in a solid phase. The consistency between the calculated and experimental FT-IR and FT-Raman data indicates that the B3LYP/6-31G (d, p can generate reliable geometry and related properties of the title compounds. Selected experimental bands were assigned and characterized on the basis of the scaled theoretical wavenumbers by their total energy distribution. The good agreement between the experimental and theoretical spectra allowed positive assignment of the observed vibrational absorption bands. Finally, the calculation results were applied to simulate the Raman and IR spectra of the title compounds, which show agreement with the observed spectra.

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.

Rapid and automatic chemical identification of the medicinal flower buds of Lonicera plants by the benchtop and hand-held Fourier transform infrared spectroscopy

Science.gov (United States)

Chen, Jianbo; Guo, Baolin; Yan, Rui; Sun, Suqin; Zhou, Qun

2017-07-01

With the utilization of the hand-held equipment, Fourier transform infrared (FT-IR) spectroscopy is a promising analytical technique to minimize the time cost for the chemical identification of herbal materials. This research examines the feasibility of the hand-held FT-IR spectrometer for the on-site testing of herbal materials, using Lonicerae Japonicae Flos (LJF) and Lonicerae Flos (LF) as examples. Correlation-based linear discriminant models for LJF and LF are established based on the benchtop and hand-held FT-IR instruments. The benchtop FT-IR models can exactly recognize all articles of LJF and LF. Although a few LF articles are misjudged at the sub-class level, the hand-held FT-IR models are able to exactly discriminate LJF and LF. As a direct and label-free analytical technique, FT-IR spectroscopy has great potential in the rapid and automatic chemical identification of herbal materials either in laboratories or in fields. This is helpful to prevent the spread and use of adulterated herbal materials in time.

Discrimination between Bacillus and Alicyclobacillus isolates in apple juice by Fourier transform infrared spectroscopy and multivariate analysis.

Science.gov (United States)

Al-Holy, Murad A; Lin, Mengshi; Alhaj, Omar A; Abu-Goush, Mahmoud H

2015-02-01

Alicyclobacillus is a causative agent of spoilage in pasteurized and heat-treated apple juice products. Differentiating between this genus and the closely related Bacillus is crucially important. In this study, Fourier transform infrared spectroscopy (FT-IR) was used to identify and discriminate between 4 Alicyclobacillus strains and 4 Bacillus isolates inoculated individually into apple juice. Loading plots over the range of 1350 and 1700 cm(-1) reflected the most distinctive biochemical features of Bacillus and Alicyclobacillus. Multivariate statistical methods (for example, principal component analysis and soft independent modeling of class analogy) were used to analyze the spectral data. Distinctive separation of spectral samples was observed. This study demonstrates that FT-IR spectroscopy in combination with multivariate analysis could serve as a rapid and effective tool for fruit juice industry to differentiate between Bacillus and Alicyclobacillus and to distinguish between species belonging to these 2 genera. © 2015 Institute of Food Technologists®

FT-IR microscopical analysis with synchrotron radiation: The microscope optics and system performance

International Nuclear Information System (INIS)

Reffner, J.A.; Martoglio, P.A.; Williams, G.P.

1995-01-01

When a Fourier transform infrared (FT-IR) microspectrometer was first interfaced with the National Synchrotron Light Source (NSLS) in September 1993, there was an instant realization that the performance at the diffraction limit had increased 40-100 times. The synchrotron source transformed the IR microspectrometer into a true IR microprobe, providing high-quality IR spectra for probe diameters at the diffraction limit. The combination of IR microspectroscopy and synchrotron radiation provides a powerful new tool for molecular spectroscopy. The ability to perform IR microspectroscopy with synchrotron radiation is still under development at Brookhaven National Laboratory, but several initial studies have been completed that demonstrate the broad-ranging applications of this technology and its potential for materials characterization

FT-IR microscopical analysis with synchrotron radiation: The microscope optics and system performance

Energy Technology Data Exchange (ETDEWEB)

Reffner, J.A.; Martoglio, P.A. [Spectra-Tech, Inc., Shelton, CT (United States); Williams, G.P. [Brookhaven National Lab., Upton, NY (United States)

1995-01-01

When a Fourier transform infrared (FT-IR) microspectrometer was first interfaced with the National Synchrotron Light Source (NSLS) in September 1993, there was an instant realization that the performance at the diffraction limit had increased 40-100 times. The synchrotron source transformed the IR microspectrometer into a true IR microprobe, providing high-quality IR spectra for probe diameters at the diffraction limit. The combination of IR microspectroscopy and synchrotron radiation provides a powerful new tool for molecular spectroscopy. The ability to perform IR microspectroscopy with synchrotron radiation is still under development at Brookhaven National Laboratory, but several initial studies have been completed that demonstrate the broad-ranging applications of this technology and its potential for materials characterization.

Characterization and quantitation of aprepitant drug substance polymorphs by attenuated total reflectance fourier transform infrared spectroscopy.

Science.gov (United States)

Helmy, Roy; Zhou, George X; Chen, Yadan W; Crocker, Louis; Wang, Tao; Wenslow, Robert M; Vailaya, Anant

2003-02-01

In this study, we report the use of attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FT-IR) for the identification and quantitation of two polymorphs of Aprepitant, a substance P antagonist for chemotherapy-induced emesis. Mixtures of the polymorph pair were prepared by weight and ATR-FT-IR spectra of the powdered samples were obtained over the wavelength range of 700-1500 cm(-1). Significant spectral differences between the two polymorphs at 1140 cm(-1) show that ATR-FT-IR can provide definitive identification of the polymorphs. To investigate the feasibility of ATR-FT-IR for quantitation of polymorphic forms of Aprepitant, a calibration plot was constructed with known mixtures of the two polymorphs by plotting the peak ratio of the second derivative of absorbance spectra against the weight percent of form II in the polymorphic mixture. Using this novel approach, 3 wt % of one crystal form could be detected in mixtures of the two polymorphs. The accuracy of ATR-FT-IR in determining polymorph purity of the drug substance was tested by comparing the results with those obtained by X-ray powder diffractometry (XRPD). Indeed, polymorphic purity results obtained by ATR-FT-IR were found to be in good agreement with the predictions made by XRPD and compared favorably with actual values in the known mixtures. The present study clearly demonstrates the potential of ATR-FT-IR as a quick, easy, and inexpensive alternative to XRPD for the determination of polymorphic identity and purity of solid drug substances. The technique is ideally suited for polymorph analysis, because it is precise, accurate, and requires minimal sample preparation.

