Principles of Fourier analysis
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 ...
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Rudin, Walter
2011-01-01
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Digital Fourier analysis advanced techniques
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced undergraduate and graduate students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Advanced Techniques" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis - Advanced Techniques" is an essential reference for students in science and engineering.
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-11-01
Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in The Physics Teacher aptly demonstrated the use of MacScope2 in just such a manner as a way to teach Fourier analysis.3 A logical continuation of this project is to use MacScope not just to analyze the Fourier composition of musical tones but also musical intervals.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
On higher order Fourier analysis
Szegedy, Balazs
2012-01-01
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the notion "higher order Fourier analysis" in terms of continuous morphisms between structures called compact $k$-step nilspaces. As a byproduct of our results we obtain a new type of limit theory for functions on abelian groups in the spirit of the so-called graph limit theory. Our proofs are based on an exact (non-approximative) version of higher order Fourier analysis which appears on ultra product groups.
Fourier Analysis of Blazar Variability
Finke, Justin D
2014-01-01
Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and time lag behaviors associated with variability in the synchrotron, synchrotron self-Compton (SSC), and external Compton (EC) emission components, from sub-mm to gamma-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We a...
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Fourier analysis and synthesis tomography.
Energy Technology Data Exchange (ETDEWEB)
Wagner, Kelvin H. (University of Colorado at Boulder, Boulder, CO); Sinclair, Michael B.; Feldkuhn, Daniel (University of Colorado at Boulder, Boulder, CO)
2010-05-01
Most far-field optical imaging systems rely on a lens and spatially-resolved detection to probe distinct locations on the object. We describe and demonstrate a novel high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially-integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth-of-field and working-distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. Finally, we present for the first time two-dimensional high-resolution image reconstructions demonstrating a three-orders-of-magnitude improvement in depth-of-field over conventional lens-based microscopy.
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Practical Fourier analysis for multigrid methods
Wienands, Roman
2004-01-01
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the detai...
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Functional Equations and Fourier Analysis
Yang, Dilian
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
Harmonic oscillator: an analysis via Fourier series
de Castro, A S
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
A New Condition for the Uniform Convergence in Fourier Analysis
Institute of Scientific and Technical Information of China (English)
周颂平; 乐瑞君
2004-01-01
@@ In Fourier analysis, since Fourier coefficients are computable and applicable, people have already established many nice results by assuming monotonicty of the coefficients. One famous classical result is done by Chaundy and Jolliffe[1] as follows:
Adaptive Fourier Decomposition Based Time-Frequency Analysis
Institute of Scientific and Technical Information of China (English)
Li-Ming Zhang
2014-01-01
The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition (AFD) offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects: instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.
Oversampling analysis in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
ZHANG Feng; TAO Ran; WANG Yue
2009-01-01
Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal Is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Generalized Fourier analysis for phase retrieval of fringe pattern.
Zhong, Jingang; Weng, Jiawen
2010-12-20
A generalized Fourier analysis, by use of an adaptive multiscale windowed Fourier transform (AWFT), has been presented for the phase retrieval of fringe patterns. The Fourier transform method can be considered as a special case of AWFT method with a maximum window. The instantaneous frequency of the local signal is introduced to estimate whether the condition for separating the first spectrum component is satisfied for the phase retrieval of fringe patterns. The adaptive window width for this algorithm is determined by the length of the local stationary fringe pattern in order to balance the frequency and space resolution. The local stationary length of fringe pattern is defined as the signal satisfying the condition that whose first spectrum component is separated from all the other spectra within the local spatial area. In comparison with Fourier transform, fixed windowed Fourier transform and wavelet transform in numerical simulation and experiment, the adaptive multiscale windowed Fourier transform can present more accurate results of phase retrieval.
Double Fourier analysis for Emotion Identification in Voiced Speech
Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.
2016-04-01
We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.
Fourier mode analysis of source iteration in spatially periodic media
International Nuclear Information System (INIS)
The standard Fourier mode analysis is an indispensable tool when designing acceleration techniques for transport iterations; however, it requires the assumption of a homogeneous infinite medium. For problems of practical interest, material heterogeneities may significantly impact iterative performance. Recent work has applied a Fourier analysis to the discretized two-dimensional transport operator with heterogeneous material properties. The results of these analyses may be difficult to interpret because the heterogeneity effects are inherently coupled to the discretization effects. Here, the authors describe a Fourier analysis of source iteration (SI) that allows the calculation of the eigenvalue spectrum for the one-dimensional continuous transport operator with spatially periodic heterogeneous media
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Preliminary Analysis of ULPC Light Curves Using Fourier Decomposition Technique
Ngeow, Chow-Choong; Kanbur, Shashi; Barrett, Brittany; Lin, Bin
2013-01-01
Recent work on Ultra Long Period Cepheids (ULPCs) has suggested their usefulness as a distance indicator, but has not commented on their relationship as compared with other types of variable stars. In this work, we use Fourier analysis to quantify the structure of ULPC light curves and compare them to Classical Cepheids and Mira variables. Our preliminary results suggest that the low order Fourier parameters of ULPCs show a continuous trend defined by Classical Cepheids after the resonance around 10 days. However their Fourier parameters also overlapped with those from Miras, which make the classification of long period variable stars difficult based on the light curves information alone.
Comparative analysis of imaging configurations and objectives for Fourier microscopy
Kurvits, Jonathan A; Zia, Rashid
2015-01-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes, which have been optimized for conventional real-space imaging. Here, we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we ide...
Fourier analysis of time series an introduction
Bloomfield, Peter
2000-01-01
A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample
Rotation-invariant texture analysis using Radon and Fourier transforms
Institute of Scientific and Technical Information of China (English)
Songshan Xiao; Yongxing Wu
2007-01-01
@@ Texture analysis is a basic issue in image processing and computer vision, and how to attain the rotationinvariant texture characterization is a key problem. This paper proposes a rotation-invariant texture analysis technique using Radon and Fourier transforms. This method uses Radon transform to convert rotation to translation, then utilizes Fourier transform and takes the moduli of the Fourier transform of these functions to make the translation invariant. A k-nearest-neighbor rule is employed to classify texture images. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. Experiment results show the feasibility of the proposed method and its robustness to additive white noise.
Fetal magnetocardiogram recordings and Fourier spectral analysis.
Anastasiadis, P; Anninos, P A; Lüdinghausen, M V; Kotini, A; Galazios, G; Limberis, B
1999-07-01
Power spectral analysis of fetal magnetocardiogram (FMCG) data was evaluated in 64 pregnancies, using the non-invasive one channel superconducting quantum interference device (DC-SQUID), in order to investigate the power spectral amplitude distribution in the frequency range between 2 and 3 Hz. In all cases with normal and uncomplicated pregnancies, the data from the fetal heart and specifically the QRS complexes, were identifiable and unaffected by any maternal cardiac activity and furthermore the power spectral amplitudes, which varied between 120 and 350 fT/Hz, were directly related to gestational age. PMID:15512338
Fourier analysis of the aerodynamic behavior of cup anemometers
International Nuclear Information System (INIS)
The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)
Discrete Fourier analysis with lattices on planar domains
Li, Huiyuan; Xu, Yuan
2009-01-01
A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible choices of lattices are discussed in the case of lattices that tile $\\RR^2$ and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained.
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Teaching Fourier Analysis and Wave Physics with the Bass Guitar
Courtney, M; Courtney, Michael; Althausen, Norm
2006-01-01
This article describes a laboratory or demonstration technique employing the bass guitar and a Vernier LabPro (or a PC soundcard) for teaching wave physics and introducing Fourier analysis. The Fourier transform of an open string provides a demonstration of oscillatory modes out to the 20th harmonic consistent with expectations containing a fundamental frequency and harmonics. The playing of "harmonics" (suppressing resonant modes by lightly touching the string to enforce nodes at desired locations) demonstrates oscillations made up (mostly) of individual modes. Students see that the complete set of Fourier components (fundamental and harmonics) present on the open string can be explicitly connected with individual resonant frequencies as described in typical textbook discussions of natural frequencies of waves on a string. The use of a bass guitar rather than the six string electric guitar allows higher harmonics to be individually excited, and it is also easier for students to play the harmonics themselves.
Fourier analysis for discontinuous Galerkin and related methods
Institute of Scientific and Technical Information of China (English)
ZHANG MengPing; SHU Chi-Wang
2009-01-01
In this paper we review a series of recent work on using a Fourier analysis technique to study the sta-bility and error estimates for the discontinuous Galerkin method and other related schemes. The ad-vantage of this approach is that it can reveal instability of certain "bad"' schemes; it can verify stability for certain good schemes which are not easily amendable to standard finite element stability analysis techniques; it can provide quantitative error comparisons among different schemes; and it can be used to study superconvergence and time evolution of errors for the discontinuous Galerkin method. We will briefly describe this Fourier analysis technique, summarize its usage in stability and error estimates for various schemes, and indicate the advantages and disadvantages of this technique in comparison with other finite element techniques.
Fractional Fourier domain analysis of decimation and interpolation
Institute of Scientific and Technical Information of China (English)
MENG XiangYi; TAO Ran; WANG Yue
2007-01-01
The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal.Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security.Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital frequency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sampling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.
Higher order Fourier analysis as an algebraic theory II
Szegedy, Balazs
2009-01-01
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of approximative statements. The present paper is the second part of a paper in which higher order characters and decompositions were introduced. We generalize the concept of the Pontrjagin dual group and introduce higher order versions of it. We study the algebraic structure of the higher order dual groups. We prove a simple formula for the Gowers uniformity norms in terms of higher order decompositions. We present a simple spectral algorithm to produce higher order decompositions. We briefly study a multi linear version of Fourier analysis. Along these lines we obtain new inverse theorems for Gowers's norms.
Higher order Fourier analysis as an algebraic theory I
Szegedy, Balazs
2009-01-01
Ergodic theory, Higher order Fourier analysis and the hyper graph regularity method are three possible approaches to Szemer\\'edi type theorems in abelian groups. In this paper we develop an algebraic theory that creates a connection between these approaches. Our main method is to take the ultra product of abelian groups and to develop a precise algebraic theory of higher order characters on it. These results then can be turned back into approximative statements about finite Abelian groups.
On One Application of Fourier Analysis in Plastic Surgery
Rakhimov, Abdumalik; Zainuddin, Hishamuddin
In present paper, we discuss the spectral methods of measurement of the degree of speech and/or quality of sound by comparing the coefficient of performance indicators depending on energy distributions, ratio of energy of the fundamental tone and energy of overtones. Such a method is very efficient for string oscillation with different initial conditions and it is useful for justification of applications of Fourier analysis in plastic surgery in treatment of some medical diseases.
Evaluation of gastric motility by Fourier analysis of condensed images
Energy Technology Data Exchange (ETDEWEB)
Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K. [Dept. of Nuclear Medicine, Univ. of Munich, Munich (Germany)
2000-10-01
In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)
Fourier Transform Infrared Spectroscopic Analysis of Protein Secondary Structures
Institute of Scientific and Technical Information of China (English)
Jilie KONG; Shaoning YU
2007-01-01
Infrared spectroscopy is one of the oldest and well established experimental techniques for the analysis of secondary structure of polypeptides and proteins. It is convenient, non-destructive, requires less sample preparation, and can be used under a wide variety of conditions. This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies. The experimental skills, data analysis, and correlations between the FTIR spectroscopic bands and protein secondary structure components are discussed. The applications of FTIR to the secondary structure analysis, conformational changes, structural dynamics and stability studies of proteins are also discussed.
Fourier analysis of conductive heat transfer for glazed roofing materials
Energy Technology Data Exchange (ETDEWEB)
Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah [Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia); Zakaria, Nor Zaini [Faculty of Applied Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia)
2014-07-10
For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.
Fourier analysis of conductive heat transfer for glazed roofing materials
International Nuclear Information System (INIS)
For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate
Vortex metrology using Fourier analysis techniques: vortex networks correlation fringes.
Angel-Toro, Luciano; Sierra-Sosa, Daniel; Tebaldi, Myrian; Bolognini, Néstor
2012-10-20
In this work, we introduce an alternative method of analysis in vortex metrology based on the application of the Fourier optics techniques. The first part of the procedure is conducted as is usual in vortex metrology for uniform in-plane displacement determination. On the basis of two recorded intensity speckled distributions, corresponding to two states of a diffuser coherently illuminated, we numerically generate an analytical signal from each recorded intensity pattern by using a version of the Riesz integral transform. Then, from each analytical signal, a two-dimensional pseudophase map is generated in which the vortices are located and characterized in terms of their topological charges and their core's structural properties. The second part of the procedure allows obtaining Young's interference fringes when Fourier transforming the light passing through a diffracting mask with multiple apertures at the locations of the homologous vortices. In fact, we use the Fourier transform as a mathematical operation to compute the far-field diffraction intensity pattern corresponding to the multiaperture set. Each aperture from the set is associated with a rectangular hole that coincides both in shape and size with a pixel from recorded images. We show that the fringe analysis can be conducted as in speckle photography in an extended range of displacement measurements. Effects related with speckled decorrelation are also considered. Our experimental results agree with those of speckle photography in the range in which both techniques are applicable.
Fourier analysis of conductive heat transfer for glazed roofing materials
Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah; Zakaria, Nor Zaini
2014-07-01
For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.
Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy
Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks
2016-06-01
Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.
Discrete Fourier Analysis and Chebyshev Polynomials with G2 Group
Directory of Open Access Journals (Sweden)
Huiyuan Li
2012-10-01
Full Text Available The discrete Fourier analysis on the 30°-60°-90° triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G2, which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of m-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type.
Some Topics in Fourier Analysis and Approximation Theory
Trigub, R M
1996-01-01
This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are given. These results are published in serious scientific journals and reported at various conferences, including international ones at Moscow,ICM66; Kaluga,1975; Kiev,1983; Haifa,1994; Zürich,ICM94; Moscow,1995. The area of investigation is the Fourier analysis and the theory of approximation of functions. Used are methods of classical analysis including special functions, Banach spaces, etc., of harmonic analysis in finitedimensional Euclidean space, of Diophantine analysis, of random choice, etc. The results due to the author and active participants of the seminar, namely E. S. Belinskii, O. I. Kuznetsova, E. R. Liflyand, Yu. L. Nosenko, V. A. Glukhov, V. P. Zastavny, Val. V. Volchkov, V. O. Leontyev, and others, are given. Besides the participants of the seminar and other ma...
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Directory of Open Access Journals (Sweden)
Ovidiu Hâruţa
2011-06-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage development of the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, centroid position, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Directory of Open Access Journals (Sweden)
Ovidiu Hâruţa
2011-02-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage developmentof the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, mass center, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Non-Harmonic Fourier Analysis for bladed wheels damage detection
Neri, P.; Peeters, B.
2015-11-01
The interaction between bladed wheels and the fluid distributed by the stator vanes results in cyclic loading of the rotating components. Compressors and turbines wheels are subject to vibration and fatigue issues, especially when resonance conditions are excited. Even if resonance conditions can be often predicted and avoided, high cycle fatigue failures can occur, causing safety issues and economic loss. Rigorous maintenance programs are then needed, forcing the system to expensive shut-down. Blade crack detection methods are beneficial for condition-based maintenance. While contact measurement systems are not always usable in exercise conditions (e.g. high temperature), non-contact methods can be more suitable. One (or more) stator-fixed sensor can measure all the blades as they pass by, in order to detect the damaged ones. The main drawback in this situation is the short acquisition time available for each blade, which is shortened by the high rotational speed of the components. A traditional Discrete Fourier Transform (DFT) analysis would result in a poor frequency resolution. A Non-Harmonic Fourier Analysis (NHFA) can be executed with an arbitrary frequency resolution instead, allowing to obtain frequency information even with short-time data samples. This paper shows an analytical investigation of the NHFA method. A data processing algorithm is then proposed to obtain frequency shift information from short time samples. The performances of this algorithm are then studied by experimental and numerical tests.
Fractional Fourier domain analysis of cyclic multirate signal processing
Institute of Scientific and Technical Information of China (English)
2008-01-01
The cyclic filter banks, which are used widely in the image subband coding, refer to signal processing on the finite field. This study investigates the fractional Fourier domain (FRFD) analysis of cyclic multirate systems based on the fractional circular convolution and chirp period. The proposed theorems include the fractional Fourier domain analysis of cyclic decimation and cyclic interpolation, the noble identities of cyclic decimation and cyclic interpolation in the FRFD, the polyphase represen-tation of cyclic signal in the FRFD, and the perfect reconstruction condition for the cyclic filter banks in the FRFD. Furthermore, this paper proposes the design methods for perfect reconstruction cyclic filter bank and cyclic filter bank with chirp modulation in the FRFD. The proposed theorems extend the multirate signal processing in the FRFD, which also advance the applications of the theorems of filter bank in the FRFD on the finite signal field, such as digital image processing. At last, the proposed design methods for the cyclic filter banks in the FRFD are validated by simulations.
Mei, Liang; Svanberg, Sune
2015-03-20
This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.
Optical polarimeter based on Fourier analysis and electronic control
International Nuclear Information System (INIS)
In this paper, we show the design and implementation of an optical polarimeter using electronic control and the Fourier analysis. The polarimeter prototype will be used as a main tool for the students of the Universidad Popular del Cesar that belong to the following university programs: Electronics engineering (optoelectronics area), Math and Physics degree and the Master in Physics Sciences, in order to learning the theory and experimental aspects of the state of optical polarization via the Stokes vector measurement. Using the electronic polarimeter proposed in this paper, the students will be able to observe (in an optical bench) and understand the different interactions of the states of optical polarization when the optical waves pass through to the polarizers and retarder waves plates. The electronic polarimeter has a software that captures the optical intensity measurement and evaluates the Stokes vector. (Author)
Higher-order Fourier analysis over finite fields and applications
Hatami, Pooya
Higher-order Fourier analysis is a powerful tool in the study of problems in additive and extremal combinatorics, for instance the study of arithmetic progressions in primes, where the traditional Fourier analysis comes short. In recent years, higher-order Fourier analysis has found multiple applications in computer science in fields such as property testing and coding theory. In this thesis, we develop new tools within this theory with several new applications such as a characterization theorem in algebraic property testing. One of our main contributions is a strong near-equidistribution result for regular collections of polynomials. The densities of small linear structures in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by approximating the indicator function of a subset by a function of bounded number of polynomials. Then, to approximate the average, it suffices to know the joint distribution of the polynomials applied to the linear forms. We prove a near-equidistribution theorem that describes these distributions for the group F(n/p) when p is a fixed prime. This fundamental fact was previously known only under various extra assumptions about the linear forms or the field size. We use this near-equidistribution theorem to settle a conjecture of Gowers and Wolf on the true complexity of systems of linear forms. Our next application is towards a characterization of testable algebraic properties. We prove that every locally characterized affine-invariant property of functions f : F(n/p) → R with n∈ N, is testable. In fact, we prove that any such property P is proximity-obliviously testable. More generally, we show that any affine-invariant property that is closed under subspace restrictions and has "bounded complexity" is testable. We also prove that any property that can be described as the property of decomposing into a known structure of low
On The Fourier And Wavelet Analysis Of Coronal Time Series
Auchère, F; Bocchialini, K; Buchlin, E; Solomon, J
2016-01-01
Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default c...