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

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

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.

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

In-situ chemical analyses of trans-polyisoprene by histochemical staining and Fourier transform infrared microspectroscopy in a rubber-producing plant, Eucommia ulmoides Oliver.

Science.gov (United States)

Bamba, Takeshi; Fukusaki, Ei-Ichiro; Nakazawa, Yoshihisa; Kobayashi, Akio

2002-10-01

The localization of polyisoprene in young stem tissues of Eucommia ulmoides Oliver was investigated by histochemical staining and Fourier transform infrared (FT-IR) microspectroscopy. The fibrous structures were stained with Oil Red O. FT-IR microspectroscopic analysis proved that the fibrous structures were trans-polyisoprene. Granular structures stained with the dye, and characteristic absorptions at 2,960 cm(-1) and 1,430 cm(-1) in FT-IR suggested that trans-polyisoprene accumulated in the vicinity of the cambium layer. We have thus successfully shown for the first time the localization of trans-polyisoprene in plant tissues, and our histological investigation allowed us to presume the main sites of biosynthesis and accumulation of trans-rubber. Furthermore, a new technical approach, the preparation of sections using an electronic freezing unit and the in situ analysis of polyisoprene using FT-IR microspectroscopy, is demonstrated to be a promising method for determining the accumulation of polyisoprene as well as other metabolites.

Development and validation of green method for estimation of clarithromycin in pharmaceutical formulation by transmission fourier transform infrared spectroscopy

International Nuclear Information System (INIS)

Mallah, M.A.; Sherazi, S.T.H.; Mahesar, S.A.; Rauf, A.

2012-01-01

A rapid, sensitive and environmental friendly analytical method for the direct determination of clarithromycin in tablet formulations through transmission Fourier Transform Infrared (FT-IR) spectroscopy has been successfully developed for routine quality control analysis. This method avoids any sample pretreatment except grinding or use of any solvent as extraction is no more required. Standards and samples were analysed in the form of KBr pellet for recording FT-IR spectra. In the final step, chemometric method was used to filter out unmatched spectral features and the converted and filtered spectra were used to build a calibration model based on partial least square (PLS) using the FT-IR carbonyl region (C=O) from 2965-1662 cm/sup -1/. The excellent correlation coefficient (R2) was achieved (0.9999). This also fulfills the ever increasing demand of pharmaceutical industries for developing sensitive, economical and less time consuming methods for the quantification of Active Pharmaceutical Ingredients (API) while monitoring quality of finished product with total analysis time of less than three minutes. (author)

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

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.

Fourier transform spectroscopy of six stars

Energy Technology Data Exchange (ETDEWEB)

Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia

1981-01-01

This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.

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

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 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.

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.

A New Green Method for the Quantitative Analysis of Enrofloxacin by Fourier-Transform Infrared Spectroscopy.

Science.gov (United States)

Rebouças, Camila Tavares; Kogawa, Ana Carolina; Salgado, Hérida Regina Nunes

2018-05-18

Background: A green analytical chemistry method was developed for quantification of enrofloxacin in tablets. The drug, a second-generation fluoroquinolone, was first introduced in veterinary medicine for the treatment of various bacterial species. Objective: This study proposed to develop, validate, and apply a reliable, low-cost, fast, and simple IR spectroscopy method for quantitative routine determination of enrofloxacin in tablets. Methods: The method was completely validated according to the International Conference on Harmonisation guidelines, showing accuracy, precision, selectivity, robustness, and linearity. Results: It was linear over the concentration range of 1.0-3.0 mg with correlation coefficients >0.9999 and LOD and LOQ of 0.12 and 0.36 mg, respectively. Conclusions: Now that this IR method has met performance qualifications, it can be adopted and applied for the analysis of enrofloxacin tablets for production process control. The validated method can also be utilized to quantify enrofloxacin in tablets and thus is an environmentally friendly alternative for the routine analysis of enrofloxacin in quality control. Highlights: A new green method for the quantitative analysis of enrofloxacin by Fourier-Transform Infrared spectroscopy was validated. It is a fast, clean and low-cost alternative for the evaluation of enrofloxacin tablets.

Economical Appraisal of Total Aflatoxin Level in the Poultry Feeds by Fourier Transform Infrared Spectroscopy

International Nuclear Information System (INIS)

Sherazai, S.T.H.; Shar, Z.; Iqbal, M.; Sumbal, G.A.

2013-01-01

Single-bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopy has been used for the quantitative determination of total aflatoxins in the broiler poultry feed. An FTIR calibration spanning the range 1-70 micro g/L aflatoxin standards in (70:30, v/v) methanol-water solvent system based on partial least square (PLS) model, developed by relating mid IR region between 3755-950 cm/ sub -1/. The excellent coefficient of various (using 0.998) was achieved with 1.49 relative mean square error of calibration (RMSEC). Aflatoxins from each of eight poultry feeds was extracted and the determined by the widely used commercially available Enzyme-linked Immunosorbent Assay (ELISA) procedure and the SB-ATR/FTIR method. The SB-ATR/FTIR aflatoxins predictions were related to those determined by the ELISA method by linear regression, producing an R value of 0.989 and a SD of +- 2.80 micro g/L. The result of the study clearly indicated that FT-IR spectroscopy due to its rapidity and simplicity along with data manipulation by advance computer software could be effectively used for routine determination of aflatoxins present in the poultry feeds at very low level. (author)

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...

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.

A Rapid Method of Crude Oil Analysis Using FT-IR Spectroscopy

African Journals Online (AJOL)

HP USER

Nigerian Journal of Basic and Applied Science (June,2016), 24(1): 47-55 ... ABSTRACT: This study determines the viability of the use of Fourier Transform ... IR spectra of Crude oil sample containing a mixture of both degraded (sample 151).

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.

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,

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)

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)

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.

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....

Analysis of gamma-ray spectra by using fast Fourier transform

International Nuclear Information System (INIS)

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

1977-01-01

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 devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. 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 in the method and a general problem to be solved in a response matrix method are described. (auth.)

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)

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.

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.

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

Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Spectroscopy as a Forensic Method to Determine the Composition of Inks Used to Print the United States One-cent Blue Benjamin Franklin Postage Stamps of the 19th Century.

Science.gov (United States)

Brittain, Harry G

2016-01-01

Through the combined use of infrared (IR) absorption spectroscopy and attenuated total reflectance (ATR) sampling, the composition of inks used to print the many different types of one-cent Benjamin Franklin stamps of the 19th century has been established. This information permits a historical evaluation of the formulations used at various times, and also facilitates the differentiation of the various stamps from each other. In two instances, the ink composition permits the unambiguous identification of stamps whose appearance is identical, and which (until now) have only been differentiated through estimates of the degree of hardness or softness of the stamp paper, or through the presence or absence of a watermark in the paper. In these instances, the use of ATR Fourier transform infrared spectroscopy (FT-IR) spectroscopy effectively renders irrelevant two 100-year-old practices of stamp identification. Furthermore, since the use of ATR sampling makes it possible to obtain the spectrum of a stamp still attached to its cover, it is no longer necessary to identify these blue Franklin stamps using their cancellation dates. © The Author(s) 2015.

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.)

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 ...

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.

A validated Fourier transform infrared spectroscopy method for quantification of total lactones in Inula racemosa and Andrographis paniculata.

Science.gov (United States)

Shivali, Garg; Praful, Lahorkar; Vijay, Gadgil

2012-01-01

Fourier transform infrared (FT-IR) spectroscopy is a technique widely used for detection and quantification of various chemical moieties. This paper describes the use of the FT-IR spectroscopy technique for the quantification of total lactones present in Inula racemosa and Andrographis paniculata. To validate the FT-IR spectroscopy method for quantification of total lactones in I. racemosa and A. paniculata. Dried and powdered I. racemosa roots and A. paniculata plant were extracted with ethanol and dried to remove ethanol completely. The ethanol extract was analysed in a KBr pellet by FT-IR spectroscopy. The FT-IR spectroscopy method was validated and compared with a known spectrophotometric method for quantification of lactones in A. paniculata. By FT-IR spectroscopy, the amount of total lactones was found to be 2.12 ± 0.47% (n = 3) in I. racemosa and 8.65 ± 0.51% (n = 3) in A. paniculata. The method showed comparable results with a known spectrophotometric method used for quantification of such lactones: 8.42 ± 0.36% (n = 3) in A. paniculata. Limits of detection and quantification for isoallantolactone were 1 µg and 10 µg respectively; for andrographolide they were 1.5 µg and 15 µg respectively. Recoveries were over 98%, with good intra- and interday repeatability: RSD ≤ 2%. The FT-IR spectroscopy method proved linear, accurate, precise and specific, with low limits of detection and quantification, for estimation of total lactones, and is less tedious than the UV spectrophotometric method for the compounds tested. This validated FT-IR spectroscopy method is readily applicable for the quality control of I. racemosa and A. paniculata. Copyright © 2011 John Wiley & Sons, Ltd.

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.

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 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).

Rapid differentiation of Listeria monocytogenes epidemic clones III and IV and their intact compared with heat-killed populations using Fourier transform infrared spectroscopy and chemometrics.

Science.gov (United States)

Nyarko, Esmond B; Puzey, Kenneth A; Donnelly, Catherine W

2014-06-01

The objectives of this study were to determine if Fourier transform infrared (FT-IR) spectroscopy and multivariate statistical analysis (chemometrics) could be used to rapidly differentiate epidemic clones (ECs) of Listeria monocytogenes, as well as their intact compared with heat-killed populations. FT-IR spectra were collected from dried thin smears on infrared slides prepared from aliquots of 10 μL of each L. monocytogenes ECs (ECIII: J1-101 and R2-499; ECIV: J1-129 and J1-220), and also from intact and heat-killed cell populations of each EC strain using 250 scans at a resolution of 4 cm(-1) in the mid-infrared region in a reflectance mode. Chemometric analysis of spectra involved the application of the multivariate discriminant method for canonical variate analysis (CVA) and linear discriminant analysis (LDA). CVA of the spectra in the wavelength region 4000 to 600 cm(-1) separated the EC strains while LDA resulted in a 100% accurate classification of all spectra in the data set. Further, CVA separated intact and heat-killed cells of each EC strain and there was 100% accuracy in the classification of all spectra when LDA was applied. FT-IR spectral wavenumbers 1650 to 1390 cm(-1) were used to separate heat-killed and intact populations of L. monocytogenes. The FT-IR spectroscopy method allowed discrimination between strains that belong to the same EC. FT-IR is a highly discriminatory and reproducible method that can be used for the rapid subtyping of L. monocytogenes, as well as for the detection of live compared with dead populations of the organism. Fourier transform infrared (FT-IR) spectroscopy and multivariate statistical analysis can be used for L. monocytogenes source tracking and for clinical case isolate comparison during epidemiological investigations since the method is capable of differentiating epidemic clones and it uses a library of well-characterized strains. The FT-IR method is potentially less expensive and more rapid compared to genetic

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.

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

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...

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.

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)

Fourier Transform Infrared (FT-IR) and Laser Ablation Inductively Coupled Plasma-Mass Spectrometry (LA-ICP-MS) Imaging of Cerebral Ischemia: Combined Analysis of Rat Brain Thin Cuts Toward Improved Tissue Classification.