Gas Analysis by Fourier Transform Mm-Wave Spectroscopy
Harris, Brent J.; Steber, Amanda L.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
Molecular rotational spectroscopy of low pressure, room temperature gases offers high chemical selectivity and sensitivity with the potential for a wide range of applications in gas analysis. A strength of the technique is the potential to identify molecules that have not been previously studied by rotational spectroscopy by comparing experimental results to predictions of the spectroscopic parameters from quantum chemistry -6 so called library-free detection. The development of Fourier transform mm-wave spectrometers using high peak power (30 mW) active multiplier chain mm-wave sources brings new measurement capabilities to the analysis of complex gas mixtures. Strategies for gas analysis based on high-throughput mm-wave spectroscopy and arbitrary waveform generator driven mm-wave sources are described. Several new measurement capabilities come from the intrinsic time-domain measurement technique. High-sensitivity double-resonance measurements can be performed to speed the analysis of a complex gas sample containing several species. This technique uses a "pi-pulse" to selectively invert the population of two selected rotational energy levels and the effect of this excitation pulse on all other transitions in the spectrometer operating range is monitored using segmented chirped-pulse Fourier transform spectroscopy. This method can lead to automated determination of the molecular rotational constants. Rapid pulse duration scan experiments can be used to estimate the magnitude and direction of the dipole moment of the molecule from an unknown spectrum. Coherent pulse echo experiments, using the traditional Hahn sequence or two-color population recovery methods, can be used to determine the collisional relaxation rate of the unknown molecule. This rate determination improves the ability to estimate the mass of the unknown molecule from the determination of the Doppler dephasing rate. By performing a suite of automated, high-throughput measurements, there is the
Motion analysis of optically trapped particles and cells using 2D Fourier analysis
DEFF Research Database (Denmark)
Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring;
2012-01-01
Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness...... of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination...
Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.
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.
Experimental display of Fourier analysis through the optical physics and its didatical utilization
International Nuclear Information System (INIS)
The properties of Fourier analysis through physical optics are displayed experimentally. Within physical optics topics that illustrate didactically Fourier analysis, a subject usually considered purely mathematical are selected. The most important properties of Fourier transform and their utilization in cleaning up images through spatial filtering are presented, in this way the properties of convolution to analyse image formation and characterize some diffraction patterns are also used. (Author)
Fourier Analysis of the Parametric Resonance in Neutrino Oscillations
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to th...
Fourier analysis of multi-tracer cosmological surveys
Abramo, L Raul; Loureiro, Arthur
2015-01-01
We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ 1994, FKP) in the case of a survey consisting of a single species of tracer. We show that the multi-tracer estimators are unbiased, and that their covariance is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013; Abramo & Leonard, MNRAS 2013). When the biases, RSDs and NGs are fixed to their fiducial values, and one is only interested in measuring the underlying power spectrum, our estimators are projected into the estimator found by Percival, Verde & Peacock ...
Quantitative analysis of iron oxides using Fourier transform infrared spectrophotometry
International Nuclear Information System (INIS)
In this study, a systematic approach based on the application of Fourier transform infrared spectrophotometry (FTIR) was taken, in order to quantitatively analyze the corrosion products formed in the secondary cycle of pressurized water reactors (PWR). Binary mixtures of iron oxides were prepared with known compositions containing pure commercial magnetite (Fe3O4), maghemite (γ-Fe2O3), and hematite (α-Fe2O3) for calibration purposes. Calcium oxide (lime) was added to all samples as a standard reference in obtaining the calibration curves. Using regression analysis, relationships were developed for intensity versus concentration for absorption bands corresponding to each of the phases in their corresponding FTIR spectrum. Correlation coefficients, R2, of 0.82, 0.87, and 0.86 were obtained for maghemite-magnetite, hematite-magnetite, and hematite-maghemite systems, respectively. The calibration curves generated were used to quantify phases in multi-component unknown field samples that were obtained from different components (moisture separators, condensers, and high- and low- pressure heaters) of the two units (units 1 and 2) of the secondary cycle of the Comanche Peak PWR
Description of shape characteristics through Fourier and wavelet analysis
Institute of Scientific and Technical Information of China (English)
Yuan Zhanwei; Li Fuguo; Zhang Peng; Chen Bo
2014-01-01
In this paper, Fourier and Wavelet transformation were adopted to analyze shape char-acteristics, with twelve simple shapes and two types of second phases from real microstructure mor-phology. According to the results of Fast Fourier transformation (FFT), the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors (SSRE) of Wavelet transformation (WT) signal sequence, including approximation signals and detail signals, was introduced to evaluate the simi-larity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric sig-natures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.
Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis
LoPresto, Michael C.
2013-01-01
What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.
Using musical intervals to demonstrate superposition of waves and Fourier analysis
LoPresto, Michael C.
2013-09-01
What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.
Mode analysis of structures using the Fourier p-element method
Institute of Scientific and Technical Information of China (English)
吴国荣; 钟伟芳
2003-01-01
The Fourier p-element method is an improvement to the finite element method, and is particularly suitable for vibration analysis due to the well-behaved Fourier series. In this paper, an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem. Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration, the plate in-plane vibration and annular plate flexural vibration modes, respectively.The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation, especially for higher mode analysis.
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
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.
Dantas, José L; Camata, Thiago V; Brunetto, Maria A C; Moraes, Antonio C; Abrão, Taufik; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in isometric and dynamic exercise. The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in isometric and dynamic exercise (P>0.05). However, the results of the variance was lower for both types of exercise in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
A Fourier analysis for a fast simulation algorithm. [for switching converters
King, Roger J.
1988-01-01
This paper presents a derivation of compact expressions for the Fourier series analysis of the steady-state solution of a typical switching converter. The modeling procedure for the simulation and the steady-state solution is described, and some desirable traits for its matrix exponential subroutine are discussed. The Fourier analysis algorithm was tested on a phase-controlled parallel-loaded resonant converter, providing an experimental confirmation.
Fourier optics for polymeric substrates and coating textures analysis
Sparavigna, Amelia
2008-01-01
Several devices for substrate texture detection based on diffractive optics, for paper, textiles and non-wovens have been proposed in the past for direct inspection during the production processes. In spite of the presence of devices totally based on image processing, the use of diffractive optics cannot be considered surpassed for many reasons. Compared with image processing procedures, it is less sensitive to vibrations and does not suffer from the presence of ambient light. Based on transmitted light, it can give information on changes in refractive indexes, thickness variation and surface conditions. We study the use of optical Fourier spectrum to identify textures of polymer films. As the power spectrum reveals, the texture is seldom homogeneous. Here we report investigation on several substrates and on thin ink coatings on substrate. Role of bulk and surface conditions is analysed.
Tow-dimensional Strain Analysis by Fourier Transform Moire Interferometry
International Nuclear Information System (INIS)
Moire interferometry using a diffraction grating and a laser is a powerful technique for analyzing small deformation of a specimen. In the method, the x and y-directional fringe patterns are obtained by using the x and y-directional sets of two beams. If the both sets of two beams are simultaneously incident to the specimen, the x and y-directional fringe patterns are super imposed. In this case, it is difficult to separate each directional fringe pattern. Therefore each fringe pattern has been separately recorded by selecting each set of two beams. In order to analyze a two-dimensional strain changing with time, Moire interferometry using the two-dimensional fourier transform method is proposed and the x and y-directional fringes are separated. By this method, the thermal deformation of a glass plate is analyzed
Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy
Directory of Open Access Journals (Sweden)
Mehrotra Ranjana
2010-12-01
Full Text Available Abstract Background Ovarian cancer is the second most common cancer among women and the leading cause of death among gynecologic malignancies. In recent years, infrared (IR spectroscopy has gained attention as a simple and inexpensive method for the biomedical study of several diseases. In the present study infrared spectra of normal and malignant ovarian tissues were recorded in the 650 cm-1 to 4000 cm-1 region. Methods Post surgical tissue samples were taken from the normal and tumor sections of the tissue. Fourier Transform Infrared (FTIR data on twelve cases of ovarian cancer with different grades of malignancy from patients of different age groups were analyzed. Results Significant spectral differences between the normal and the ovarian cancerous tissues were observed. In particular changes in frequency and intensity in the spectral region of protein, nucleic acid and lipid vibrational modes were observed. It was evident that the sample-to-sample or patient-to-patient variations were small and the spectral differences between normal and diseased tissues were reproducible. Conclusion The measured spectroscopic features, which are the spectroscopic fingerprints of the tissues, provided the important differentiating information about the malignant and normal tissues. The findings of this study demonstrate the possible use of infrared spectroscopy in differentiating normal and malignant ovarian tissues.
Fourier Analysis for Demand Forecasting in a Fashion Company
Directory of Open Access Journals (Sweden)
Andrea Fumi
2013-08-01
sectors. The entire analysis was performed on a common spreadsheet, in order to demonstrate that accurate results exploiting advanced numerical computation techniques can be carried out without necessarily using expensive software.
On the Fourier Spectra of Distributions in Clifford Analysis
Institute of Scientific and Technical Information of China (English)
Fred BRACKX; Bram De KNOCK; Hennie De SCHEPPER
2006-01-01
In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional distributions have been reconsidered in the framework of Clifford analysis,eventually leading to the introduction of four broad classes of new distributions in Euclidean space. In the current paper we continue the in-depth study of these distributions, more specifically the study of their behaviour in frequency space, thus extending classical results of harmonic analysis.
A COMPARISION BETWEEN WALSHHADAMARD AND FOURIER ANALYSIS OF THE EEG SIGNALS
Directory of Open Access Journals (Sweden)
AZADEH BASTANI
2011-07-01
Full Text Available Electroencephalography (EEG is one of the most important diagnostic tools in neurology and getting information about the brain activity. One of this is real-time and quantified study of brain activities to measure the stage of unconsciousness due to injection drug in operation room. EEG signal is a stochastic non-stationary process. Regarding the complexity of brain activities on EEG process, studies are based on time-frequency features analysis of EEG signals. Most of these analyses are based on Fourier Transform and the most significant are classic and parametric estimation of power spectral density analysis. Considering the origins of EEG in the brain, it seems that Walsh-Hadamard transform is more effective than Fourier transform in feature extracting of these signals. In this paper the efficiency of Walsh-Hadamard transform features were comparedwith extracted features from Fourier transform. To evaluate these features, three different classifying algorithms are used. The results showed that Walsh-Hadamard extracted features are suitable tools for recognition of difference between different stages of EEG signals. Simplicity and speed of Walsh-Hadamard transform calculation made it preferable then Fourier spectral features. The fast Walsh-Hadamard transform is an attractive alternative to the fast fourier transform because it is computationally more efficient, and thus faster to perform on a digital computer.
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Ovidiu Hâruţa
2011-01-01
Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression ...
The combined use of order tracking techniques for enhanced Fourier analysis of order components
Wang, K. S.; Heyns, P. S.
2011-04-01
Order tracking is one of the most important vibration analysis techniques for diagnosing faults in rotating machinery. It can be performed in many different ways, each of these with distinct advantages and disadvantages. However, in the end the analyst will often use Fourier analysis to transform the data from a time series to frequency or order spectra. It is therefore surprising that the study of the Fourier analysis of order-tracked systems seems to have been largely ignored in the literature. This paper considers the frequently used Vold-Kalman filter-based order tracking and computed order tracking techniques. The main pros and cons of each technique for Fourier analysis are discussed and the sequential use of Vold-Kalman filtering and computed order tracking is proposed as a novel idea to enhance the results of Fourier analysis for determining the order components. The advantages of the combined use of these order tracking techniques are demonstrated numerically on an SDOF rotor simulation model. Finally, the approach is also demonstrated on experimental data from a real rotating machine.
The methods and computer structures for adaptive Fourier descriptive image analysis
V.Perzhu; A. Gurau
1997-01-01
New architectures of image processing computer systems, based on the algorithms of Fourier - descriptive (FD) analysis have been developed. A new computing processes organisation method on the basis of FD image features has been proposed. The structures of two problem-oriented optical-electronic computer systems have been developed. The estimation of time expenditures in the systems have been carried out.
Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images
Yamahata, C.; Sarajlic, E.; Stranczl, M.; Krijnen, G.J.M.; Gijs, M.A.M.
2011-01-01
We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope
Fourier and wavelet spectral analysis of EMG signals in supramaximal constant load dynamic exercise.
Camata, Thiago V; Dantas, Jose L; Abrao, Taufik; Brunetto, Maria A C; Moraes, Antonio C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in supramaximal constant load dynamic exercise (110% VO(2peak)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in supramaximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Fourier and wavelet spectral analysis of EMG signals in maximal constant load dynamic exercise.
Costa, Marcelo V; Pereira, Lucas A; Oliveira, Ricardo S; Pedro, Rafael E; Camata, Thiago V; Abrao, Taufik; Brunetto, Maria A C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in maximal constant load dynamic exercise (100% W(max)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in maximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P〈0.05) indicating more variability in the EMG signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Fourier analysis of time series of NOAA-AVHRR NDVI composites to map isogrowth zones
Menenti, M.; Azzali, S.; Verhoef, W.
1995-01-01
A measurement of the quality of vegetation zones in dynamic terms is provided by the Fourier analysis of time series of AVHRR/NDVI monthly observations over ten years. The present approach is shown to be a powerful way to classify and extract various dynamic parameters of the vegetation in Southern
Laplace-Fourier analysis and instabilities of a gainy slab
Hågenvik, Hans Olaf
2015-01-01
The idealization of monochromatic plane waves leads to considerable simplifications in the analysis of electromagnetic systems. However, for active systems this idealization may be dangerous due to the presence of growing waves. Here we consider a gainy slab, and use a realistic incident beam, which is both causal and has finite width. This clarifies some apparent paradoxes arising from earlier analyses of this setup. In general it turns out to be necessary to involve complex frequencies $\\omega$ and/or complex transversal wavenumbers $k_x$. Simultaneously real $\\omega$ and $k_x$ cannot describe amplified waves in a slab which is infinite in the transversal direction. We also show that the only possibility to have an absolute instability for a finite width beam, is if a normally incident plane wave would experience an instability.
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Comparison of Solar Wind Speeds Using Wavelet Transform and Fourier Analysis in IPS Data
Aguilar-Rodriguez, E.; Mejia-Ambriz, J. C.; Jackson, B. V.; Buffington, A.; Romero-Hernandez, E.; Gonzalez-Esparza, J. A.; Rodriguez-Martinez, M.; Hick, P.; Tokumaru, M.; Manoharan, P. K.
2015-09-01
The power spectra of intensity fluctuations in interplanetary scintillation (IPS) observations can be used to estimate solar-wind speeds in the inner heliosphere. We obtain and then compare IPS spectra from both wavelet and Fourier analyses for 12 time series of the radio source 3C48; these observations were carried out at Japan's Solar-Terrestrial Environment Laboratory (STEL) facility, at 327 MHz. We show that wavelet and Fourier analyses yield very similar power spectra. Thus, when fitting a model to spectra to determine solar-wind speeds, both yield comparable results. Although spectra from wavelet and Fourier closely match each other for solar-wind speed purposes, those from the wavelet analysis are slightly cleaner, which is reflected in an apparent level of intensity fluctuations that is enhanced, being ≈ 13 % higher. This is potentially useful for records that show a low signal-to-noise ratio.
Analysis of Index Gases of Coal Spontaneous Combustion Using Fourier Transform Infrared Spectrometer
Xiaojun Tang; Yuntao Liang; Haozhe Dong; Yong Sun; Haizhu Luo
2014-01-01
Analysis of the index gases of coal for the prevention of spontaneous combustion is of great importance for the enhancement of coal mine safety. In this work, Fourier Transform Infrared Spectrometer (FTIRS) is presented to be used to analyze the index gases of coal in real time to monitor spontaneous combustion conditions. Both the instrument parameters and the analysis method are introduced at first by combining characteristics of the absorption spectra of the target analyte with the analysi...
Nanometrology on gratings with GISAXS: FEM reconstruction and fourier analysis
Soltwisch, Victor; Wernecke, Jan; Haase, Anton; Probst, Jürgen; Schoengen, Max; Krumrey, Michael; Scholze, Frank
2014-04-01
The aim of the semiconductor industry to decrease the feature size of integrated circuits poses a huge technological endeavor. Consequently, new challenges are arising for metrology on structures in the nanometer regime. Scatterometry is a fast method which provides non-contact non-destructive characterization of structures on photomasks or exposed wafers. However, the determination of important line structure parameters with subnanometer accuracy still needs further investigation. Grazing incidence small-angle X-ray scattering (GISAXS) is a scatterometry technique to measure both vertical and lateral structural features in the nanometer range with high sensitivity. We apply GISAXS to the investigation of structural parameters such as period length, sidewall angle, linewidth and height on silicon gratings. Our test structures with nominal widths of 35 nm to 100 nm and a pitch from 100 nm to 250 nm were fabricated by electron beam lithography. The diffraction patterns have been analyzed by power spectral density analysis which directly yields periodical modulations of the structured surface such as line width or groove width. We also apply a finite element method (FEM) to the diffraction peak intensity of the grating structure obtained with GISAXS for the geometric reconstruction of the line shape.
Interpreting the Phase Spectrum in Fourier Analysis of Partial Ranking Data
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Ramakrishna Kakarala
2012-01-01
Full Text Available Whenever ranking data are collected, such as in elections, surveys, and database searches, it is frequently the case that partial rankings are available instead of, or sometimes in addition to, full rankings. Statistical methods for partial rankings have been discussed in the literature. However, there has been relatively little published on their Fourier analysis, perhaps because the abstract nature of the transforms involved impede insight. This paper provides as its novel contributions an analysis of the Fourier transform for partial rankings, with particular attention to the first three ranks, while emphasizing on basic signal processing properties of transform magnitude and phase. It shows that the transform and its magnitude satisfy a projection invariance and analyzes the reconstruction of data from either magnitude or phase alone. The analysis is motivated by appealing to corresponding properties of the familiar DFT and by application to two real-world data sets.