Science.gov (United States)

Balbekova, Anna; Lohninger, Hans; van Tilborg, Geralda A F; Dijkhuizen, Rick M; Bonta, Maximilian; Limbeck, Andreas; Lendl, Bernhard; Al-Saad, Khalid A; Ali, Mohamed; Celikic, Minja; Ofner, Johannes

2018-02-01

Microspectroscopic techniques are widely used to complement histological studies. Due to recent developments in the field of chemical imaging, combined chemical analysis has become attractive. This technique facilitates a deepened analysis compared to single techniques or side-by-side analysis. In this study, rat brains harvested one week after induction of photothrombotic stroke were investigated. Adjacent thin cuts from rats' brains were imaged using Fourier transform infrared (FT-IR) microspectroscopy and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The LA-ICP-MS data were normalized using an internal standard (a thin gold layer). The acquired hyperspectral data cubes were fused and subjected to multivariate analysis. Brain regions affected by stroke as well as unaffected gray and white matter were identified and classified using a model based on either partial least squares discriminant analysis (PLS-DA) or random decision forest (RDF) algorithms. The RDF algorithm demonstrated the best results for classification. Improved classification was observed in the case of fused data in comparison to individual data sets (either FT-IR or LA-ICP-MS). Variable importance analysis demonstrated that both molecular and elemental content contribute to the improved RDF classification. Univariate spectral analysis identified biochemical properties of the assigned tissue types. Classification of multisensor hyperspectral data sets using an RDF algorithm allows access to a novel and in-depth understanding of biochemical processes and solid chemical allocation of different brain regions.

Rapid and quantitative detection of the microbial spoilage of meat by fourier transform infrared spectroscopy and machine learning.

Science.gov (United States)

Ellis, David I; Broadhurst, David; Kell, Douglas B; Rowland, Jem J; Goodacre, Royston

2002-06-01

Fourier transform infrared (FT-IR) spectroscopy is a rapid, noninvasive technique with considerable potential for application in the food and related industries. We show here that this technique can be used directly on the surface of food to produce biochemically interpretable "fingerprints." Spoilage in meat is the result of decomposition and the formation of metabolites caused by the growth and enzymatic activity of microorganisms. FT-IR was exploited to measure biochemical changes within the meat substrate, enhancing and accelerating the detection of microbial spoilage. Chicken breasts were purchased from a national retailer, comminuted for 10 s, and left to spoil at room temperature for 24 h. Every hour, FT-IR measurements were taken directly from the meat surface using attenuated total reflectance, and the total viable counts were obtained by classical plating methods. Quantitative interpretation of FT-IR spectra was possible using partial least-squares regression and allowed accurate estimates of bacterial loads to be calculated directly from the meat surface in 60 s. Genetic programming was used to derive rules showing that at levels of 10(7) bacteria.g(-1) the main biochemical indicator of spoilage was the onset of proteolysis. Thus, using FT-IR we were able to acquire a metabolic snapshot and quantify, noninvasively, the microbial loads of food samples accurately and rapidly in 60 s, directly from the sample surface. We believe this approach will aid in the Hazard Analysis Critical Control Point process for the assessment of the microbiological safety of food at the production, processing, manufacturing, packaging, and storage levels.

Antioxidant activity and FT-IR analysis of Datura innoxia and Datura ...

African Journals Online (AJOL)

Materials and Methods: Determination of total phenolic content and total flavonoid content and antioxidant activity in terms of total antioxidant assay, ABTS assay, DPPH assay and in-vitro lipid peroxidation inhibiting activity were determined along with the FT-IR (Fourier transform infrared spectroscopy) analysis of the ...

Fourier transform-infrared spectroscopic methods for microbial ecology: analysis of bacteria, bacteria-polymer mixtures and biofilms

Science.gov (United States)

Nichols, P. D.; Henson, J. M.; Guckert, J. B.; Nivens, D. E.; White, D. C.

1985-01-01

Fourier transform-infrared (FT-IR) spectroscopy has been used to rapidly and nondestructively analyze bacteria, bacteria-polymer mixtures, digester samples and microbial biofilms. Diffuse reflectance FT-IR (DRIFT) analysis of freeze-dried, powdered samples offered a means of obtaining structural information. The bacteria examined were divided into two groups. The first group was characterized by a dominant amide I band and the second group of organisms displayed an additional strong carbonyl stretch at approximately 1740 cm-1. The differences illustrated by the subtraction spectra obtained for microbes of the two groups suggest that FT-IR spectroscopy can be utilized to recognize differences in microbial community structure. Calculation of specific band ratios has enabled the composition of bacteria and extracellular or intracellular storage product polymer mixtures to be determined for bacteria-gum arabic (amide I/carbohydrate C-O approximately 1150 cm-1) and bacteria-poly-beta-hydroxybutyrate (amide I/carbonyl approximately 1740 cm-1). The key band ratios correlate with the compositions of the material and provide useful information for the application of FT-IR spectroscopy to environmental biofilm samples and for distinguishing bacteria grown under differing nutrient conditions. DRIFT spectra have been obtained for biofilms produced by Vibrio natriegens on stainless steel disks. Between 48 and 144 h, an increase in bands at approximately 1440 and 1090 cm-1 was seen in FT-IR spectra of the V. natriegens biofilm. DRIFT spectra of mixed culture effluents of anaerobic digesters show differences induced by shifts in input feedstocks. The use of flow-through attenuated total reflectance has permitted in situ real-time changes in biofilm formation to be monitored and provides a powerful tool for understanding the interactions within adherent microbial consortia.

Application of Fourier transform infrared spectroscopy and chemometrics for differentiation of Salmonella enterica serovar Enteritidis phage types.

Science.gov (United States)

Preisner, Ornella; Guiomar, Raquel; Machado, Jorge; Menezes, José Cardoso; Lopes, João Almeida

2010-06-01

Fourier transform infrared (FT-IR) spectroscopy and chemometric techniques were used to discriminate five closely related Salmonella enterica serotype Enteritidis phage types, phage type 1 (PT1), PT1b, PT4b, PT6, and PT6a. Intact cells and outer membrane protein (OMP) extracts from bacterial cell membranes were subjected to FT-IR analysis in transmittance mode. Spectra were collected over a wavenumber range from 4,000 to 600 cm(-1). Partial least-squares discriminant analysis (PLS-DA) was used to develop calibration models based on preprocessed FT-IR spectra. The analysis based on OMP extracts provided greater separation between the Salmonella Enteritidis PT1-PT1b, PT4b, and PT6-PT6a groups than the intact cell analysis. When these three phage type groups were considered, the method based on OMP extract FT-IR spectra was 100% accurate. Moreover, complementary local models that considered only the PT1-PT1b and PT6-PT6a groups were developed, and the level of discrimination increased. PT1 and PT1b isolates were differentiated successfully with the local model using the entire OMP extract spectrum (98.3% correct predictions), whereas the accuracy of discrimination between PT6 and PT6a isolates was 86.0%. Isolates belonging to different phage types (PT19, PT20, and PT21) were used with the model to test its robustness. For the first time it was demonstrated that FT-IR analysis of OMP extracts can be used for construction of robust models that allow fast and accurate discrimination of different Salmonella Enteritidis phage types.

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

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

Rapid measurement of human milk macronutrients in the neonatal intensive care unit: accuracy and precision of fourier transform mid-infrared spectroscopy.

Science.gov (United States)

Smilowitz, Jennifer T; Gho, Deborah S; Mirmiran, Majid; German, J Bruce; Underwood, Mark A

2014-05-01

Although it is well established that human milk varies widely in macronutrient content, it remains common for human milk fortification for premature infants to be based on historic mean values. As a result, those caring for premature infants often underestimate protein intake. Rapid precise measurement of human milk protein, fat, and lactose to allow individualized fortification has been proposed for decades but remains elusive due to technical challenges. This study aimed to evaluate the accuracy and precision of a Fourier transform (FT) mid-infrared (IR) spectroscope in the neonatal intensive care unit to measure human milk fat, total protein, lactose, and calculated energy compared with standard chemical analyses. One hundred sixteen breast milk samples across lactation stages from women who delivered at term (n = 69) and preterm (n = 5) were analyzed with the FT mid-IR spectroscope and with standard chemical methods. Ten of the samples were tested in replicate using the FT mid-IR spectroscope to determine repeatability. The agreement between the FT mid-IR spectroscope analysis and reference methods was high for protein and fat and moderate for lactose and energy. The intra-assay coefficients of variation for all outcomes were less than 3%. The FT mid-IR spectroscope demonstrated high accuracy in measurement of total protein and fat of preterm and term milk with high precision.

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.

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.

Attenuated total internal reflection Fourier transform infrared spectroscopy: a quantitative approach for kidney stone analysis.

Science.gov (United States)

Gulley-Stahl, Heather J; Haas, Jennifer A; Schmidt, Katherine A; Evan, Andrew P; Sommer, André J

2009-07-01

The impact of kidney stone disease is significant worldwide, yet methods for quantifying stone components remain limited. A new approach requiring minimal sample preparation for the quantitative analysis of kidney stone components has been investigated utilizing attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FT-IR). Calcium oxalate monohydrate (COM) and hydroxylapatite (HAP), two of the most common constituents of urinary stones, were used for quantitative analysis. Calibration curves were constructed using integrated band intensities of four infrared absorptions versus concentration (weight %). The correlation coefficients of the calibration curves range from 0.997 to 0.93. The limits of detection range from 0.07 +/- 0.02% COM/HAP where COM is the analyte and HAP is the matrix, to 0.26 +/- 0.07% HAP/COM where HAP is the analyte and COM is the matrix. This study shows that linear calibration curves can be generated for the quantitative analysis of stone mixtures provided the system is well understood especially with respect to particle size.

Direct and simultaneous detection of organic and inorganic ingredients in herbal powder preparations by Fourier transform infrared microspectroscopic imaging.

Science.gov (United States)

Chen, Jian-Bo; Sun, Su-Qin; Tang, Xu-Dong; Zhang, Jing-Zhao; Zhou, Qun

2016-08-05

Herbal powder preparation is a kind of widely-used herbal product in the form of powder mixture of herbal ingredients. Identification of herbal ingredients is the first and foremost step in assuring the quality, safety and efficacy of herbal powder preparations. In this research, Fourier transform infrared (FT-IR) microspectroscopic identification method is proposed for the direct and simultaneous recognition of multiple organic and inorganic ingredients in herbal powder preparations. First, the reference spectrum of characteristic particles of each herbal ingredient is assigned according to FT-IR results and other available information. Next, a statistical correlation threshold is determined as the lower limit of correlation coefficients between the reference spectrum and a larger number of calibration characteristic particles. After validation, the reference spectrum and correlation threshold can be used to identify herbal ingredient in mixture preparations. A herbal ingredient is supposed to be present if correlation coefficients between the reference spectrum and some sample particles are above the threshold. Using this method, all kinds of herbal materials in powder preparation Kouqiang Kuiyang San are identified successfully. This research shows the potential of FT-IR microspectroscopic identification method for the accurate and quick identification of ingredients in herbal powder preparations. Copyright © 2016 Elsevier B.V. All rights reserved.

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

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.

Growth and phase transformations of Ir on Ge(111)

Science.gov (United States)

Mullet, C. H.; Stenger, B. H.; Durand, A. M.; Morad, J. A.; Sato, Y.; Poppenheimer, E. C.; Chiang, S.