Advantages Of A Time Series Analysis Using Wavelet Transform As Compared With A Fourier Analysis
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Sleziak Patrik
2015-06-01
Full Text Available The paper presents an analysis of changes in the structure of the average annual discharges, average annual air temperature, and average annual precipitation time series in Slovakia. Three time series with lengths of observation from 1961 to 2006 were analyzed. An introduction to spectral analysis with Fourier analysis (FA is given. This method is used to determine significant periods of a time series. Later in this article a description of a wavelet transform (WT is reviewed. This method is able to work with non-stationary time series and detect when significant periods are presented. Subsequently, models for the detection of potential changes in the structure of the time series analyzed were created with the aim of capturing changes in the cyclical components and the multiannual variability of the time series selected for Slovakia. Finally, some of the comparisons of the time series analyzed are discussed. The aim of the paper is to show the advantages of time series analysis using WT compared with FT. The results were processed in the R software environment.
Application of Fourier analysis to the study of roughness profiles of eroded samples
International Nuclear Information System (INIS)
Fourier transforms are applied to analyse surface roughness profiles recorded on samples coming from erosion-corrosion essays. The information retrieved using this method clearly complements that revealed by the more classical roughness amplitude parameters. The analysis procedure here proposed can be applied not only to characterise the surface of corroded samples but, in general, to evaluate the quality of any surface after application of finishing treatments. (Author) 7 refs
A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
DANCHIN; Raphaёl
2012-01-01
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations.In this survey paper,we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space.We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.
Measuring sperm movement within the female reproductive tract using Fourier analysis.
Nicovich, Philip R; Macartney, Erin L; Whan, Renee M; Crean, Angela J
2015-02-01
The adaptive significance of variation in sperm phenotype is still largely unknown, in part due to the difficulties of observing and measuring sperm movement in its natural, selective environment (i.e., within the female reproductive tract). Computer-assisted sperm analysis systems allow objective and accurate measurement of sperm velocity, but rely on being able to track individual sperm, and are therefore unable to measure sperm movement in species where sperm move in trains or bundles. Here we describe a newly developed computational method for measuring sperm movement using Fourier analysis to estimate sperm tail beat frequency. High-speed time-lapse videos of sperm movement within the female tract of the neriid fly Telostylinus angusticollis were recorded, and a map of beat frequencies generated by converting the periodic signal of an intensity versus time trace at each pixel to the frequency domain using the Fourier transform. We were able to detect small decreases in sperm tail beat frequency over time, indicating the method is sensitive enough to identify consistent differences in sperm movement. Fourier analysis can be applied to a wide range of species and contexts, and should therefore facilitate novel exploration of the causes and consequences of variation in sperm movement.
Tang, Kwong-Tin
2007-01-01
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
Response of Autonomic Nervous System to Body Positions: Fourier and Wavelet Analysis
Xu, A; Federici, A; Stramaglia, S; Simone, F; Zenzola, A; Santostasi, R; Xu, Aiguo
2003-01-01
Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1), and the second half (HD2) of $90^{\\circ}$ head down tilt and during recovery (REC). The wavelet transform was performed using the Haar function of period $T=2^j$ ($% j=1$,2,$... $,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frquency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident difference than the R-R intervals. This study s...
Fourier analysis of short-period SMC Cepheids: A comparison with Galactic Cepheids
Buchler, J. Robert; Moskalik, Pawel
1994-12-01
A Fourier analysis has been made of the Small Magellanic Cloud (SMC) classical Cepheid data of Smith et al. It is shown that the grouping into fundamental and first overtone pulsators, implied by the period-luminosity diagram, survives when the Fourier coefficients are plotted versus period. A comparison with the Galactic Cepheid data corroborates the existing evidence that the short period Galactic s-Cepheids are indeed first overtone pulsators. The only long period overtone Cepheid in the sample that is reliably covered (P = 3.49 d) also conforms with the corresponding s-Cepheids. On the other hand, the hypothesis of Gieren et al. that the long period s-Cepheids are fundamental pulsators is refuted. The data show systematic differences between the SMC Cepheids and their Galactic counterparts, differences that are of theoretical interest. The need for a further observational effort devoted to SMC and to Large Magellanic cloud (LMC) Cepheids is stressed.
A new approach to the Fourier analysis on semi-direct products of groups
Farashahi, Arash Ghaani
2012-01-01
Let $H$ and $K$ be locally compact groups and also $\\tau:H\\to Aut(K)$ be a continuous homomorphism and $G_\\tau=H\\ltimes_\\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\\tau$. This paper presents a novel approach to the Fourier analysis of $G_\\tau$, when $K$ is abelian. We define the $\\tau$-dual group $G_{\\hat{\\tau}}$ of $G_\\tau$ as the semi-direct product $H\\ltimes_{\\hat{\\tau}}\\hat{K}$, where $\\hat{\\tau}:H\\to Aut(\\hat{K})$ defined via (\\ref{A}). We prove a Ponterjagin duality Theorem and also we study $\\tau$-Fourier transforms on $G_\\tau$. As a concrete application we show that how these techniques apply for the affine group and also we compute the $\\tau$-dual group of Euclidean groups and the Weyl-Heisenberg groups.
de Beer, N A M; Andriessen, P; Berendsen, R C M; Oei, S G; Wijn, P F F; Oetomo, S Bambang
2004-12-01
A customized filtering technique is introduced and compared with fast Fourier transformation (FFT) for analyzing heart rate variability (HRV) in neonates from short-term recordings. FFT is classically the most commonly used spectral technique to investigate cardiovascular fluctuations. FFT requires stability of the physiological signal within a 300 s time window that is usually analyzed in adults. Preterm infants, however, show characteristics of rapidly fluctuating heart rate and blood pressure due to an immature autonomic regulation, resulting in non-stationarity of these signals. Therefore neonatal studies use (half-overlapping or moving) windows of 64 s length within a recording time of 2-5 min. The proposed filtering technique performs a filtering operation in the frequency range of interest before calculating the spectrum, which allows it to perform an analysis of shorter periods of only 42 s. The frequency bands of interest are 0.04-0.15 Hz (low frequency, LF) and 0.4-1.5 Hz (high frequency, HF). Although conventional FFT analysis as well as the proposed alternative technique result in errors in the estimation of LF power, due to spectral leakage from the very low frequencies, FFT analysis is more sensitive to this effect. The response times show comparable behavior for both the techniques. Applying both the methods to heart rate data obtained from a neonate before and after atropine administration (inducing a wide range of HRV), shows a very significant correlation between the two methods in estimating LF and HF power. We conclude that a customized filtering technique might be beneficial for analyzing HRV in neonates because it reduces the necessary time window for signal stability.
Siminoff, R
1991-01-01
Fourier analysis is used to study resolution of images processed by the matrix of simulated red-center (BCR) and green-center (BCG) bipolar cells (BC) of the human central fovea. Simulated achromatic and chromatic sine and square waves, and a two-bar stimulus are used to activate the BCs. Due to the "honeycomb" packing of the cones and BC matrices Fourier transforms are computed row by row using a one-dimensional FFT. Resolution computed by the Fourier transform is compared with the resolution index (RI), which is a method for determining resolution based on two-point discrimination in the space domain. In general the harmonic with the maximum amplitude gives the best correlation with RI for the three stimuli. Amplitudes at all spatial frequencies are enhanced by increasing the number of cycles in the sine and square wave gratings. Results with simulated BCs compare favorably with human and macaque psychophysics measuring contrast sensitivity. Square wave gratings are better than sine wave greetings for studying resolution.
Processing of gamma-ray spectra employing a Fourier deconvolver for the analysis of complex spectra
International Nuclear Information System (INIS)
Processing of a nuclear spectrum e.g. gamma ray spectrum is concerned with the estimation of energies and intensities of radiation. The processing involves filtering, peak detection and its significance, baseline delineation, the qualitative and the quantitative analysis of singlets and multiplets present in the spectrum. The methodology for the analysis of singlets is well established. However, the analysis of multiplets provides a challenge and is a extremely difficult problem. This report incorporates a Fourier deconvolver for the quantitative analysis of doublets separated by more than a full width at half maximum. The method is easy to implement. The report discusses the methodology, mathematical analysis, and the results obtained by analyzing both synthetic and observed spectra. A computer program, developed for the analysis of a nuclear spectrum, was verified by analyzing a 152Eu gamma ray spectrum. The proposed technique compared favourably with SAMPO and MDFT method. (author). 16 refs., 3 tabs
Fourier and Wavelet Transform Analysis of Pressure Signals during Explosive Boiling
Institute of Scientific and Technical Information of China (English)
YIN Tie-Nan; HUAI Xiu-Lan
2008-01-01
@@ The transient pressure in a liquid-pool during explosive boiling of acetone is measured by a micro-pressure-measuring system.The Fast Fourier transform and continuous wavelet transform methods are applied to investigate the frequency characteristics.The results show that the dominant frequency of the explosive boiling is 0-2MHz,and the bubble cluster formed by numerous tiny bubbles departs twice.Analysis and discussions are also conducted to explain the bubble evolution during the explosive boiling.
Fourier analysis of the forehead shape of skull and sex determination by use of computer.
Inoue, M
1990-09-01
The forehead shape of the skull was quantified with the Fourier analysis method by using 100 male and 100 female radiographic lateral views of the skull, and sex difference in the forehead shape was studied. Furthermore to predict the sex of cranial specimens, an automated sexing computer system based on the quantification was created. The effectiveness of the system was evaluated by checking 56 male and 56 female specimens of skulls. This system was proved to discriminate male and female skulls from forehead shapes with 85% accuracy.
Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse
Kalasinsky, Kathryn S.; Levine, Barry K.; Smith, Michael L.; Magluilo, Joseph J.; Schaefer, Teresa
1994-01-01
Cryogenic deposition techniques for Gas Chromatography/Fourier Transform Infrared (GC/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography/Mass Spectrometry (GC/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of abuse can be confused with over-the-counter medications or naturally occurring amines. Hair analysis has been important in drug testing when adulteration of urine samples has been a question. Functional group mapping can further assist the analysis and track drug use versus time.
Institute of Scientific and Technical Information of China (English)
Muthuramalingam Uthaya Siva; Mohideen Abdul Badhul Haq; Deivasigamani Selvam; Ganesan Dinesh Babu; Rathinam Bakyaraj
2013-01-01
Objective: To investigate functional groups of toxic spines in stingray by Fourier transform infrared spectroscopic analysis.Methods:sephen were centrifuged at 6000 r/min for 10 min. The supernatant was collected and preserved separately in methanol, ethanol, chloroform, acetone (1:2) and then soaked in the mentioned solvents for 48 h. Then extracts were filtered and used for Fourier transform infrared spectroscopic analysis.Results:The venom extract of Himantura gerrardi, Himantura imbricata and Pastinachus and random coiled secondary structure. The presence of O-H stretch, C=O stretch, C-H stretch, N-H deformation, O-H deformation and C-O stretch in the sample aligned with standard bovine serum albumin. The influence of functional groups within the molecule was because of the impact of preferred spatial orientation, chemical and physical interaction on the molecule. In conclusion, compared to bovine serum albumin, Himantura imbricata consists of two C=O stretch, are involved in the hydrogen bonding that takes place between the different elements of secondary structure.Conclusions:The results identified that the presence of free amino acids and protein having β-sheet medicine not available for treatment against injuries causing stingray. Therefore, it's the baseline study, to motivate further process and produce effective antibiotics. The venom of poisonous animals has been extensively studied, since standard.
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Muthuramalingam Uthaya Siva
2013-10-01
Full Text Available Objective: To investigate functional groups of toxic spines in stingray by Fourier transform infrared spectroscopic analysis. Methods: The venom extract of Himantura gerrardi, Himantura imbricata and Pastinachus sephen were centrifuged at 6 000 r/min for 10 min. The supernatant was collected and preserved separately in methanol, ethanol, chloroform, acetone (1:2 and then soaked in the mentioned solvents for 48 h. Then extracts were filtered and used for Fourier transform infrared spectroscopic analysis. Results: The results identified that the presence of free amino acids and protein having β-sheet and random coiled secondary structure. The presence of O-H stretch, C=O stretch, C-H stretch, N-H deformation, O-H deformation and C-O stretch in the sample aligned with standard bovine serum albumin. The influence of functional groups within the molecule was because of the impact of preferred spatial orientation, chemical and physical interaction on the molecule. In conclusion, compared to bovine serum albumin, Himantura imbricata consists of two C=O stretch, are involved in the hydrogen bonding that takes place between the different elements of secondary structure. Conclusions: The venom of poisonous animals has been extensively studied, since standard medicine not available for treatment against injuries causing stingray. Therefore, it's the baseline study, to motivate further process and produce effective antibiotics.
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Measurement of absolute optical thickness of mask glass by wavelength-tuning Fourier analysis.
Kim, Yangjin; Hbino, Kenichi; Sugita, Naohiko; Mitsuishi, Mamoru
2015-07-01
Optical thickness is a fundamental characteristic of an optical component. A measurement method combining discrete Fourier-transform (DFT) analysis and a phase-shifting technique gives an appropriate value for the absolute optical thickness of a transparent plate. However, there is a systematic error caused by the nonlinearity of the phase-shifting technique. In this research the absolute optical-thickness distribution of mask blank glass was measured using DFT and wavelength-tuning Fizeau interferometry without using sensitive phase-shifting techniques. The error occurring during the DFT analysis was compensated for by using the unwrapping correlation. The experimental results indicated that the absolute optical thickness of mask glass was measured with an accuracy of 5 nm.
Fourier mode analysis of slab-geometry transport iterations in spatially periodic media
International Nuclear Information System (INIS)
We describe a Fourier analysis of the diffusion-synthetic acceleration (DSA) and transport-synthetic acceleration (TSA) iteration schemes for a spatially periodic, but otherwise arbitrarily heterogeneous, medium. Both DSA and TSA converge more slowly in a heterogeneous medium than in a homogeneous medium composed of the volume-averaged scattering ratio. In the limit of a homogeneous medium, our heterogeneous analysis contains eigenvalues of multiplicity two at ''resonant'' wave numbers. In the presence of material heterogeneities, error modes corresponding to these resonant wave numbers are ''excited'' more than other error modes. For DSA and TSA, the iteration spectral radius may occur at these resonant wave numbers, in which case the material heterogeneities most strongly affect iterative performance
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Manokaran Kalaiselvi
2012-02-01
Full Text Available Ananas comosus (L. Merrill is belonging to the family Bromeliaceae which act as an anti-inflammatory, antitumor effect. The present study is aimed to appraise the antioxidant potential and Fourier transform infrared spectroscopy (FTIR analysis in Ananus comosus peel. The enzymatic and non enzymatic antioxidants profiles were analyzed in fresh peel of pineapple with the standard protocols and the FTIR was applied and Infrared spectrum in mid infrared region 4000–400 cm–1 was used for discriminating and to identify various functional groups present in the ethanolic extract of Ananus comosus. The fresh peel shows the significant amount of antioxidants and the FTIR analysis also found the presence of amino acids, alkenes, nitrates, nitrites, ethers, esters, aldehydes, alkynes, aromatic compounds, organic halogen compounds, carbohydrates, sulphur derivatives and polysaccharides. In conclusion, the results presented in the peel of Ananus comosus have strong antioxidant content which may be act as good pharmacotherapeutic agents in future.
Marica, Aurora
2014-01-01
This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quad...
Grünberger, J; Linzmayer, L; Grünberger, M; Saletu, B
1994-01-01
While the changes in pupillary size during wakefulness and drowsiness are easy to understand, the origin of pupillary oscillations is quite mysterious. Waves of spontaneous pupillary constriction and dilation accompany periods of increasing sleepiness and spontaneous arousal. Lowenstein et al. (1963) demonstrated that in the dark, the pupils of young normal alert subjects show waves of dilatation and contraction lasting from about 4 to 40 s and measuring up to 0.5 mm. Furthermore, superimposed fast and very extensive oscillations were observed. The first described oscillations seemed to reflect central nervous activation. Therefore we analysed pupillary oscillations during the recording period of static pupillometry (described by the authors in 1992) which lasted for 25.6 s. Before calculating the Fourier analysis, blinks have to be identified and eliminated by means of a new technique which is called "smoothing". Using the Fourier analysis, the spectrum was divided into 5 frequency bands (0.0-0.2; 0.21-0.4; 0.41-0.60; 0.61-0.8; 0.81-1 Hz). We were also interested in the total spectrum. In order to demonstrate utilisation of the new technique, 146 male and female depressed patients (ICD-Diagnosis 296.1, 296.3, 296.1, 296.3 + 300, respectively, 300.4, 301.1, 296.1, 296.3 + 290, respectively), aged between 18 and 45 years, were investigated by means of pupillometry, followed by analysis of pupillary oscillations. The whole group of depressive patients who received antidepressive medication was compared with 64 healthy subjects of similar age to demonstrate differences in the frequency bands.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:8197747
Chen, Cheng; Liang, Jingqiu; Liang, Zhongzhu; Lü, Jinguang; Qin, Yuxin; Tian, Chao; Wang, Weibiao
2015-12-01
A method of "slope splicing" is proposed to build a tall-stepped mirror with high precision in a stepped-mirror-based static Fourier transform infrared spectrometer. The structural parameters were designed, and their errors were analyzed. We present the test results and an analysis of the combined effect of the errors on the recovered spectrum. The spectrum-constructing error of the constructed spectrum, 5.81%, meets the requirements for the system and suitable for realization of a miniaturized spectrometer. We performed experiments with the tall-stepped mirror to obtain the interferogram and spectrum of a silicon carbide light source. Further work is needed to optimize the capability of the system.
Rohman, A; Man, Yb Che; Sismindari
2009-10-01
Today, virgin coconut oil (VCO) is becoming valuable oil and is receiving an attractive topic for researchers because of its several biological activities. In cosmetics industry, VCO is excellent material which functions as a skin moisturizer and softener. Therefore, it is important to develop a quantitative analytical method offering a fast and reliable technique. Fourier transform infrared (FTIR) spectroscopy with sample handling technique of attenuated total reflectance (ATR) can be successfully used to analyze VCO quantitatively in cream cosmetic preparations. A multivariate analysis using calibration of partial least square (PLS) model revealed the good relationship between actual value and FTIR-predicted value of VCO with coefficient of determination (R2) of 0.998.