2017-12-01

The growth of Ir on Ge(111) as a function of temperature between 23 °C and 820 °C is characterized with low energy electron microscopy (LEEM), low energy electron diffraction (LEED), scanning tunneling microscopy (STM), and x-ray photoemission spectroscopy (XPS). Deposition onto a substrate at 350 °C revealed a novel growth mode consisting of multilayer Ir islands with (√3 × √3)R30° (abbreviated as √3) structure interconnected by ;bridges; of single-layer Ir several atoms wide. For deposition onto substrates above 500 °C, the √3 Ir phase grows with dendritic morphology, and substrate step bunches act as barriers to √3 Ir growth. LEEM images showed Stranski-Krastanov growth for 650-820 °C: after the √3 phase covers the surface, corresponding to 2 monolayers (ML) Ir coverage, multilayer hexagonal-shaped Ir islands form, surrounded by regions of IrGe alloy. Hexagonal-shaped Ir islands also formed upon heating 1.2 ML of √3 Ir beyond 830 °C, which resulted in the elimination of √3 structure from the surface. The transformation from √3 to (1 × 1) structure upon heating to 830 °C was an irreversible surface phase transition. Annealing > 2.0 ML of Ir in the √3 phase above the 830 °C disorder temperature, followed by cooling, produced a (3 × 1) structure. Subsequent heating and cooling through 830 °C give evidence for a reversible (3 × 1) to (1 × 1) phase transition.

Identification of a Methane Oxidation Intermediate on Solid Oxide Fuel Cell Anode Surfaces with Fourier Transform Infrared Emission.

Science.gov (United States)

Pomfret, Michael B; Steinhurst, Daniel A; Owrutsky, Jeffrey C

2013-04-18

Fuel interactions on solid oxide fuel cell (SOFC) anodes are studied with in situ Fourier transform infrared emission spectroscopy (FTIRES). SOFCs are operated at 800 °C with CH4 as a representative hydrocarbon fuel. IR signatures of gas-phase oxidation products, CO2(g) and CO(g), are observed while cells are under load. A broad feature at 2295 cm(-1) is assigned to CO2 adsorbed on Ni as a CH4 oxidation intermediate during cell operation and while carbon deposits are electrochemically oxidized after CH4 operation. Electrochemical control provides confirmation of the assignment of adsorbed CO2. FTIRES has been demonstrated as a viable technique for the identification of fuel oxidation intermediates and products in working SOFCs, allowing for the elucidation of the mechanisms of fuel chemistry.

Detection of metanil yellow contamination in turmeric using FT-Raman and FT-IR spectroscopy

Science.gov (United States)

Dhakal, Sagar; Chao, Kuanglin; Qin, Jianwei; Kim, Moon; Schmidt, Walter; Chan, Dian

2016-05-01

Turmeric is well known for its medicinal value and is often used in Asian cuisine. Economically motivated contamination of turmeric by chemicals such as metanil yellow has been repeatedly reported. Although traditional technologies can detect such contaminants in food, high operational costs and operational complexities have limited their use to the laboratory. This study used Fourier Transform Raman Spectroscopy (FT-Raman) and Fourier Transform - Infrared Spectroscopy (FT-IR) to identify metanil yellow contamination in turmeric powder. Mixtures of metanil yellow in turmeric were prepared at concentrations of 30%, 25%, 20%, 15%, 10%, 5%, 1% and 0.01% (w/w). The FT-Raman and FT-IR spectral signal of pure turmeric powder, pure metanil yellow powder and the 8 sample mixtures were obtained and analyzed independently to identify metanil yellow contamination in turmeric. The results show that FT-Raman spectroscopy and FT-IR spectroscopy can detect metanil yellow mixed with turmeric at concentrations as low as 1% and 5%, respectively, and may be useful for non-destructive detection of adulterated turmeric powder.

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.)

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.

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...

Portable Gas Analyzer Based on Fourier Transform Infrared Spectrometer for Patrolling and Examining Gas Exhaust

Directory of Open Access Journals (Sweden)

Yuntao Liang

2015-01-01

Full Text Available Aimed at monitoring emission of organic gases such as CH4, C2H6, C3H8, iso-C4H10, n-C4H10, C2H4, C3H6, C2H2, CO, and CO2, from coal mines, petroleum refineries, and other plants, a Fourier Transform Infrared (FT-IR spectrometer was used to develop a portable gas analyzer for patrolling and examining gas exhaust. Firstly, structure of the instrument was introduced. Then, a spectral analysis approach was presented. Finally, instrument was tested with standard gases and with actual gases emitted from a petroleum refinery. For the latter test, a gas chromatograph (GC was used as a reference instrument. The test results showed that the detection limit of every component of analyte was less than 10 × 10−6. The maximum test error of every analyte was less than 15 × 10−6 when its practical concentration was no more than 500 × 10−6. A final comparison showed that the result curves of analytes obtained with FT-IR spectrometer almost overlapped with those obtained with GC, and their resulting noise was less than 6.4% when the practical gas concentration was above 100 × 10−6. As a result, our instrument was suitable to be used as a portable instrument for monitoring exhaust gases.

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/

Probing specific molecular processes and intermediates by time-resolved Fourier transform infrared spectroscopy: application to the bacteriorhodopsin photocycle.

Science.gov (United States)

Lórenz-Fonfría, Víctor A; Kandori, Hideki; Padrós, Esteve

2011-06-23

We present a general approach for probing the kinetics of specific molecular processes in proteins by time-resolved Fourier transform infrared (IR) spectroscopy. Using bacteriorhodopsin (bR) as a model we demonstrate that by appropriately monitoring some selected IR bands it is possible obtaining the kinetics of the most important events occurring in the photocycle, namely changes in the chromophore and the protein backbone conformation, and changes in the protonation state of the key residues implicated in the proton transfers. Besides confirming widely accepted views of the bR photocycle, our analysis also sheds light into some disputed issues: the degree of retinal torsion in the L intermediate to respect the ground state; the possibility of a proton transfer from Asp85 to Asp212; the relationship between the protonation/deprotonation of Asp85 and the proton release complex; and the timing of the protein backbone dynamics. By providing a direct way to estimate the kinetics of photocycle intermediates the present approach opens new prospects for a robust quantitative kinetic analysis of the bR photocycle, which could also benefit the study of other proteins involved in photosynthesis, in phototaxis, or in respiratory chains.

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.

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.

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.

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

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.

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

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....

Fourier Transform Infrared Imaging analysis of dental pulp inflammatory diseases.

Science.gov (United States)

Giorgini, E; Sabbatini, S; Conti, C; Rubini, C; Rocchetti, R; Fioroni, M; Memè, L; Orilisi, G

2017-05-01

Fourier Transform Infrared microspectroscopy let characterize the macromolecular composition and distribution of tissues and cells, by studying the interaction between infrared radiation and matter. Therefore, we hypothesize to exploit this analytical tool in the analysis of inflamed pulps, to detect the different biochemical features related to various degrees of inflammation. IR maps of 13 irreversible and 12 hyperplastic pulpitis, together with 10 normal pulps, were acquired, compared with histological findings and submitted to multivariate (HCA, PCA, SIMCA) and statistical (one-way ANOVA) analysis. The fit of convoluted bands let calculate meaningful band area ratios (means ± s.d., P < 0.05). The infrared imaging analysis pin-pointed higher amounts of water and lower quantities of type I collagen in all inflamed pulps. Specific vibrational markers were defined for irreversible pulpitis (Lipids/Total Biomass, PhII/Total Biomass, CH 2 /CH 3 , and Ty/AII) and hyperplastic ones (OH/Total Biomass, Collagen/Total Biomass, and CH 3 Collagen/Total Biomass). The study confirmed that FTIR microspectroscopy let discriminate tissues' biological features. The infrared imaging analysis evidenced, in inflamed pulps, alterations in tissues' structure and composition. Changes in lipid metabolism, increasing amounts of tyrosine, and the occurrence of phosphorylative processes were highlighted in irreversible pulpitis, while high amounts of water and low quantities of type I collagen were detected in hyperplastic samples. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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.

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.)

Fourier Transform Infrared and Resonance Raman Spectroscopic Studies of Bacteriorhodopsin.

Science.gov (United States)

Earnest, Thomas Nixon

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

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.

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.

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.

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.

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

Evaluation of Turmeric Powder Adulterated with Metanil Yellow Using FT-Raman and FT-IR Spectroscopy

Directory of Open Access Journals (Sweden)

Sagar Dhakal

2016-05-01

Full Text Available Turmeric powder (Curcuma longa L. is valued both for its medicinal properties and for its popular culinary use, such as being a component in curry powder. Due to its high demand in international trade, turmeric powder has been subject to economically driven, hazardous chemical adulteration. This study utilized Fourier Transform-Raman (FT-Raman and Fourier Transform-Infra Red (FT-IR spectroscopy as separate but complementary methods for detecting metanil yellow adulteration of turmeric powder. Sample mixtures of turmeric powder and metanil yellow were prepared at concentrations of 30%, 25%, 20%, 15%, 10%, 5%, 1%, and 0.01% (w/w. FT-Raman and FT-IR spectra were acquired for these mixture samples as well as for pure samples of turmeric powder and metanil yellow. Spectral analysis showed that the FT-IR method in this study could detect the metanil yellow at the 5% concentration, while the FT-Raman method appeared to be more sensitive and could detect the metanil yellow at the 1% concentration. Relationships between metanil yellow spectral peak intensities and metanil yellow concentration were established using representative peaks at FT-Raman 1406 cm−1 and FT-IR 1140 cm−1 with correlation coefficients of 0.93 and 0.95, respectively.

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.

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....

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

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.

Fourier transform infrared emission spectra of atomic rubidium: g- and h-states

Czech Academy of Sciences Publication Activity Database

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

2012-01-01

Roč. 45, č. 17 (2012), s. 175002 ISSN 0953-4075 R&D Projects: GA AV ČR IAAX00100903 Institutional support: RVO:61388955 Keywords : Fourier transform infrared emission spectra * atomic rubidium * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.031, year: 2012

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.

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.

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...

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

DEFF Research Database (Denmark)

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

2017-01-01

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

Engineering Model Panchromatic Fourier Transform Spectrometer (PanFTS) Instrument for the GEO-CAPE Mission

Data.gov (United States)

National Aeronautics and Space Administration — The Panchromatic Fourier Transform Spectrometer (PanFTS) is an imaging spectrometer that can measure pollutants, greenhouse gases, and aerosols as called for in the...

Symmetries of the second-difference matrix and the finite Fourier transform

International Nuclear Information System (INIS)

Aguilar, A.; Wolf, K.B.

1979-01-01

The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)

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

Science.gov (United States)

Dixit, Rahul; Naskar, Ruchira

2018-03-01

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

10th International Conference on Progress in Fourier Transform Spectroscopy

CERN Document Server

Keresztury, Gábor; Kellner, Robert

1997-01-01

19 plenary lectures and 203 poster papers presented at the 10th International Conference of Fourier Transform Spectroscopy in Budapest 1995 give an overview on the state-of-the art of this technology and its wide range of applications. The reader will get information on any aspects of FTS including the latest instrumental developments, e.g. in diode array detection, time resolution FTS, microscopy and spectral mapping, double modulation and two-dimensional FTS.

On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

International Nuclear Information System (INIS)

Atakishiyeva, M K; Atakishiyev, N M

2015-01-01

We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control

Science.gov (United States)

Pugel, Diane

2012-01-01

Progress has been made into adapting and enhancing a commercially available infrared spectrometer for the development of a handheld device for in-field measurements of the chemical composition of various samples of materials. The intent is to duplicate the functionality of a benchtop Fourier transform infrared spectrometer (FTIR) within the compactness of a handheld instrument with significantly improved spectral responsivity. Existing commercial technology, like the deuterated L-alanine triglycine sulfide detectors (DLATGS), is capable of sensitive in-field chemical analysis. This proposed approach compares several subsystem elements of the FTIR inside of the commercial, non-benchtop system to the commercial benchtop systems. These subsystem elements are the detector, the preamplifier and associated electronics of the detector, the interferometer, associated readout parameters, and cooling. This effort will examine these different detector subsystem elements to look for limitations in each. These limitations will be explored collaboratively with the commercial provider, and will be prioritized to meet the deliverable objectives. The tool design will be that of a handheld gun containing the IR filament source and associated optics. It will operate in a point-and-shoot manner, pointing the source and optics at the sample under test and capturing the reflected response of the material in the same handheld gun. Data will be captured via the gun and ported to a laptop.