Singular Spectrum Analysis: A Note on Data Processing for Fourier Transform Hyperspectral Imagers.
Rafert, J Bruce; Zabalza, Jaime; Marshall, Stephen; Ren, Jinchang
2016-09-01
Hyperspectral remote sensing is experiencing a dazzling proliferation of new sensors, platforms, systems, and applications with the introduction of novel, low-cost, low-weight sensors. Curiously, relatively little development is now occurring in the use of Fourier transform (FT) systems, which have the potential to operate at extremely high throughput without use of a slit or reductions in both spatial and spectral resolution that thin film based mosaic sensors introduce. This study introduces a new physics-based analytical framework called singular spectrum analysis (SSA) to process raw hyperspectral imagery collected with FT imagers that addresses some of the data processing issues associated with the use of the inverse FT. Synthetic interferogram data are analyzed using SSA, which adaptively decomposes the original synthetic interferogram into several independent components associated with the signal, photon and system noise, and the field illumination pattern.
Institute of Scientific and Technical Information of China (English)
Bing DENG; Jun-bao LUAN; Shi-qi CUI
2014-01-01
Parameter estimation is analyzed using two kinds of common sampling-type DFRFT (discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial fre-quency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively;and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].
Zhang, Xiaoxing; Liu, Heng; Ren, Jiangbo; Li, Jian; Li, Xin
2015-02-01
Gas-insulated switchgear (GIS) internal SF6 gas produces specific decomposition components under partial discharge (PD). By detecting these characteristic decomposition components, such information as the type and level of GIS internal insulation deterioration can be obtained effectively, and the status of GIS internal insulation can be evaluated. SF6 was selected as the background gas for Fourier transform infrared spectroscopy (FTIR) detection in this study. SOF2, SO2F2, SO2, and CO were selected as the characteristic decomposition components for system analysis. The standard infrared absorption spectroscopy of the four characteristic components was measured, the optimal absorption peaks were recorded and the corresponding absorption coefficient was calculated. Quantitative detection experiments on the four characteristic components were conducted. The volume fraction variation trend of four characteristic components at different PD time were analyzed. And under five different PD quantity, the quantitative relationships among gas production rate, PD time, and PD quantity were studied.
Nagornov, Konstantin O; Gorshkov, Mikhail V; Kozhinov, Anton N; Tsybin, Yury O
2014-09-16
A multielectrode ion cyclotron resonance (ICR) cell, herein referred to as the "4X cell", for signal detection at the quadruple frequency multiple was implemented and characterized on a commercial 10 T Fourier transform ICR mass spectrometer (FT-ICR MS). Notably, with the 4X cell operating at a 10 T magnetic field we achieved a 4-fold increase in MS acquisition rate per unit of resolving power for signal detection periods typically employed in FTMS, viz., shorter than 6 s. Effectively, the obtained resolution performance represents the limit of the standard measurement principle with dipolar signal detection and FT signal processing at an equivalent magnetic field of 40 T. In other words, the achieved resolving powers are 4 times higher than those provided by 10 T FT-ICR MS with a standard ICR cell. For example, resolving powers of 170,000 and 70,000 were obtained in magnitude-mode Fourier spectra of 768 and 192 ms apodized transient signals acquired for a singly charged fluorinated phosphazine (m/z 1422) and a 19-fold charged myoglobin (MW 16.9 kDa), respectively. In peptide analysis, the baseline-resolved isotopic fine structures were obtained with as short as 768 ms transients. In intact protein analysis, the average resolving power of 340,000 across the baseline-resolved (13)C isotopic pattern of multiply charged ions of bovine serum albumin was obtained with 1.5 s transients. The dynamic range and the mass measurement accuracy of the 4X cell were found to be comparable to the ones obtained for the standard ICR cell on the same mass spectrometer. Overall, the reported results validate the advantages of signal detection at frequency multiples for increased throughput in FT-ICR MS, essential for numerous applications with time constraints, including proteomics.
Analysis of Index Gases of Coal Spontaneous Combustion Using Fourier Transform Infrared Spectrometer
Directory of Open Access Journals (Sweden)
Xiaojun Tang
2014-01-01
Full Text Available Analysis of the index gases of coal for the prevention of spontaneous combustion is of great importance for the enhancement of coal mine safety. In this work, Fourier Transform Infrared Spectrometer (FTIRS is presented to be used to analyze the index gases of coal in real time to monitor spontaneous combustion conditions. Both the instrument parameters and the analysis method are introduced at first by combining characteristics of the absorption spectra of the target analyte with the analysis requirements. Next, more than ten sets of the gas mixture containing ten components (CH4, C2H6, C3H8, iso-C4H10, n-C4H10, C2H4, C3H6, C2H2, CO, and CO2 are included and analyzed with a Spectrum Two FTIRS made by Perkin Elmer. The testing results show that the detection limit of most analytes is less than 2×10-6. All the detection limits meet the monitoring requirements of coal spontaneous combustion in China, which means that FTIRS may be an ideal instrument and the analysis method used in this paper is sufficient for spontaneous combustion gas monitoring on-line and even in situ, since FTIRS has many advantages such as fast analysis, being maintenance-free, and good safety.
Fourier-Analysis of Sawtooth Heat Pulse-Propagation and Comparison with Other Methods Using Jet Data
Mantica, P.; De Luca, F.; Gorini, G.; Jacchia, A.; Hogeweij, G. M. D.; Cardozo, N. J. L.; Kramer, G. J.; Sips, A.C.C.
1992-01-01
A new method for the analysis of sawtooth heat pulse propagation is presented. The method is based on Fourier analysis of data where the statistical noise is reduced by a suitable noise reduction procedure. Besides the value of the incremental heat diffusivity (chi(inc)), information on the magnitud
Rajačić, M M; Todorović, D J; Krneta Nikolić, J D; Janković, M M; Djurdjević, V S
2016-09-01
Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity. PMID:27396670
An improved model for whole genome phylogenetic analysis by Fourier transform.
Yin, Changchuan; Yau, Stephen S-T
2015-10-01
DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees
An improved model for whole genome phylogenetic analysis by Fourier transform.
Yin, Changchuan; Yau, Stephen S-T
2015-10-01
DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees
Fourier optics analysis of phase-mask-based path-length-multiplexed optical coherence tomography.
Yin, Biwei; Dwelle, Jordan; Wang, Bingqing; Wang, Tianyi; Feldman, Marc D; Rylander, Henry G; Milner, Thomas E
2015-11-01
Optical coherence tomography (OCT) is an imaging technique that constructs a depth-resolved image by measuring the optical path-length difference between broadband light backscattered from a sample and a reference surface. For many OCT sample arm optical configurations, sample illumination and backscattered light detection share a common path. When a phase mask is placed in the sample path, features in the detected signal are observed, which suggests that an analysis of a generic common path OCT imaging system is warranted. In this study, we present a Fourier optics analysis using a Fresnel diffraction approximation of an OCT system with a path-length-multiplexing element (PME) inserted in the sample arm optics. The analysis may be generalized for most phase-mask-based OCT systems. A radial-angle-diverse PME is analyzed in detail, and the point spread function, coherent transfer function, sensitivity of backscattering angular diversity detection, and signal formation in terms of sample spatial frequency are simulated and discussed. The analysis reveals important imaging features and application limitations of OCT imaging systems with a phase mask in the sample path optics.
Hourani, Nadim
2013-10-01
Rationale Polycyclic aromatic sulfur heterocycles (PASHs) are detrimental species for refining processes in petroleum industry. Current mass spectrometric Methods that determine their composition are often preceded by derivatization and dopant addition approaches. Different ionization Methods have different impact on the molecular assignment of complex PASHs. The analysis of such species under atmospheric pressure chemical ionization (APCI) is still considered limited due to uncontrolled ion generation with low- and high-mass PASHs. Methods The ionization behavior of a model mixture of five selected PASH standards was investigated using an APCI source with nitrogen as the reagent gas. A complex thiophenic fraction was separated from a vacuum gas oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same ionization pattern was observed for the real thiophenic sample. It was found that S1 class species were the major sulfur-containing species found in the VGO sample. These species indicated the presence of alkylated benzothiophenic (BT), dibenzothiophenic (DBT) and benzonaphthothiophenic (BNT) series that were detected by APCI-FTICR MS. CONCLUSIONS This study provides an established APCI-FTICR MS method for the analysis of complex PASHs. PASHs were detected without using any derivatization and without fragmentation. The method can be used for the analysis of S-containing crude oil samples. © 2013 John Wiley & Sons, Ltd.
Fourier transform infrared and fluorescence spectroscopy for analysis of vegetable oils
Directory of Open Access Journals (Sweden)
Nigri S.
2013-09-01
Full Text Available Fourier transform infrared (FTIR and fluorescence spectroscopy, combined with chemometric approaches have been developed to analysis of extra virgin olive oil adulterated with pomace olive oil. The measurements were made on pure vegetable oils: extra virgin oil, pomace olive oil and that adulterated with varying concentration of pomace olive oil. Today, the application of FTIR spectroscopy has increased in food studied, and particularly has become a powerful analytical tool in the study of edible oils and fats. The spectral regions where the variations were observed chosen for developing models and cross validation was used. The synchronous fluorescence spectrometry takes advantage of the hardware capability to vary both the excitation and emission wavelengths during the analysis with constant wavelength difference is maintained between the two. The region between 300 and 400 nm is attributed to the tocopherols and phenols, the derivatives of vitamin E are associated with the region 400–600 nm and the bands in the region of 600–700 nm are attributed to the chlorophyll and peophytin pigments. The results presented in this study suggest that FTIR and fluorescence may be a useful tool for analysis and detecting adulteration of extra virgin olive oil with pomace oil.
von Aulock, F. W.; Kennedy, B. M.; Schipper, C. I.; Castro, J. M.; Martin, D. E.; Oze, C.; Watkins, J. M.; Wallace, P. J.; Puskar, L.; Bégué, F.; Nichols, A. R. L.; Tuffen, H.
2014-10-01
Fourier transform infrared spectroscopy (FTIR) is an analytical technique utilized to measure the concentrations of H and C species in volcanic glasses. Water and CO2 are the most abundant volatile species in volcanic systems. Water is present in magmas in higher concentrations than CO2 and is also more soluble at lower pressures, and, therefore it is the dominant volatile forming bubbles during volcanic eruptions. Dissolved water affects both phase equilibria and melt physical properties such as density and viscosity, therefore, water is important for understanding magmatic processes. Additionally, quantitative measurements of different volatile species using FTIR can be achieved at high spatial resolution. Recent developments in analytical equipment such as synchrotron light sources and the development of focal plane array (FPA) detectors allow higher resolution measurements and the acquisition of concentration maps. These new capabilities are being used to characterize spatial gradients (or lack thereof) around bubbles and other textural features, which in turn lead to new insights into the behavior of volcanic feeder systems. Here, practical insights about sample preparation and analysis of the distribution and speciation of volatiles in volcanic glasses using FTIR spectroscopy are discussed. New advances in the field of FTIR analysis produce reliable data at high spatial resolution that can be used to produce datasets on the distribution, dissolution and diffusion of volatiles in volcanic materials.
Fourier Analysis of the OMC1 Image at 1.1 mm Wavelength
Youn, Soyoung
2012-01-01
We present a 1.1 mm emission map of the OMC1 region observed with AzTEC, a new large-format array composed of 144 silicon-nitride micromesh bolometers that was in use at the James Clerk Maxwell Telescope (JCMT). The AzTEC observations of the OMC1 region at 1.1 mm reveal dozens of cloud cores and a tail of filaments in a manner that is almost identical to the submillimeter continuum emission of the entire OMC1 region at 450 and 850 micronm. We perform Fourier analysis of the image with a modified periodogram and the density power spectrum which provides the distribution of length scale of the structures is measured. The expected value of the periodogram converges to the resulting power spectrum in the mean squared sense. From the present analysis of the OMC1 filaments at the 1.1 mm emission, the power spectrum steepens at relatively smaller scales. At largest scales, the power spectrum flattens and the large scale power law becomes shallower. The power spectra of the 1.1 mm emission show clear deviations from ...
Energy Technology Data Exchange (ETDEWEB)
Anderson, Timothy J. [Ames Laboratory; Ai, Yongfeng [Iowa State University; Jones, Roger W. [Ames Laboratory; Houk, Robert S. [Ames Laboratory; Jane, Jay-lin [Iowa State University; Zhao, Yinsheng [Iowa State University; Birt, Diane F. [Iowa State University; McClelland, John F. [Ames Laboratory
2013-01-29
Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) qualitatively and quantitatively measured resistant starch (RS) in rat cecal contents. Fisher 344 rats were fed diets of 55% (w/w, dry basis) starch for 8 weeks. Cecal contents were collected from sacrificed rats. A corn starch control was compared against three RS diets. The RS diets were high-amylose corn starch (HA7), HA7 chemically modified with octenyl succinic anhydride, and stearic-acid-complexed HA7 starch. To calibrate the FTIR-PAS analysis, samples from each diet were analyzed using an enzymatic assay. A partial least-squares cross-validation plot generated from the enzymatic assay and FTIR-PAS spectral results for starch fit the ideal curve with a R2 of 0.997. A principal component analysis plot of components 1 and 2 showed that spectra from diets clustered significantly from each other. This study clearly showed that FTIR-PAS can accurately quantify starch content and identify the form of starch in complex matrices.
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.
Directory of Open Access Journals (Sweden)
Sohel Rana
2014-01-01
Full Text Available Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE and finite element method (FEM. The non-Fourier heat conduction has been investigated where the maximum likelihood (ML and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML, another well-conditioned scheme, called mass effect (ME T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.
Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme
2015-11-01
An interferogram conditioning procedure, for subsequent phase retrieval by Fourier demodulation, is presented here as a fast iterative approach aiming at fulfilling the classical boundary conditions imposed by Fourier transform techniques. Interference fringe patterns with typical edge discontinuities were simulated in order to reveal the edge artifacts that classically appear in traditional Fourier analysis, and were consecutively used to demonstrate the correction efficiency of the proposed conditioning technique. Optimization of the algorithm parameters is also presented and discussed. Finally, the procedure was applied to grating-based interferometric measurements performed in the hard X-ray regime. The proposed algorithm enables nearly edge-artifact-free retrieval of the phase derivatives. A similar enhancement of the retrieved absorption and fringe visibility images is also achieved.
Moffat, Jonathan G; Mayes, Andrew G; Belton, Peter S; Craig, Duncan Q M; Reading, Mike
2010-01-01
Photothermal-Fourier transform-infrared (PT-FT-IR) microspectroscopy employs a thermal probe mounted in a scanning probe microscope (SPM). By placement of the tip of the probe on the surface of a solid sample, it can obtain localized IR spectra of a wide range of samples. A second mode of analysis is also available; a sample can be taken from the selected location using a technique called thermally assisted nanosampling (TAN), then a spectrum can be obtained of the nanosample while the probe is remote from the surface. We report a novel method of local compositional analysis that combines both of these types of measurement; a reagent is attached to the tip using TAN, then the reagent is placed in contact with analyte. IR spectroscopy can then be used to analyze any interaction between the reagent and surface it is placed in contact with. All of these modes of analysis were illustrated using a metal chelating agent. In the surface mode, changes to a solid bead of a chelating resin were measured using standard PT-FT-IR. In the nanosampling mode of analysis, a particle of a chelating polymer was attached to the tip of the probe using TAN and this was placed in contact with a concentrated calcium solution. Strong spectral changes were observed that mirrored those found when exposing the surface bound chelating resin bead to a solution of the same ion. A semiquantitative simulation of the PT spectrum for a chelating resin bead was achieved using a thermal diffusion model derived from photoacoustic spectroscopy indicating that semiquantitative or quantitative measurements will be possible in such a system. PMID:19957959
Fourier Analysis and Structure Determination. Part II: Pulse NMR and NMR Imaging.
Chesick, John P.
1989-01-01
Uses simple pulse NMR experiments to discuss Fourier transforms. Studies the generation of spin echoes used in the imaging procedure. Shows that pulse NMR experiments give signals that are additions of sinusoids of differing amplitudes, frequencies, and phases. (MVL)
Theoretical Analysis and Experimental Evidence of NonFourier Heat Conduction Behavior
Institute of Scientific and Technical Information of China (English)
蒋方明; 刘登瀛; 蔡睿贤
2001-01-01
This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.
DPL Model Analysis of Non-Fourier Heat Conduction Restricted by Continuous Boundary Interface
Institute of Scientific and Technical Information of China (English)
Jiang Fangming; Liu Dengying
2001-01-01
Dual-phase lag (DPL) model is used to describe the non-Fourier heat conduction in a finite medium where the boundary at x=-0 is heated by a rectangular pulsed energy source and the other boundary is tightly contacted with another medium and satisfies the continuous boundary condition. Numerical solution of this kind of. non-Fourier heat conduction is presented in this paper. The results are compared with those predicted by the hyperbolic heat conduction (HHC) equation.
International Nuclear Information System (INIS)
One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an
Temporal behavior of lung motion assested by xenon-127 scintigraphy using temporal Fourier analysis
International Nuclear Information System (INIS)
Temporal Fourier Analysis (TFA) was applied to standard 127Xe ventilation studies to determine the time-activity curves up to the third harmonic for a single composite respiratory cycle. A global respiratory index, RI3, defined as the ratio of the amplitude for the first three harmonics. Three nonobstructed subjects, two subjects with only small airway disease, five subjects with chronic ostructive pulmonary disease (COPD) and onne subject with restrictive lung disease were studied. Geometric mean values of posterior and anterior images gave a closer relationship between RI3 and flow or volume parameters than either image alone. RI3 of the first three harmonics correlated linearly with the values of 1-s forced expiratory volume (FEV1)(r 0.783, p 3 values for the five COPD subjects were significantly lower (t = 2.582, p 127Xe ventilation data therefore appears to be a potentially useful, noninvasive, in vivo technique for evaluation of lung ventilation at the localized level. (author). 20 refs.; 6 figs.; 3 tabs
Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control
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.
Institute of Scientific and Technical Information of China (English)
ZUOSong-lin; GAOShang-yu; YUANXi-gen; XUBo-sen
2003-01-01
Bamboo was carbonized at different temperatures ranging from 200℃ to 600℃.The dependence of the change of hemicellulose,cellulose,and lignin on the temperature was investigated by means of elemental analysis and Fourier Transform Infrared (FTIR) spectra of the residual solid products.The results showed:(1)Below 200℃,hemicellulose in bamboo wasdecomposed and a large amount of hydroxyl groups are dislocated from hemicellulose and cellulose,accompanied by the evolution of water to escape.(2)200℃-250℃,cellulose in bamboo was brastically decomposed whereas the net structure of lignin keep stable,with the except of the dislocation of methoxyl groups from lignin.(3)250℃-400℃,the net structure of lignin collapse,up to 400℃,followed by that the more position in aryl groups are substituted.(4)For bamboo carbonization,the aromatization of residual carbon has approximately completed at the temperature as high as 600℃.But the fusion of aromatic rings possibly does not occur.
Mello, Maria Luiza S; Vidal, Benedicto C
2014-06-01
The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an "all reflecting objective" (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.
Verification of the helioseismic Fourier-Legendre analysis for meridional flow measurements
Roth, Markus; Hartlep, Thomas
2016-01-01
Measuring the Sun's internal meridional flow is one of the key issues of helioseismology. Using the Fourier-Legendre analysis is a technique for addressing this problem. We validate this technique with the help of artificial helioseismic data. The analysed data set was obtained by numerically simulating the effect of the meridional flow on the seismic wave field in the full volume of the Sun. In this way, a 51.2-hour long time series was generated. The resulting surface velocity field is then analyzed in various settings: Two $360^\\circ \\times 90^\\circ$ halfspheres, two $120^\\circ \\times 60^\\circ$ patches on the front and farside of the Sun (North and South, respectively) and two $120^\\circ \\times 60^\\circ$ patches on the northern and southern frontside only. We compare two possible measurement setups: observations from Earth and from an additional spacecraft on the solar farside, and observations from Earth only, in which case the full information of the global solar oscillation wave field was available. We ...
Energy Technology Data Exchange (ETDEWEB)
Ota, T. A. [AWE, Aldermaston, Reading, Berkshire RG7 4PR (United Kingdom)
2013-10-15
Photonic Doppler velocimetry, also known as heterodyne velocimetry, is a widely used optical technique that requires the analysis of frequency modulated signals. This paper describes an investigation into the errors of short time Fourier transform analysis. The number of variables requiring investigation was reduced by means of an equivalence principle. Error predictions, as the number of cycles, samples per cycle, noise level, and window type were varied, are presented. The results were found to be in good agreement with analytical models.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...... modelling and analysis....
Fourier transform infrared spectroscopic analysis of sperm chromatin structure and DNA stability.
Oldenhof, H; Schütze, S; Wolkers, W F; Sieme, H
2016-05-01
Sperm chromatin structure and condensation determine accessibility for damage, and hence success of fertilization and development. The aim of this study was to reveal characteristic spectral features coinciding with abnormal sperm chromatin packing (i.e., DNA-protein interactions) and decreased fertility, using Fourier transform infrared spectroscopy. Chromatin structure in spermatozoa obtained from different stallions was investigated. Furthermore, spermatozoa were exposed to oxidative stress, or treated with thiol-oxidizing and disulfide-reducing agents, to alter chromatin structure and packing. Spectroscopic studies were corroborated with flow cytometric analyses using the DNA-intercalating fluorescent dye acridine orange. Decreased fertility of individuals correlated with increased abnormal sperm morphology and decreased stability toward induced DNA damage. Treatment with the disulfide reducing agent dithiothreitol resulted in increased sperm chromatin decondensation and DNA accessibility, similar as found for less mature epididymal spermatozoa. In situ infrared spectroscopic analysis revealed that characteristic bands arising from the DNA backbone (ν1230, ν1086, ν1051 cm(-1) ) changed in response to induced oxidative damage, water removal, and decondensation. This coincided with changes in the amide-I region (intensity at ν1620 vs. ν1640 cm(-1) ) denoting concomitant changes in protein secondary structure. Reduction in protein disulfide bonds resulted in a decreased value of the asymmetric to symmetric phosphate band intensity (ν1230/ν1086 cm(-1) ), suggesting that this band ratio is sensitive for the degree of chromatin condensation. Moreover, when analyzing spermatozoa from different individuals, it was found that the asymmetric/symmetric phosphate band ratio negatively correlated with the percentage of morphologically abnormal spermatozoa. PMID:26916383
Wang, Ya-Mei; Ma, Shu-Ling; Feng, Li-Qun
2014-03-01
Wood preservative treatment can improve defects of plantation wood such as easy to corrupt and moth eaten. Among them heat-treatment is not only environmental and no pollution, also can improve the corrosion resistance and dimension stability of wood. In this test Poplar and Mongolian Seoteh Pine was treated by soybean oil as heat-conducting medium, and the heat treatment wood was studied for indoor decay resistance; wood chemical components before and after treatment, the effect of heat treatment on wood decay resistance performance and main mechanism of action were analysed by Fourier infrared spectrometric. Results showed that the mass loss rate of poplar fell from 19.37% to 5% and Mongolian Seoteh Pine's fell from 8.23% to 3.15%, so oil heat treatment can effectively improve the decay resistance. Infrared spectrum analysis shows that the heat treatment made wood's hydrophilic groups such as hydroxyl groups in largely reduced, absorbing capacity decreased and the moisture of wood rotting fungi necessary was reduced; during the heat treatment wood chemical components such as cellulose, hemicellu lose were degraded, and the nutrient source of wood rotting fungi growth necessary was reduced. Wood decay fungi can grow in the wood to discredit wood is because of that wood can provide better living conditions for wood decay fungi, such as nutrients, water, oxygen, and so on. The cellulose and hemicellulose in wood is the main nutrition source of wood decay fungi. So the oil heat-treatment can reduce the cellulose, hemicellulose nutrition source of wood decay fungi so as to improve the decay resistance of wood.
Wang, Ya-Mei; Ma, Shu-Ling; Feng, Li-Qun
2014-03-01
Wood preservative treatment can improve defects of plantation wood such as easy to corrupt and moth eaten. Among them heat-treatment is not only environmental and no pollution, also can improve the corrosion resistance and dimension stability of wood. In this test Poplar and Mongolian Seoteh Pine was treated by soybean oil as heat-conducting medium, and the heat treatment wood was studied for indoor decay resistance; wood chemical components before and after treatment, the effect of heat treatment on wood decay resistance performance and main mechanism of action were analysed by Fourier infrared spectrometric. Results showed that the mass loss rate of poplar fell from 19.37% to 5% and Mongolian Seoteh Pine's fell from 8.23% to 3.15%, so oil heat treatment can effectively improve the decay resistance. Infrared spectrum analysis shows that the heat treatment made wood's hydrophilic groups such as hydroxyl groups in largely reduced, absorbing capacity decreased and the moisture of wood rotting fungi necessary was reduced; during the heat treatment wood chemical components such as cellulose, hemicellu lose were degraded, and the nutrient source of wood rotting fungi growth necessary was reduced. Wood decay fungi can grow in the wood to discredit wood is because of that wood can provide better living conditions for wood decay fungi, such as nutrients, water, oxygen, and so on. The cellulose and hemicellulose in wood is the main nutrition source of wood decay fungi. So the oil heat-treatment can reduce the cellulose, hemicellulose nutrition source of wood decay fungi so as to improve the decay resistance of wood. PMID:25208386
Bochner's theorem on Fourier-Stieltjes integrals in the framework of quaternion analysis
Georgiev, S.; Morais, J.
2012-11-01
Let σ(x) be a nondecreasing function, such that σ(-∞) = 0,σ(∞) = 1 and let us denote by B the class of functions which can be represented by a Fourier-Stieltjes integral f(t) = ∫ -∞∞eitxdσ(x). In continuation to [12], we prove a generalization of the classical theorem of Bochner on Fourier integral transforms to quaternion functions belonging to a subclass of B. The underlying functions are continuous functions of bounded variation defined in R2 and taking values on the quaternion algebra. Additionally, we introduce the definition of convolution of quaternion functions of bounded variation.
Glaucia Braz Alcantara; Andersson Barison; Maiara da Silva Santos; Luis P. S. Santos; José F. F. de Toledo; Antonio Gilberto Ferreira
2010-01-01
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 convent...
M. E. Ali; Nina Naquiah, A. N.; Mustafa, S; S. B. A. Hamid
2015-01-01
The agro-based production and consumption of frogs coupled with world-wide trading have been increased in the recent years giving rise to the risk of frog fat adulteration in expensive vegetable and marine oils. For the first time, we profiled here frog fats using Fourier Transform Infrared (FTIR) Spectroscopy coupled with multivariate principal component analysis (PCA). The comparison of the FTIR spectral absorbance intensities demonstrated linkage of frog fats to other edible fats and oils....
Fourier transform mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
International Nuclear Information System (INIS)
This study presents an analysis of trabecular bone structure in standard radiographs using Fourier transforms and principal components analysis (PCA) to identify contributions to hip fracture risk. Radiographs were obtained from 26 hip fracture patients and 24 controls. They were digitised and five regions of interest (ROI) were identified from the femoral head and neck for analysis. The power spectrum was obtained from the Fourier transform of each region and three profiles were produced; a circular profile and profiles parallel and perpendicular to the preferred orientation of the trabeculae. PCA was used to generate a score from each profile, which we hypothesised could be used to discriminate between the fracture and control groups. The fractal dimension was also calculated for comparison. The area under the receiver operating characteristic curve (Az) discriminating the hip fracture cases from controls was calculated for each analysis. Texture analysis of standard radiographs using the fast Fourier transform yielded variables that were significantly associated with fracture and not significantly correlated with age, body mass index or femoral neck bone mineral density. The anisotropy of the trabecular structure was important; both the perpendicular and circular profiles were significantly better than the parallel-profile (P < 0.05). No significant differences resulted from using the various ROI within the proximal femur. For the best three groupings of profile (circular, parallel or perpendicular), method (PCA or fractal) and ROI (Az = 0.84 – 0.93), there were no significant correlations with femoral neck bone mineral density, age, or body mass index. PCA analysis was found to perform better than fractal analysis (P = 0.019). Both PCA and fractal analysis of the FFT data could discriminate successfully between the fracture and control groups, although PCA was significantly stronger than fractal dimension. This method appears to provide a powerful tool for
The analysis of linear partial differential operators I distribution theory and Fourier analysis
Hörmander, Lars
2003-01-01
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comm...
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).
Fourier Transform Analysis of STM Images of Multilayer Graphene Moir\\'e Patterns
Joucken, Frédéric; Frising, Fernande; Sporken, Robert
2014-01-01
With the help of a simple model, we analyze Scanning Tunneling Microscopy images of simple and double moir\\'e patterns resulting from misoriented bi- and tri-layers graphene stacks. It is found that the model reproduces surprisingly well non-trivial features observed in the Fast Fourier Transform of the images. We point out difficulties due to those features in interpreting the patterns seen on the FFT.
Institute of Scientific and Technical Information of China (English)
Jian Ye(叶坚); Zichun Le(乐孜纯); Jingqiu Liang(梁静秋); Kai Liu(刘恺); Bisheng Quan(全必胜); Yali Qin(覃亚丽); Guangxin Zhu(朱广信)
2004-01-01
It is important to predict the intensity distribution in focusing plane for designing the X-ray compound refractive lenses. On the basis of analyzing the structure of X-ray compound lenses and comparing it with Fraunhofer diffraction system, it is concluded that the X-ray focusing system can be regarded as a kind of Fraunhofer diffraction system. Therefore, a method based on Fourier spectrum analysis is presented to predict the intensity distribution in the focusing plane for the X-ray lenses. A brief analysis on the relationship between the parameters of X-ray lenses and their focusing performance is also given in this paper.
Leszczyński, Adam
2015-01-01
We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far field images of several gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images reveals phase differences between typically 5 movable points on the modulator. Repeating this measurement yields wavefront surface. Next, the amplitude efficiency is calibrated be registering near field image. As a verification we produced a superposition of 7th and 8th Bessel beams with different phase velocities and observed their interference.
An application of linear programming duality to discrete Fourier analysis and additive problems
Croot, Ernie
2007-01-01
Suppose that f is a function from Z_p -> [0,1] (Z_p is my notation for the integers mod p, not the p-adics), and suppose that a_1,...,a_k are some places in Z_p. In some additive number theory applications it would be nice to perturb f slightly so that Fourier transform f^ vanishes at a_1,...,a_k, while additive properties are left intact. In the present paper, we show that even if we are unsuccessful in this, we can at least say something interesting by using the principle of the separating ...
Beecken, Brian P.; Kleinman, Randall R.
2004-01-01
New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.
Analysis of the Interference Modulation Depth in the Fourier Transform Spectrometer
Directory of Open Access Journals (Sweden)
Rilong Liu
2015-01-01
Full Text Available Based on the principle of the Michelson interferometer, the paper briefly describes the theoretical significance and calculates and deduces three expressions of the interference modulation depth. The influence of the surface shape error of plane mirror on modulation depth is analyzed, and the tolerance of error is also pointed out. Moreover, the dependence of modulation depth on the reflectance change of beam splitter interface is also analyzed, and the curve is given. It is concluded that this paper is of general significance for the Fourier transform spectrometer based on the principle of the Michelson two-beam interference.
[The principle and analysis of micro-Fourier transform spectrometer based on MEMS micro-mirror].
Chen, Jian-Jun; Zhu, Yong; Liu, Bo; Wei, Wei; Zhang, Jie; Wang, Ning
2012-11-01
The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wave-length accuracy is approximately 1 nm and the sampling period of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR.
Drifting Sub-Pulse Analysis Using the Two-Dimensional Fourier Transform
Edwards, R,A; Stappers, B. W.
2002-01-01
The basic form of drifting sub-pulses is that of a periodicity whose phase depends (approximately linearly) on both pulse longitude and pulse number. As such, we argue that the two-dimensional Fourier transform of the longitude-time data (called the Two-Dimensional Fluctuation Spectrum; 2DFS) presents an ideal basis for studies of this phenomenon. We examine the 2DFS of a pulsar signal synthesized using the parameters of an empirical model for sub-pulse behaviour. We show that the transform c...
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.
Characterizing the Nanoscale Layers of Tomorrow___s Electronics An Application of Fourier Analysis
Energy Technology Data Exchange (ETDEWEB)
Payne, Christopher Bishop; /Princeton U. /SLAC
2012-08-24
Thin film applications are of great interest to the semiconductor industry due to the important role they play in cutting edge technology such as thin film solar cells. X-Ray Reflectivity (XRR) characterizes thin films in a non-destructive and efficient manner yet complications exist in extracting these characteristics from raw XRR data. This study developed and tested two different algorithms to extract quantity of layers and thickness information on the nanometer scale from XRR data. It was concluded that an algorithm involving a local averaging technique revealed this information clearly in Fourier space.
DEFF Research Database (Denmark)
Thomsen, C; Ståhlberg, F; Stubgaard, M;
1990-01-01
images. The phase information in the resultant image was converted to flow velocity with a calibration curve with the slope 26.5 radian.m-1.sec. The velocity versus time function was Fourier transformed and a continuous curve was fitted to the measured data with use of the first three harmonics....... The in vivo measurements showed a significant variation in flow velocities in the cerebral aqueduct (range, 6-51 mm/sec). Calculated CSF production was in the range of 0.6-1.2 L/24 h. The present method gives valuable information about CSF hydrodynamics in an imaging time of less than 8 minutes....
A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.
Barlow, Euan; Mulholland, Anthony J
2011-11-01
The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.
Energy Technology Data Exchange (ETDEWEB)
Iwamoto, T. [Graduate School of Engineering, Hiroshima Univ., Kagamiyama, Hiroschima (Japan); Tsuta, T. [Faculty of Health Science, Hiroshima International Univ., Hiroshima (Japan)
2003-07-01
Due to strain-induced martensitic transformation, TRIP steel possesses favorable mechanical properties such as high strength, ductility and toughness. From SEM observations, it was clarified that the martensitic particles orient geometrically against the loading axis in the micro region. It is necessary to evaluate their orientations in TRIP steel to describe in detail deformation behavior of TRIP steel. Here, in order to discuss the geometrical orientation distribution of the micrograph, the Fourier and Wavelet transformation image analysis (FTIA and WTIA) are used. Then, the dependence of their orientation on plastic strain, temperature and stress state will be investigated by the FTIA and WTIA. (orig.)
Puyo, L; Rancillac, A; Simonutti, M; Paques, M; Sahel, J A; Fink, M; Atlan, M
2015-01-01
We report on wide-field imaging of pulsatile microvascular blood flow in the exposed cerebral cortex of a mouse by holographic interferometry. We recorded interferograms of laser light backscattered by the tissue, beating against an off-axis reference beam with a 50 kHz framerate camera. Videos of local Doppler contrasts were rendered numerically by Fresnel transformation and short-time Fourier transform analysis. This approach enabled instantaneous imaging of pulsatile blood flow contrasts in superficial blood vessels over 256 x 256 pixels with a spatial resolution of 10 microns and a temporal resolution of 20 ms.
Directory of Open Access Journals (Sweden)
Piotr CZECH
2007-01-01
Full Text Available This paper presents the results of an experimental application of artificial neural network as a classifier of the degree of cracking of a tooth root in a gear wheel. The neural classifier was based on the artificial neural network of Probabilistic Neural Network type (PNN. The input data for the classifier was in a form of matrix composedof statistical measures, obtained from fast Fourier transform (FFT and principal component analysis (PCA. The identified model of toothed gear transmission, operating in a circulating power system, served for generation of the teaching and testing set applied for the experiment.
International Nuclear Information System (INIS)
Air samples from F-Canyon effluents were collected at the F-Canyon stack and transported to a laboratory at the Savannah River Technology Center (SRTC) for analysis using a Fourier transform infrared spectrometer in conjunction with a multipath cell. Air samples were collected during the decladding and acid cuts of the dissolution of the irradiated aluminum-cladded slugs. The FTIR analyses of the air samples show the presence of NO2, NO, HNO2, N2O, SF6, and 85Kr during the dissolution cycle. The concentration time profiles of these effluents corresponded with expected release rates from the F-Canyon operations
ANALYSIS OF NON-FOURIER THERMAL BEHAVIOUR FOR MULTI-LAYER SKIN MODEL
Directory of Open Access Journals (Sweden)
Kuo-Chi Liu
2011-01-01
Full Text Available This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes' model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.