CO 2 Capture Capacity and Swelling Measurements of Liquid-like Nanoparticle Organic Hybrid Materials via Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy

KAUST Repository

Park, Youngjune

2012-01-12

Novel nanoparticle organic hybrid materials (NOHMs), which are comprised of organic oligomers or polymers tethered to an inorganic nanosized cores of various sizes, have been synthesized, and their solvating property for CO 2 was investigated using attenuated total reflectance (ATR) Fourier transform infrared (FT-IR) spectroscopy. Simultaneous measurements of CO 2 capture capacity and swelling behaviors of polyetheramine (Jeffamine M-2070) and its corresponding NOHMs (NOHM-I-PE2070) were reported at temperatures of (298, 308, 323 and 353) K and CO 2 pressure conditions ranging from (0 to 5.5) MPa. The polymeric canopy, or polymer bound to the nanoparticle surface, showed significantly less swelling behavior with enhanced or comparable CO 2 capture capacity compared to pure unbound polyetheramine. © 2011 American Chemical Society.

VUV Fourier-Transform absorption study of the np pi (1)Pi(-)(u) nu,N

NARCIS (Netherlands)

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

2015-01-01

Abstract The DESIRS beamline of the SOLEIL synchrotron facility, equipped with a vacuum ultraviolet Fourier-Transform spectrometer has been used to measure Q(N″)(N-N″=0) absorption transitions of the D

Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

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.

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.

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

Science.gov (United States)

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

2015-12-01

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

State of dissolved water in triglycerides as determined by Fourier transform infrared and near infrared spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Kurashige, J. (Ajinomoto Co. Inc., Tokyo (Japan)); Takaoka, K.; Takasago, M.; Taru, Y.; Kobayashi, K. (Musashi Institute of Technology, Tokyo (Japan))

1991-07-20

The states of dissolved water in triglycerides (TG) such as tristearin, triolein, trilinolein and trilinolenin were analyzed by Fourier transform infrared (FT-IR) and near infrared (FT-NIR) spectroscopy, and compared with those of water itself. In the case of water, its states were considered to be mainly polymer clusters larger than dimer ones at 20{degree}C, and mostly monomer or dimer clusters at 120{degree}C. In TG, the states varied widely from monomer to polymer clusters at 20{degree}C. The distribution ratios of the water clusters observed in TG depended on the kinds of fatty acids of TG, and the water state was noted to change due to the interaction between unsaturated bonds and dissolved water. Although the states of dissolved water in trilinolein were similar to those of original water at 20{degree}C, the ratio of monomer water decreased and polymer clusters bigger than those in original water increased with an increase in number of unsaturated bonds of TG. 9 refs., 6 figs., 3 tabs.

Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

Science.gov (United States)

Volkov, V V; Han, M G; Zhu, Y

2013-11-01

We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.

Application of second derivative spectroscopy for increasing molecular specificity of Fourier transform infrared spectroscopic imaging of articular cartilage.

Science.gov (United States)

Rieppo, L; Saarakkala, S; Närhi, T; Helminen, H J; Jurvelin, J S; Rieppo, J

2012-05-01

Fourier transform infrared (FT-IR) spectroscopic imaging is a promising method that enables the analysis of spatial distribution of biochemical components within histological sections. However, analysis of FT-IR spectroscopic data is complicated since absorption peaks often overlap with each other. Second derivative spectroscopy is a technique which enhances the separation of overlapping peaks. The objective of this study was to evaluate the specificity of the second derivative peaks for the main tissue components of articular cartilage (AC), i.e., collagen and proteoglycans (PGs). Histological bovine AC sections were measured before and after enzymatic removal of PGs. Both formalin-fixed sections (n = 10) and cryosections (n = 6) were investigated. Relative changes in the second derivative peak heights caused by the removal of PGs were calculated for both sample groups. The results showed that numerous peaks, e.g., peaks located at 1202 cm(-1) and 1336 cm(-1), altered less than 5% in the experiment. These peaks were assumed to be specific for collagen. In contrast, two peaks located at 1064 cm(-1) and 1376 cm(-1) were seen to alter notably, approximately 50% or more. These peaks were regarded to be specific for PGs. The changes were greater in cryosections than formalin-fixed sections. The results of this study suggest that the second derivative spectroscopy offers a practical and more specific method than routinely used absorption spectrum analysis methods to obtain compositional information on AC with FT-IR spectroscopic imaging. Copyright © 2012 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Temperature-dependent absorption cross-section measurements of 1-butene (1-C4H8) in VUV and IR

KAUST Repository

Es-sebbar, Et-touhami; Bé nilan, Yves; Farooq, Aamir

2013-01-01

synchrotron radiation as a tunable VUV light source. Fourier Transform Infrared (FTIR) spectroscopy is employed to measure absorption cross-section and band strengths in the IR region between 1.54 and 25μm (~6500-400cm-1). The measured room-temperature VUV

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

Science.gov (United States)

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

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

A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

OpenAIRE

Fedorenko, Sergei V.

2011-01-01

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.

Segment density profiles of polyelectrolyte brushes determined by Fourier transform ellipsometry

Science.gov (United States)

Biesalski, Markus; Rühe, Jürgen; Johannsmann, Diethelm

1999-10-01

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

Study of influence with fourier transform on long cable in measurement of fall time of DPF neutron profile