Zimmerman, G. A.; Gulkis, S.
1991-01-01
The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).
Energy Technology Data Exchange (ETDEWEB)
Narayanamurthy, C S [Department of Physics, Indian Institute of Space Science and Technology (IIST), Department of Space (Govt of India), ATF Campus, VSSC, ISRO - PO, Thiruvananthapuram 695 022 (India)], E-mail: naamu.s@gmail.com
2009-01-15
Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in Principles of Optics by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer have never been analysed seriously in any book. Because Michelson's interferometer is one of the important and fundamental optical experiments taught at both undergraduate and graduate levels, it would be appropriate to explain the localization of these fringes. In this paper, we analyse the localization of Michelson interferometer fringes using Fourier optics and temporal coherence, and show that they never localize at any plane even at infinity.
Fourier Power Spectrum Analysis of Exons for the Period-3 Behavior
Institute of Scientific and Technical Information of China (English)
Yuan Xin TIAN; Chao CHEN; Xiao Yong ZOU; Jian Ding QIU; Pei Xiang CAI; Jin Yuan MO
2005-01-01
The period-3 behaviors of 105 exons from 20 genes in human were studied by Fourier power spectrum. The results indicated that not all exons show the period-3 behavior. The exons were adjusted in order to make them accord with the order of the protein translated, and we found that the period-3 character is relation to the length of exons and the bases distribution in the three codon position. Furthermore, as long as the exons with period-3 behavior accord with the order of protein translated, they would exhibit the synonymous codons usage preference, and the codons with g/c at the third position are used in higher frequency. The results are significant to the gene prediction and the research on the introns.
Energy Technology Data Exchange (ETDEWEB)
El-Agez, T M; Taya, S A, E-mail: staya@iugaza.edu.p [Physics Department, Islamic University of Gaza, PO Box 108, Gaza (Palestinian Territory, Occupied)
2011-02-15
A full description of a scanning ellipsometer that incorporates the rotation of two polarizing elements simultaneously is presented in detail in this paper. Both the polarizer and the analyzer are rotating synchronously such that the angular speed of the analyzer is two times that of the polarizer. The intensity of the detected light is modulated by the rotation of these elements and by the reflection from the surface of the sample. The ideal Fourier spectrum of this signal includes nine coefficients, of which five are even and the rest are odd. All of these coefficients contain valuable information about the physical properties of the studied sample. Therefore, it is feasible to extract the ellipsometric parameters {psi} and {Delta} as well as the optical parameters of the sample by using any set containing three different coefficients. A comparison between these sets regarding the effect of noise on these parameters and on the results is presented.
SOUND AND VIBRATION SIGNAL ANALYSIS USING IMPROVED SHORT-TIME FOURIER REPRESENTATION
Directory of Open Access Journals (Sweden)
June-Yule Lee
2013-06-01
Full Text Available Time-frequency imaging provides a straightforward means to understanding machinery conditions. The methods of short-time Fourier transform (STFT, Wigner-Ville distribution (WVD and smooth-windowed Wigner-Ville distribution (SWWVD are applied to the condition monitoring of rotating machines. The sound and vibration signals of a rotating fan are tested, and time-frequency images are illustrated in terms of STFT, WVD and SWWVD. The results show that the resolution of STFT is low, and the resolution of WVD is high but with interference. To overcome the interference in the WVD image, a variable smooth-windowed weighting function is applied. The smoothing window function resulted in interference attenuation but also in reducing the concentration. The SWWVD is a compromise between STFT and WVD. The SWWVD exhibits better resolution than STFT and has less interference than WVD.
Fourier Analysis of Blazar Variability: Klein-Nishina Effects and the Jet Scattering Environment
Finke, Justin D
2015-01-01
The strong variability of blazars can be characterized by power spectral densities (PSDs) and Fourier frequency-dependent time lags. In previous work, we created a new theoretical formalism for describing the PSDs and time lags produced via a combination of stochastic particle injection and emission via the synchrotron, synchrotron self-Compton, and external Compton (EC) processes. This formalism used the Thomson cross section and simple $\\delta$-function approximations to model the synchrotron and Compton emissivities. Here we expand upon this work, using the full Compton cross section and detailed and accurate emissivities. Our results indicate good agreement between the PSDs computed using the $\\delta$-function approximations and those computed using the accurate expressions, provided the observed photons are produced primarily by electrons with energies exceeding the lower limit of the injected particle population. Breaks are found in the PSDs at frequencies corresponding to the cooling timescales of the ...
Directory of Open Access Journals (Sweden)
Cheshmedzhiev Mihail V.
2014-08-01
Full Text Available AIM: To assess infrainguinal arterial reconstructions by intraoperative flowmetry under the distal anastomosis using a fast Fourier transformation; calculate and compare the amplitude ratios of peripheral arterial blood pressure and volume flow before and after drug-induced vasodilation of occluded bypass grafts and bypass grafts that have been patent at least for 1 year. To find what magnitude of the change of these ratios indicate a long-term patency of the bypass grafting. PATIENTS AND METHODS: We compared the results of the intraoperative flowmetry tests of 97 patients with infrainguinal arterial reconstructions. The patients were divided into two groups based on the graft status: the grafts in 49 patients were patent for at least a year, and 48 patients had failed bypass. We used a fast Fourier transform (FFT of the pressure and blood flow waves and compared the ratios of their amplitudes before and after administration of a vasodilator drug into the graft. Comparing the ratios obtained before and those after administration of the drug we quantified their change in each group and analysed them. RESULTS: After a drug-induced vasodilation, the blood pressure and flow amplitude ratios for the group with compromised reconstructions were less than 1.9 times smaller than those before drug infusion, while for the group with bypass grafts that had been functional for at least 12 months the ratios declined by more than 1.9≈2 times. CONCLUSION: The magnitude of the change of amplitude ratios of the peripheral pressure and volume flow after drug-induced vasodilation can be used to make an assessment of the bypass graft and the distal arterial segment.
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
Directory of Open Access Journals (Sweden)
Christian Nansen
2010-03-01
Full Text Available Many food products are subjected to quality control analyses for detection of surface residue/contaminants, and there is a trend of requiring more and more documentation and reporting by farmers regarding their use of pesticides. Recent outbreaks of food borne illnesses have been a major contributor to this trend. With a growing need for food safety measures and “smart applications” of insecticides, it is important to develop methods for rapid and accurate assessments of surface residues on food and feed items. As a model system, we investigated detection of a miticide applied to maize leaves and its miticidal bioactivity over time, and we compared two types of reflectance data: fourier transformed infrared (FTIR data and hyperspectral imaging (HI data. The miticide (bifenazate was applied at a commercial field rate to maize leaves in the field, with or without application of a surfactant, and with or without application of a simulated “rain event”. In addition, we collected FTIR and HI from untreated control leaves (total of five treatments. Maize leaf data were collected at seven time intervals from 0 to 48 hours after application. FTIR data were analyzed using conventional analysis of variance of miticide-specific vibration peaks. Two unique FTIR vibration peaks were associated with miticide application (1,700 cm−1 and 763 cm−1. The integrated intensities of these two peaks, miticide application, surfactant, rain event, time between miticide application, and rain event were used as explanatory variables in a linear multi-regression fit to spider mite mortality. The same linear multi-regression approach was applied to variogram parameters derived from HI data in five selected spectral bands (664, 683, 706, 740, and 747 nm. For each spectral band, we conducted a spatial structure analysis, and the three standard variogram parameters (“sill”, “range”, and “nugget” were examined as possible “indicators” of miticide
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Attenuated total reflectance fourier transform infrared analysis of fly ash geopolymer gel aging.
Rees, Catherine A; Provis, John L; Lukey, Grant C; van Deventer, Jannie S J
2007-07-17
Structural changes in fly ash geopolymers activated with different sodium hydroxide and silicate concentrations are investigated using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy over a period of 200 days. A strong correlation is found between the concentration of silicate monomer in the activating solution and the position of the main Si-O-T stretching band in the FTIR spectrum, which gives an indication of the relative changes in the gel Si/Al ratio. The FTIR spectra of geopolymer samples with activating solution concentrations of up to 1.2 M SiO2 indicate that an Al-rich gel forms before the final gel composition is reached. The time required for the system to reach a steady gel composition depends on the silicate activating solution concentration and speciation. Geopolymers activated with solutions containing predominantly high-order silicate species rapidly reach a steady gel composition without first forming an Al-rich gel. A minimum silicate monomer concentration of approximately 0.6 M is required to shift the geopolymer synthesis mechanism from hydroxide activation to silicate activation. Silicate speciation in the activating solutions also affects zeolite formation and geopolymer microstructures, with a more homogeneous microstructure and less zeolite formation observed at a higher SiO2 content.
THE SPECTRUM AND TERM ANALYSIS OF CO iii MEASURED USING FOURIER TRANSFORM AND GRATING SPECTROSCOPY
Energy Technology Data Exchange (ETDEWEB)
Smillie, D. G.; Pickering, J. C. [Blackett Laboratory, Imperial College London, London SW7 2AZ (United Kingdom); Nave, G. [National Institute of Standards and Technology, Gaithersburg, MD 20899-8422 (United States); Smith, P. L., E-mail: j.pickering@imperial.ac.uk [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
2016-03-15
The spectrum of Co iii has been recorded in the region 1562–2564 Å (64,000 cm{sup −1}–39,000 cm{sup −1}) by Fourier transform (FT) spectroscopy, and in the region 1317–2500 Å (164,000 cm{sup −1}–40,000 cm{sup −1}) using a 10.7 m grating spectrograph with phosphor image plate detectors. The spectrum was excited in a cobalt–neon Penning discharge lamp. We classified 514 Co iii lines measured using FT spectroscopy, the strongest having wavenumber uncertainties approaching 0.004 cm{sup −1} (approximately 0.2 mÅ at 2000 Å, or 1 part in 10{sup 7}), and 240 lines measured with grating spectroscopy with uncertainties between 5 and 10 mÅ. The wavelength calibration of 790 lines of Raassen and Ortí Ortin and 87 lines from Shenstone has been revised and combined with our measurements to optimize the values of all but one of the 288 previously reported energy levels. Order of magnitude reductions in uncertainty for almost two-thirds of the 3d{sup 6}4s and almost half of the 3d{sup 6}4p revised energy levels are obtained. Ritz wavelengths have been calculated for an additional 100 forbidden lines. Eigenvector percentage compositions for the energy levels and predicted oscillator strengths have been calculated using the Cowan code.
Messaoudi, Imen; Elloumi-Oueslati, Afef; Lachiri, Zied
2014-01-01
Investigating the roles and functions of DNA within genomes is becoming a primary focus of genomic research. Thus, the research works are moving towards cooperation between different scientific disciplines which aims at facilitating the interpretation of genetic information. In order to characterize the DNA of living organisms, signal processing tools appear to be very suitable for such study. However, a DNA sequence must be converted into a numerical sequence before processing; which defines the concept of DNA coding. In line with this, we propose a new one dimensional model based on the chaos game representation theory called Frequency Chaos Game Signal: FCGS. Then, we perform a Smoothed Fourier Transform to enhance hidden periodicities in the C.elegans DNA sequences. Through this study, we demonstrate the performance of our coding approach in highlighting characteristic periodicities. Indeed, several periodicities are shown to be involved in the 1D spectra and the 2D spectrograms of FCGSs. To investigate further about the contribution of our method in the enhancement of characteristic spectral attributes, a comparison with a range of binary indicators is established.
Fourier spatial frequency analysis for image classification: training the training set
Johnson, Timothy H.; Lhamo, Yigah; Shi, Lingyan; Alfano, Robert R.; Russell, Stewart
2016-04-01
The Directional Fourier Spatial Frequencies (DFSF) of a 2D image can identify similarity in spatial patterns within groups of related images. A Support Vector Machine (SVM) can then be used to classify images if the inter-image variance of the FSF in the training set is bounded. However, if variation in FSF increases with training set size, accuracy may decrease as the size of the training set increases. This calls for a method to identify a set of training images from among the originals that can form a vector basis for the entire class. Applying the Cauchy product method we extract the DFSF spectrum from radiographs of osteoporotic bone, and use it as a matched filter set to eliminate noise and image specific frequencies, and demonstrate that selection of a subset of superclassifiers from within a set of training images improves SVM accuracy. Central to this challenge is that the size of the search space can become computationally prohibitive for all but the smallest training sets. We are investigating methods to reduce the search space to identify an optimal subset of basis training images.
Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks
Energy Technology Data Exchange (ETDEWEB)
Balzar, D.; Ledbetter, H. (Materials Science and Engineering Lab., National Inst. of Standards and Technology, Boulder, CO (United States))
1993-02-01
With the assumption that both size- and strain-broadened profiles of the pure-specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren-Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the 'hook' effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from [proportional to]1.31, for the minimum allowed Cauchy content, to 2, when the size-broadened profile is given solely by a Cauchy function. If the distortion coefficient is approximated by a harmonic term, mean-square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance. (orig.).
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.
Institute of Scientific and Technical Information of China (English)
Liu Zhi-Ming; Liu Wen-qing; Gao Ming-Guang; Tong Jing-Jing; Zhang Wian-Shu; Xu Liang; Wei Xiuai
2008-01-01
Passive Fourier transform infrared (FTIR) remote sensing measurement of chemical gas cloud is a vital technology.It takes an important part in many fields for the detection of released gases.The principle of concentration measurement is based on the Beer-Lambert law.Unlike the active measurement,for the passive remote sensing,in most cases,the difference between the temperature of the gas cloud and the brightness temperature of the background is usually a few kelvins.The gas cloud emission is almost equal to the background emission,thereby the emission of the gas cloud cannot be ignored.The concentration retrieval algorithm is quite different from the active measurement.In this paper,the concentration retrieval algorithm for the passive FTIR remote measurement of gas cloud is presented in detail,which involves radiative transfer model,radiometric calibration,absorption coefficient calculation,et al.The background spectrum has a broad feature,which is a slowly varying function of frequency.In this paper,the background spectrum is fitted with a polynomial by using the Levenberg-Marquardt method which is a kind of nonlinear least squares fitting algorithm.No background spectra are required.Thus,this method allows mobile,real-time and fast measurements of gas clouds.
Mandibular shape analysis in fossil hominins: Fourier descriptors in norma lateralis.
Lestrel, P E; Wolfe, C A; Bodt, A
2013-08-01
Biological shape can be defined as the boundary of a form in 2-space (R(2)). An earlier study (Lestrel et al., 2010, HOMO-J. Comp. Hum. Biol.) of the cranial vault found that there were statistically significant differences between each of the three groups: H. erectus, H. heidelbergensis, and H. neanderthalensis compared with H. sapiens. In contrast, there was no statistically significant difference among the first three groups. These results suggest that these three groups may have formed single evolving lineage while H. sapiens represents a separate evolutionary development. The purpose of the current research was to discern if the mandible reflected a similar pattern as the cranial vault data. This study used lateral jpeg images of the mandible. Five fossil samples were used: A. robustus (n=7), H. erectus (n=12), H. heidelbergensis (n=4), H. neanderthalensis (n=22) and H. sapiens (n=61). Each mandible image was pre-processed with Photoshop Elements. Each image was then submitted to a specially written routine that digitized the 84 points along the mandible boundary. Each mandible was fitted with elliptical Fourier functions (EFFs). Procrustes superimposition was imposed to insure minimum shape differences. The mandible results largely mirrored the earlier cranial vault study with one exception. Statistically significant results were obtained for the mandible between the H. erectus and H. neanderthalensis samples in contrast to the earlier cranial vault data. F-tests disclosed that the statistical significance was limited to the anterior symphysis of the mandible. This mosaic pattern may be explained by the reduction in prognathism with the concomitant if rudimentary development of the chin as seen in H. neanderthalensis compared to H. erectus. PMID:23769600
International Nuclear Information System (INIS)
Sample of Lincomycin were irradiated by means of gamma radiation (60Co) at dose rate ca. (408 kGy/h) in the range (3, 5, 15, 20)kGy in presence of air. Samples were investigated using two techniques: Thermal analysis (Differential Scanning Calorimetry (DSC) and Thermogravimetry (TG)) and Fourier Transform Infrared (FTIR). DSC purity study, which depends on Vant Hof equation, showed that the purity of Lincomycin reduced by means of gamma radiation. The purity of theses samples decreased by increasing the dose, and the purity of lincomycin was still above (99%) at dose (10 kGy). To follow up this effects, (FTIR) spectrums of these sample were recorded before and after irradiation. The two peaks at (1500 - 1750 Cm-1) which belong to amide group, and the peak at (1050 - 1100 Cm-1) which belongs to the S-C groups have reduced. (author)
Mackie, David M; Jahnke, Justin P; Benyamin, Marcus S; Sumner, James J
2016-01-01
The standard methodologies for quantitative analysis (QA) of mixtures using Fourier transform infrared (FTIR) instruments have evolved until they are now more complicated than necessary for many users' purposes. We present a simpler methodology, suitable for widespread adoption of FTIR QA as a standard laboratory technique across disciplines by occasional users.•Algorithm is straightforward and intuitive, yet it is also fast, accurate, and robust.•Relies on component spectra, minimization of errors, and local adaptive mesh refinement.•Tested successfully on real mixtures of up to nine components. We show that our methodology is robust to challenging experimental conditions such as similar substances, component percentages differing by three orders of magnitude, and imperfect (noisy) spectra. As examples, we analyze biological, chemical, and physical aspects of bio-hybrid fuel cells.
Samlan, C T; Naik, Dinesh N; Viswanathan, Nirmal K
2016-09-14
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-01-01
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena. PMID:27625210
Rajiv, P.; Rajeshwari, Sivaraj; Venckatesh, Rajendran
2013-12-01
Fourier transform infrared spectroscopy (FT-IR) and Gas chromatography-mass spectroscopy have been carried out to investigate the chemical composition of Parthenium mediated vermicompost. Four different concentrations of Parthenium and cow dung mixtures were vermicomposted using the earthworms (Eudrilus eugeniae). FT-IR spectra reveal the absence of Parthenin toxin (sesquiterpene lactone) and phenols in vermicompost which was obtained from high concentration of cow dung mixed treatments. GC-MS analysis shows no phenolic compounds and predominant level of intermediate metabolites such as 4,8,12,16-Tetramethylheptadecan-4-olide (7.61%), 2-Pentadecanone, 6,10,14-trimethyl- (5.29%) and Methyl 16-methyl-heptadecanoate (4.69%) during the vermicomposting process. Spectral results indicated that Parthenin toxin and phenols can be eradicated via vermicomposting if mixed with appropriate quantity of cow dung.
International Nuclear Information System (INIS)
We report experimental results on the correlations between welding penetration depth and the frequencies of the radiation from the welding pool. Various welding samples such as SUS304, brass, SUS316, etc. have been investigated with 2 kW CW Nd:YAG laser welding machine. The radiation signals from the plume generated by the interactions between the welding sample and laser with respect to the defocusing length was measured with fiber system collecting the plume signal. Analysis of the frequencies by using fast Fourier transform (FFT) shows that the penetration depth is deep as plume signal frequencies are low, shallow penetration depth for high frequencies. Frequencies up to 250 Hz for obtained signals can be analyzed with the discrete FFT. This is the useful method fur closed loop control of the laser power with respect to the welding penetration depth and is used for real time inspection of the welding quality
Directory of Open Access Journals (Sweden)
Robert W. Johnson
2013-06-01
Full Text Available The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numerically the energy and reconstruction theorems; however, transform pairs based on a variable window or nonuniform frequency sampling in general do not. Instead of selecting the shape of the window as some function of the central frequency, we propose constructing a single window with unit energy from an arbitrary set of windows that is applied over the entire frequency axis. By virtue of using a fixed window with uniform frequency sampling, such a transform satisfies the energy and reconstruction theorems. The shape of the window can be tailored to meet the requirements of the investigator in terms of time/frequency resolution. The algorithm extends naturally to the case of nonuniform signal sampling without modification beyond identification of the Nyquist interval.
Zhang, Xue-Xi; Yin, Jian-Hua; Mao, Zhi-Hua; Xia, Yang
2015-06-01
Fourier transform infrared imaging (FTIRI) combined with chemometrics algorithm has strong potential to obtain complex chemical information from biology tissues. FTIRI and partial least squares-discriminant analysis (PLS-DA) were used to differentiate healthy and osteoarthritic (OA) cartilages for the first time. A PLS model was built on the calibration matrix of spectra that was randomly selected from the FTIRI spectral datasets of healthy and lesioned cartilage. Leave-one-out cross-validation was performed in the PLS model, and the fitting coefficient between actual and predicted categorical values of the calibration matrix reached 0.95. In the calibration and prediction matrices, the successful identifying percentages of healthy and lesioned cartilage spectra were 100% and 90.24%, respectively. These results demonstrated that FTIRI combined with PLS-DA could provide a promising approach for the categorical identification of healthy and OA cartilage specimens.
Debnath, Lokenath
2012-07-01
The profound study of nature is the most fertile source of mathematical discoveries. Not only does this study, by offering a definite goal to research, have the advantage of excluding vague questions and futile calculations, but it is also a sure means of moulding analysis itself, and discerning those elements in it which it is still essential to know and which science ought to conserve. These fundamental elements are those which recur in all natural phenomena. Joseph Fourier pure mathematics enables us to discover the concepts and laws connecting them, which gives us the key to the understanding of the phenomena of nature. Albert Einstein 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 to his splendid research contributions to mathematical physics, pure and applied mathematics and his unprecedented public service accomplishments in the history of France. This is followed by historical comments about the significant and major impact of Fourier analysis on mathematical physics, probability and mathematical statistics, mathematical economics and many areas of pure and applied mathematics including geometry, harmonic analysis, signal analysis, wave propagation and wavelet analysis. Special attention is also given to the Fourier integral formula, Brownian motion and stochastic processes and many examples of applications including isoparametric inequality, everywhere continuous but nowhere differentiable functions, Heisenberg uncertainty principle, Dirichlets' theorem on primes in arithmetic progression, the Poisson summation formula and solutions of wave and diffusion equations. It is also shown that Fourier coefficients c n (t) in the Fourier expansion of a scalar field
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The values of mosaic block size and microstrain measured by the method of Voigt function are sometimes largely erroneous and difficult to be revised. In this paper, the causes of the “hook effect” which inevitably exists in the method of Fourier analysis are explained; then the method for resolving this effect is put forward; and finally the method of hypothetical function is used to simplify the method of the Fourier analysis from multi-peak to single-peak. By introducing the parameter m, this method can not only indicate the degree of errors, but also revise them as well. It is simple, clear and able to accomplish the intricate pattern calculation quickly by the aid of computer. In the end, we argue the identity between method of the approximate function and the Fourier analysis, and give a more accurate proportional coefficient k.
Zhu, Ying; Tan, Tuck Lee
2016-04-01
An effective and simple analytical method using Fourier transform infrared (FTIR) spectroscopy to distinguish wild-grown high-quality Ganoderma lucidum (G. lucidum) from cultivated one is of essential importance for its quality assurance and medicinal value estimation. Commonly used chemical and analytical methods using full spectrum are not so effective for the detection and interpretation due to the complex system of the herbal medicine. In this study, two penalized discriminant analysis models, penalized linear discriminant analysis (PLDA) and elastic net (Elnet),using FTIR spectroscopy have been explored for the purpose of discrimination and interpretation. The classification performances of the two penalized models have been compared with two widely used multivariate methods, principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLSDA). The Elnet model involving a combination of L1 and L2 norm penalties enabled an automatic selection of a small number of informative spectral absorption bands and gave an excellent classification accuracy of 99% for discrimination between spectra of wild-grown and cultivated G. lucidum. Its classification performance was superior to that of the PLDA model in a pure L1 setting and outperformed the PCDA and PLSDA models using full wavelength. The well-performed selection of informative spectral features leads to substantial reduction in model complexity and improvement of classification accuracy, and it is particularly helpful for the quantitative interpretations of the major chemical constituents of G. lucidum regarding its anti-cancer effects.
International Nuclear Information System (INIS)
We have developed a rapid method to screen large numbers of mutant plants for a broad range of cell wall phenotypes using Fourier transform infrared (FTIR) microspectroscopy of leaves. We established and validated a model that can discriminate between the leaves of wild-type and a previously defined set of cell-wall mutants of Arabidopsis. Exploratory principal component analysis indicated that mutants deficient in different cell-wall sugars can be distinguished from each other. Discrimination of cell-wall mutants from wild-type was independent of variability in starch content or additional unrelated mutations that might be present in a heavily mutagenised population. We then developed an analysis of FTIR spectra of leaves obtained from over 1000 mutagenised flax plants, and selected 59 plants whose spectral variation from wild-type was significantly out of the range of a wild-type population, determined by Mahalanobis distance. Cell wall sugars from the leaves of selected putative mutants were assayed by gas chromatography-mass spectrometry and 42 showed significant differences in neutral sugar composition. The FTIR spectra indicated that six of the remaining 17 plants have altered ester or protein content. We conclude that linear discriminant analysis of FTIR spectra is a robust method to identify a broad range of structural and architectural alterations in cell walls, appearing as a consequence of developmental regulation, environmental adaptation or genetic modification. (author)
International Nuclear Information System (INIS)
High resolution Fourier transform spectrometry has been used to perform line width and line shape analysis of eighty-one iron I emision lines in the spectral range 290 to 390nm originating in the normal analytical zone of an inductively coupled plasma. Computer programs using non-linear least squares fitting techniques for line shape analysis were applied to the fully resolved spectra to determine Gaussian and Lorentzian components of the total observed line width. The effect of noise in the spectrum on the precision of the line fitting technique was assessed, and the importance of signal to noise ratio for line shape analysis is discussed. Translational (Doppler) temperatures were calculated from the Gaussian components of the line width and were found to be on the order of 63000K. The excitation temperature of iron I was also determined from the same spectral data by the spectroscopic slope method based on the Einstein-Boltzmann expression for spectral intensity and was found to be on the order of 47000K. 31 references
Directory of Open Access Journals (Sweden)
Ashraf Adamu Ahmad
2015-11-01
Full Text Available The electronic intelligence (ELINT system is used by the military to detect, extract information and classify incoming radar signals. This work utilizes short time Fourier transform (STFT - time frequency distribution (TFD for inter-pulse analysis of the radar signal in order to estimate basic radar signal time parameters (pulse width and pulse repetition period. Four well-known windows functions of different and unique characteristics were used for the localization of STFT to determine their various effects on the analysis. The window functions are Hamming, Hanning, Bartlett and Blackman window functions. Monte Carlo simulation is carried out to determine the performance of the signal analysis in presence of additive white Gaussian noise (AWGN. Results show that the lower the transition of main lobe width and higher the peak side lobe, the better the performance of the window function irrespective of time parameter being estimated. This is because 100 percent probability of correct estimation is achieved at signal to noise ratio of about -2dB for Bartlett, 4dB for both Hamming and Hanning, and 9dB for Blackman.
Fourier techniques in X-ray timing
M. van der Klis
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Mass Spectrometry and Fourier Transform Infrared Spectroscopy for Analysis of Biological Materials
Energy Technology Data Exchange (ETDEWEB)
Anderson, Timothy J. [Iowa State Univ., Ames, IA (United States)
2014-12-01
Time-of-flight mass spectrometry along with statistical analysis was utilized to study metabolic profiles among rats fed resistant starch (RS) diets. Fischer 344 rats were fed four starch diets consisting of 55% (w/w, dbs) starch. A control starch diet consisting of corn starch was compared against three RS diets. The RS diets were high-amylose corn starch (HA7), HA7 chemically modified with octenyl succinic anhydride, and stearic-acid-complexed HA7 starch. A subgroup received antibiotic treatment to determine if perturbations in the gut microbiome were long lasting. A second subgroup was treated with azoxymethane (AOM), a carcinogen. At the end of the eight week study, cecal and distal-colon contents samples were collected from the sacrificed rats. Metabolites were extracted from cecal and distal colon samples into acetonitrile. The extracts were then analyzed on an accurate-mass time-of-flight mass spectrometer to obtain their metabolic profile. The data were analyzed using partial least-squares discriminant analysis (PLS-DA). The PLS-DA analysis utilized a training set and verification set to classify samples within diet and treatment groups. PLS-DA could reliably differentiate the diet treatments for both cecal and distal colon samples. The PLS-DA analyses of the antibiotic and no antibiotic treated subgroups were well classified for cecal samples and modestly separated for distal-colon samples. PLS-DA analysis had limited success separating distal colon samples for rats given AOM from those not treated; the cecal samples from AOM had very poor classification. Mass spectrometry profiling coupled with PLS-DA can readily classify metabolite differences among rats given RS diets.
Fourier-Domain Analysis of Hydriding Kinetics Using Pneumato-Chemical Impedance Spectroscopy
Millet, P.; C. Decaux; R. Ngameni; Guymont, M.
2007-01-01
Analysis of phase transformation processes observed in hydrogen absorbing materials (pure metals, alloys, or compounds) is still a matter of active research. Using pneumato-chemical impedance spectroscopy (PIS), it is now possible to analyze the mechanism of hydriding reactions induced by the gas phase. Experimental impedance diagrams, measured on activated LaNi5 in single- and two-phase domains, are reported in this paper. It is shown that their shape is mostly affected by the slope of the i...
Zhou, Xibin; Shi, Quan; Zhang, Yahe; Zhao, Suoqi; Zhang, Rui; Chung, Keng H; Xu, Chunming
2012-04-01
A novel technique was developed for characterization of saturated hydrocarbons. Linear alkanes were selectively oxidized to ketones by ruthenium ion catalyzed oxidation (RICO). Branched and cyclic alkanes were oxidized to alcohols and ketones. The ketones were then reduced to alcohols by lithium aluminum hydride (LiAlH(4)). The monohydric alcohols (O(1)) in the products obtained from the RICO and RICO-LiAlH(4) reduction reactions were characterized using negative-ion electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) for identification of iso-paraffins, acyclic paraffins and cyclic paraffins. Various model saturated compounds were used to determine the RICO reaction and ionization selectivity. The results from the FTICR MS analysis on the petroleum distillates derived saturated fraction were in agreement with those from field ionization gas chromatography time-of-flight mass spectrometry (FI GC-TOF MS) analysis. The technique was also used to characterize a petroleum vacuum residue (VR) derived saturates. The results showed that the saturated molecules in the VR contained up to 11 cyclic rings, and the maximum carbon number was up to 92. PMID:22424498
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.
均值有界变差条件及其在Fourier分析中的应用%Mean Bounded Variation Condition and Applications in Fourier Analysis
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier(trigonometric) coefficient sequences.We prove this condition cannot be weakened any further to guarantee the uniform convergence of the sine series.Some interesting and important classical results in Fourier analysis are re-established under this ultimate condition.Over ninty year research history is surveyed in this announcement.The first original paper of this series of papers is posted in arXiv:math.CA/0611805 vl,November 27,2006.
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.
Pezzolo, Alessandra De Lorenzi
2011-01-01
The diffuse reflectance infrared Fourier transform (DRIFT) spectra of sand samples exhibit features reflecting their composition. Basic multivariate analysis (MVA) can be used to effectively sort subsets of homogeneous specimens collected from nearby locations, as well as pointing out similarities in composition among sands of different origins.…
Nielen, M.W.F.; Engelen, M.C. van; Zuiderent, R.; Ramaker, R.
2007-01-01
An emerging trend is recognised in hormone and veterinary drug residue analysis from liquid chromatography tandem mass spectrometry (LC/MS/MS) based screening and confirmation towards accurate mass alternatives such as LC coupled with time-of-flight (TOF), Fourier transform ion cyclotron resonance (
An X-ray Fourier line shape analysis in cold-worked hexagonal titanium base alloys
International Nuclear Information System (INIS)
X-ray diffraction is an established technique for the analysis of microstructural parameters such as domain sizes, microstrains within the domains, and deformation fault densities in the deformed state of metals and alloys. These microstructural parameters influence the flow of dislocation in the lattice under deformation and thus regulate the strength and hardenability of the materials. The evaluation of such microdefects is this necessary for understanding the mechanical behavior of materials. In the present study, considering the wide applicability of titanium-base alloys in aviation industry, two alloy systems, i.e., titanium-base aluminum and titanium-base zirconium, have been selected. A number of X-ray diffraction profiles belonging to both fault-affected (H - K = 3N ± 1) and fault-unaffected (H - K = 3N) reflections have been recorded by a SIEMENS Kristolloflex-4 diffractometer using Cu Kα radiation, and the profiles have been analyzed to evaluate the microstructural parameters
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Benetti, Carolina; Kazarain, Sergei G.; Alves, Marco A. V.; Blay, Alberto; Correa, Luciana; Zezell, Denise M.
2014-03-01
The cutting of bone is routinely required in medical procedures, especially in dental applications. In such cases, bone regeneration and new bone quality can determine the success of the treatment. This study investigated the main spectral differences of undamaged and healed bone using the ATR-FTIR spectroscopy technique. Three rabbits were submitted to a surgical procedure; a small piece of bone (3x3 mm2) was removed from both sides of their jaws using a high speed drill. After 15 days, the rabbits were euthanized and the jaws were removed. A bone slice was cut from each side of the jaw containing regions of undamaged and newly formed bone, resulting in six samples which were polished for spectroscopic comparison. The samples were analyzed by FTIR spectroscopy using a diamond ATR accessory. Spectral characteristics were compared and particular attention was paid to the proportion of phosphate to amide I bands and the width of the phosphate band. The results show that the ratio of phosphate to amide I is smaller in new bone tissue than in the undamaged bone, indicating a higher organic content in the newly formed bone. The analysis of the width of the phosphate band suggests a crystallinity difference between both tissues, since the width was higher in the new bone than in the natural bone. These results suggest that the differences observed in bone aging processes by FTIR spectroscopic can be applied to the study of healing processes.
Hyatt, C J; Maughan, D W
1994-01-01
A method for determining and analyzing the wing beat frequency in Diptera is presented. This method uses an optical tachometer to measure Diptera wing movement during flight. The resulting signal from the optical measurement is analyzed using a Fast Fourier Transform (FFT) technique, and the dominant frequency peak in the Fourier spectrum is selected as the wing beat frequency. Also described is a method for determining quantitatively the degree of variability of the wing beat frequency about...
Ross, Charles W.; Simonsick, William J.; Bogusky, Michael J.; Celikay, Recep W.; Guare, James P.; Newton, Randall C.
2016-01-01
Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI), sheath flow electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) and high-field nuclear magnetic resonance (NMR) analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry. PMID:27367671
International Nuclear Information System (INIS)
For many years, the IAEA has fostered the more widespread use of stable isotope techniques to assess body composition in different population groups to address priority areas in public health nutrition in Member States. The objective is to support national and regional nutrition projects through both the IAEA's technical cooperation programme and its coordinated research projects. In particular, during the last few years, the increased access to analyses of deuterium enrichment by Fourier transform infrared (FTIR) spectrometry has increased the application of this technique in Africa, Asia and Latin America. This publication was developed by an international group of experts to provide practical, hands-on guidance in the use of this technique in settings where the analysis of deuterium enrichment in saliva samples will be made by FTIR. It is targeted at new users of this technique, for example nutritionists, analytical chemists and other professionals. More detailed information on the theoretical background and the practical application of state of the art methodologies to monitor changes in body composition can be found in an IAEA publication entitled Assessment of Body Composition and Total Energy Expenditure in Humans by Stable Isotope Techniques (IAEA Human Health Series No. 3)
Wang, Jun; Kim, Kyung Ho; Kim, Sungkyun; Kim, Yong Soo; Li, Qing X; Jun, Soojin
2010-11-15
Bacterial contamination continues to be a serious concern for food safety. Although washing fresh produce helps in reducing pathogen levels, pathogen internalization often limits the effectiveness of washing. When pathogens internalize in leafy vegetables, the method of identification and quantitative measurement would be called into question. This study was aimed to use Fourier Transform Infrared (FTIR) spectroscopy integrated with an attenuated total reflectance kit for quantification of Escherichia coli K-12 internalized in baby spinach. The bacteria were inoculated into vascular and intracellar tissues of spinach leaves by syringe injection and the distribution of internalized E. coli K-12 cells was confirmed under scanning electron microscopy (SEM). FTIR measurement following the preparation of bacterial suspension from spinach leaves with high speed pulverizing enabled to detect the absorbance peaks in the amide II region between 1590 and 1490 cm⁻¹ as a fingerprint for the microbes. It was found that the estimated concentrations of E. coli K-12 agreed well with the concentrations determined by plate counting with R² values of 0.98 and 0.97 in peptone water and spinach extracts, respectively. The results demonstrated that FTIR can identify and quantify E. coli K-12 in baby spinach extracts at a limit of detection of approximately 100 CFU/mL in 5 min. The developed method is expected to be suitable for the analysis of pathogenic E. coli strains and other bacterial species in fresh vegetables.
Directory of Open Access Journals (Sweden)
Charles W. Ross
2016-06-01
Full Text Available Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI, sheath flow electrospray ionization (ESI Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS and high-field nuclear magnetic resonance (NMR analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry.
Ruíz, A; Ayora Cañada, M J; Lendl, B
2001-02-01
The development of an automated, rapid and highly precise method for determination of the peroxide value in edible oils based on a continuous flow system and Fourier transform infrared (FTIR) spectroscopic detection is described. The sample stream was mixed with a solvent mixture consisting of 25% (v/v) toluene in hexanol which contained triphenylphosphine (TPP). The hydroperoxides present in the sample reacted stoichiometrically with TPP to give triphenylphosphine oxide (TPPO) which has a characteristic and intense absorption band at 542 cm-1. A 10% (m/v) TPP solution in the solvent mixture and a 100 cm reaction coil were necessary for complete reaction. FTIR transmission spectra were recorded using a flow cell equipped with CsI windows having an optical pathlength of 100 microns. By using tert-butyl hydroperoxide spiked oil standards and evaluation of the band formed at 542 cm-1 a linear calibration graph covering the range 1-100 PV (peroxide value; mequiv O2 kg-1 oil) was obtained. The relative standard deviation was 0.23% (n = 11) and the throughput 24 samples h-1. The developed system was also applied to the determination of PV in olive, sunflower and corn oils, showing good agreement with the official reference method of the European Community which is based on titration using organic solvents. The results obtained clearly show that the developed method is superior to the standard wet chemical method, hence suggesting its application in routine analysis and quality control. PMID:11235111
Directory of Open Access Journals (Sweden)
Wan-You Li
2014-01-01
Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.
Ross, Charles W; Simonsick, William J; Bogusky, Michael J; Celikay, Recep W; Guare, James P; Newton, Randall C
2016-01-01
Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI), sheath flow electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) and high-field nuclear magnetic resonance (NMR) analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry.
Hendrickson, Christopher L; Quinn, John P; Kaiser, Nathan K; Smith, Donald F; Blakney, Greg T; Chen, Tong; Marshall, Alan G; Weisbrod, Chad R; Beu, Steven C
2015-09-01
We describe the design and initial performance of the first 21 tesla Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The 21 tesla magnet is the highest field superconducting magnet ever used for FT-ICR and features high spatial homogeneity, high temporal stability, and negligible liquid helium consumption. The instrument includes a commercial dual linear quadrupole trap front end that features high sensitivity, precise control of trapped ion number, and collisional and electron transfer dissociation. A third linear quadrupole trap offers high ion capacity and ejection efficiency, and rf quadrupole ion injection optics deliver ions to a novel dynamically harmonized ICR cell. Mass resolving power of 150,000 (m/Δm(50%)) is achieved for bovine serum albumin (66 kDa) for a 0.38 s detection period, and greater than 2,000,000 resolving power is achieved for a 12 s detection period. Externally calibrated broadband mass measurement accuracy is typically less than 150 ppb rms, with resolving power greater than 300,000 at m/z 400 for a 0.76 s detection period. Combined analysis of electron transfer and collisional dissociation spectra results in 68% sequence coverage for carbonic anhydrase. The instrument is part of the NSF High-Field FT-ICR User Facility and is available free of charge to qualified users.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The mass spectra of five peptides with biological activities are reported. All mass spectra were recorded using a 4.7-T Fourier transform ion cyclotron resonance mass spectrometer equipped with an external electrospray source. The accurate molecular weights for the five peptides prepared by solid phase synthesis were measured as 1765.9013, 1063.5420, 1092.5254, 820.3804 and 1078.5193, respectively. All the data were obtained with the external calibration. Differences between observed and theoretical monoisotopic molecular weights were in the (0.2-1.0)×10-6 range. The complete primary sequence for the five polypep-tides were determined using the method of in-source electro-spray ionization/collision induced dissociation (ESI/CID). All the intact y series ions and b series ions were obtained from various peptides respectively, thus determining the sequences of the five polypeptides. We found that the measured accura-te molecular mass of sample 4 was not in agreement with that expected from the planned synthetic peptide. The se-quences of sample 4 were determined through analysis. The corresponding accurate masses of b series ions and y series ions were gained, which proved that it was correct to re-determine the sequences.
Hendrickson, Christopher L.; Quinn, John P.; Kaiser, Nathan K.; Smith, Donald F.; Blakney, Greg T.; Chen, Tong; Marshall, Alan G.; Weisbrod, Chad R.; Beu, Steven C.
2015-09-01
We describe the design and initial performance of the first 21 tesla Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The 21 tesla magnet is the highest field superconducting magnet ever used for FT-ICR and features high spatial homogeneity, high temporal stability, and negligible liquid helium consumption. The instrument includes a commercial dual linear quadrupole trap front end that features high sensitivity, precise control of trapped ion number, and collisional and electron transfer dissociation. A third linear quadrupole trap offers high ion capacity and ejection efficiency, and rf quadrupole ion injection optics deliver ions to a novel dynamically harmonized ICR cell. Mass resolving power of 150,000 ( m/Δm 50% ) is achieved for bovine serum albumin (66 kDa) for a 0.38 s detection period, and greater than 2,000,000 resolving power is achieved for a 12 s detection period. Externally calibrated broadband mass measurement accuracy is typically less than 150 ppb rms, with resolving power greater than 300,000 at m/z 400 for a 0.76 s detection period. Combined analysis of electron transfer and collisional dissociation spectra results in 68% sequence coverage for carbonic anhydrase. The instrument is part of the NSF High-Field FT-ICR User Facility and is available free of charge to qualified users.
Directory of Open Access Journals (Sweden)
Shijun eLi
2015-07-01
Full Text Available Background and objective: The relationship between EEG source signals and action-related visual and auditory stimulation is still not well understood. The objective of this study was to identify EEG source signals and their associated action-related visual and auditory responses, especially independent components of EEG.Methods: A hand-moving-Hanoi video paradigm was used to study neural correlates of the action-related visual and auditory information processing determined by mu rhythm (8-12 Hz in 16 healthy young subjects. Independent component analysis (ICA was applied to identify separate EEG sources, and further computed in the frequency domain by applying-Fourier transform ICA (F-ICA.Results: F-ICA found more sensory stimuli-related independent components located within the sensorimotor region than ICA did. The total number of independent components of interest from F-ICA was 768, twice that of 384 from traditional time-domain ICA (p0.05.Conclusions: These results support the hypothesis that mu rhythm was sensitive to detection of the cognitive expression, which could be reflected by the function in the parietal lobe sensory-motor region. The results of this study could potentially be applied into early diagnosis for those with visual and hearing impairments in the future.
Ross, Charles W; Simonsick, William J; Bogusky, Michael J; Celikay, Recep W; Guare, James P; Newton, Randall C
2016-01-01
Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI), sheath flow electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) and high-field nuclear magnetic resonance (NMR) analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry. PMID:27367671
Directory of Open Access Journals (Sweden)
Jiran L.
2016-06-01
Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.
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 (...
Ogawa, T; Shibata, A; Maeda, Y; Uno, Y; Okano, M; Nishizaki, K; Ohsaki, K
2003-06-01
A quite rare case of nasopharyngeal calculus in a woman in her twenties associated with the nasal discharge of pseudomonas infection was reported. As the substance was irregularly large in size, we extracted it partially by piecemeal resection using forceps and also by cracking technique using the holmium yttrium-aluminum-garnet (YAG) laser, under saline irrigation and stereotactic microscopic navigator (SMN) system under endoscopic observation. The substance was firmly fixed to the pharyngeal tonsil bed. The final extract was a small piece of singly folded bandage, which is probably the focal background for calculus formation. In a cross section of calculus specimen removed during surgery, Fourier transform infrared (FT-IR) analysis revealed that a) signal ratio of methylene group (organic substance) to amide I (protein) was 21.6% at the nasal cavity side, gradually decreased toward nasal mucous membrane showing approximate 50%, b) signal ratio of amide I to P04(3-) (inorganic substance) ranged between 17.7% and 26.7% at the different sites and inside the calculus, the protein content was approximate 1/5 of the inorganic substance, and c) signal ratio of the methylene group to amide I at the nasal cavity site showed that their contents were almost equal. The quantity of the organic substance was estimated at approximate 1/2 quantity of the protein at both the central part and the part contacted with the mucous membrane. From these results, it seems that throughout the course of calculus growth, both inorganic substance and protein remain almost constant inside the calculus, while organic substance is released from the internal part of the calculus being probably formed at an early stage. PMID:12899453
International Nuclear Information System (INIS)
Gas chromatography/mass spectrometry(GC/MS) is commonly used for oil fingerprinting and provides investigators with good forensic data. However, new challenges face oil spill forensic chemistry with the growing use of biodiesel as well as the recycling and reprocessing of used oil, particularly lubricating oils. This paper demonstrated that Fourier transform infrared (FTIR) spectroscopy may be a fast, cost effective and complementary method for forensic analysis of biodiesels (fatty acid methyl esters) and lubricating oils. Attenuated total reflectance (ATR)-FTIR spectroscopy was shown to be an interesting analytic method because of its use in monitoring and quantifying minor chemical compounds in sample matrices and its ability to identify a broad range or organic compounds. Unlike chromatography, FTIR spectroscopy with ATR can provide results without compound separation or lengthy sample preparation steps. This study described the combined use of GC and ATR-FTIR in environmental oil spill identification through the matching of source lube oil samples with artificially weathered samples. Samples recovered from a biodiesel spill incident were also investigated. ATR-FTIR provided detailed spectral information for rapid lube oil differentiation. This study was part of a continuing effort to develop a methodology to deal with chemical spills of unknown origin, which is an important aspect in environmental protection and emergency preparedness. This method was only successfully applied to the short term artificially weathered and fresh lube oil characterization, and to limited cases of biodiesel spills. It was concluded that further validation tests are needed to determine if this method can be applied to real-world weather lube oil samples. 10 refs., 11 figs.
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.
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Riedel, Thomas; Dittmar, Thorsten
2014-08-19
Fourier Transform Ion Cyclotron Resonance mass spectra (FT-ICR-MS) of natural organic matter are complex and consist of several thousands of peaks. The corresponding mass to charge ratios (m/z) and signal intensities result from analytes and noise. The most commonly applied way of distinguishing between analyte and noise is a fixed signal-to-noise ratio below which a detected peak is considered noise. However, this procedure is problematic and can yield ambiguous results. For example, random noise peaks can occur slightly above the signal-to-noise threshold (false positives), while peaks of low abundance analytes may occasionally fall below the fixed threshold (false negatives). Thus, cumulative results from repeated measurements of the same sample contain more peaks than a single measurement. False positive and false negative signals are difficult to distinguish, which affects the reproducibility between replicates of a sample. To target this issue, we tested the feasibility of a method detection limit (MDL) for the analysis of natural organic matter to identify peaks that can reliably be distinguished from noise by estimating the uncertainty of the noise. We performed 556 replicate analyses of a dissolved organic matter sample from the deep North Pacific on a 15 T FT-ICR-MS; each of these replicate runs consisted of 500 cumulated broadband scans. To unambiguously identify analyte peaks in the mass spectra, the sample was also run at time-consuming high-sensitivity settings. The resulting data set was used to establish and thoroughly test a MDL. The new method is easy to establish with software help, does only require the additional analysis of replicate blanks (low time increase), and can implement all steps of sample preparation. Especially when analysis time does not allow for replicate runs, major merits of the MDL are reliable removal of false positive (noise) peaks and better reproducibility, while the risk of losing analytes with low signal intensities
Choe, E.; Meer, van der F.; Rossiter, D.; Salm, van der C.; Kim, K.W.
2010-01-01
This study aimed at examining effective sample treatments and spectral processing for an alternate method of soil nitrate determination using the attenuated total reflectance (ATR) of Fourier transform infrared (FTIR) spectroscopy. Prior to FTIR measurements, soil samples were prepared as paste to e
Fourier analysis of blood plasma laser images phase maps in the diagnosis of cancer in human organs
Ushenko, A. G.; Boychuk, T. M.; Mincer, O. P.; Kushnerick, L. Y.; Angelsky, P. O.; Bodnar, N. B.; Oleinichenko, B. P.
2013-09-01
The optical model of polycrystalline networks of histological sections of rectum wall is suggested. The results of investigating the interrelation between the values of statistical (statistical moments of the 1st-4th order) parameters are presented. They characterize the coordinate polarization distributions of Fourier transforms of laser images of blood plasma and oncological changes. The diagnostic criteria of rectum cancer are determined.
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared.
Indian Academy of Sciences (India)
Pavitra Tandon; K Sunanda; M N Deo; M D Saksena; K N Uttam
2011-04-01
The emission spectra of $B^3 ^-_u (0^+_u) - X^3 ^-_g (0^+_g)$ transition of the isotopic species 80Se2, excited in an electrodeless discharge lamp by the microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and -centroid values.
Shakib, Farzin; Hughes, Thomas J. R.
1991-01-01
A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.
Signal Analysis from Fourier Transform to Wavelet Transform%信号分析从傅氏变换到小波变换
Institute of Scientific and Technical Information of China (English)
余小勇
2001-01-01
In this paper, the signal analysis methods are expounded from Fourier transform to wavelet transform in the aspect of development of the signal analysis, their respective advantages and shortcomings are analyzed and compared, and the inner development regularity of the signal analysis methods is uncovered.%从信号分析的发展着重阐述了从傅氏变换到小波变换的信号分析方法，分析并比较了各自的优缺点，揭示了信号分析方法发展的内在规律性。
A Two-Color Fourier Transform Mm-Wave Spectrometer for Gas Analysis Operating from 260-295 GHZ
Steber, Amanda L.; Harris, Brent J.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
We have designed a two-color mm-wave spectrometer for Fourier transform mm-wave spectroscopy that uses consumer level components for the tunable synthesizers, digital control of the pulse modulators, and digitization of the coherent free induction decay (FID). The excitation pulses are generated using an x24 active multiplier chain (AMC) that produces a peak power of 30 mW. The microwave input to the AMC is generated in a frequency up conversion circuit that accepts a microwave input frequency from about 2-4 GHz. This circuit also generates the input to the mm-wave subhamonic mixer that creates the local oscillator from a separate 2-4 GHz microwave input. Excitation pulses at two independently tunable frequencies are generated using a dual-channel source based on a low-cost, wideband synthesizer integrated circuit (Valon Technology Model 5008). The outputs of the synthesizer are pulse modulated using a PIN diode switch that is driven using the arbitrary waveform generator (AWG) output of a USB-controlled high-speed digitizer / arbitrary waveform generator combination unit (Tie Pie HS-5 530 XM). The two pulses are combined using a Wilkinson power divider before input to the up conversion circuit. The FID frequency is down converted in a two-stage mixing process to 65 MHz. The two LO frequencies used in the receiver are provided by a second Valon 5008. The FID is digitized at 200 MSamples/s using the 12-bit Tie Pie digitizer. The digital oscilloscope (and its AWG channel) and the two synthesizers use a 10 MHz reference signal from a Rubidium clock to permit time-domain signal averaging. A key feature of the digital oscilloscope is its deep memory of 32 Mpts (complemented by the 64 Mpt memory in the 240 MS/s AWG). This makes it possible to perform several one- and two-color coherent measurements, including pulse echoes and double-resonance spectroscopy, in a single "readout" experiment to speed the analysis of mm-wave rotational spectra. The spectrometer sensitivity
Lanusse, F.; Rassat, A.; Starck, J.-L.
2015-06-01
Context. Upcoming spectroscopic galaxy surveys are extremely promising to help in addressing the major challenges of cosmology, in particular in understanding the nature of the dark universe. The strength of these surveys, naturally described in spherical geometry, comes from their unprecedented depth and width, but an optimal extraction of their three-dimensional information is of utmost importance to best constrain the properties of the dark universe. Aims: Although there is theoretical motivation and novel tools to explore these surveys using the 3D spherical Fourier-Bessel (SFB) power spectrum of galaxy number counts Cℓ(k,k'), most survey optimisations and forecasts are based on the tomographic spherical harmonics power spectrum C(ij)_ℓ. The goal of this paper is to perform a new investigation of the information that can be extracted from these two analyses in the context of planned stage IV wide-field galaxy surveys. Methods: We compared tomographic and 3D SFB techniques by comparing the forecast cosmological parameter constraints obtained from a Fisher analysis. The comparison was made possible by careful and coherent treatment of non-linear scales in the two analyses, which makes this study the first to compare 3D SFB and tomographic constraints on an equal footing. Nuisance parameters related to a scale- and redshift-dependent galaxy bias were also included in the computation of the 3D SFB and tomographic power spectra for the first time. Results: Tomographic and 3D SFB methods can recover similar constraints in the absence of systematics. This requires choosing an optimal number of redshift bins for the tomographic analysis, which we computed to be N = 26 for zmed ≃ 0.4, N = 30 for zmed ≃ 1.0, and N = 42 for zmed ≃ 1.7. When marginalising over nuisance parameters related to the galaxy bias, the forecast 3D SFB constraints are less affected by this source of systematics than the tomographic constraints. In addition, the rate of increase of the
International Nuclear Information System (INIS)
Full text: Determinants of bone fracture risk include indices of bone 'quantity' such as bone mineral content (BMC, mineral mass per unit scanned bone length), plus 'environmental' (eg impact force) and 'quality' factors (Melton L.J. III et al, Bone and Min 2: 321, 1987). Bone 'quality' refers largely to the micro-geometry of bone (∼ 10-200μ), but has been less well studied because of the need for bone slices from (invasive) bone biopsies. Such studies often compare the geometry of trabecular networks (eg trabecular bone volume, trabecular number) with clinical outcomes such as fracture rates. Another (invasive) approach is to examine the two-dimensional (2-D) Fourier transform (FT) of a high-resolution radiographic image of the bone slice, since structural information is in theory encoded in the 2-D spatial-frequency (ν) spectrum. Additionally, the FT method can be applied to bone images obtained in-vivo, though superposition of information from the third dimension is a major confounding factor in their interpretation. Quantitative radiography of the ultradistal (UD) forearm permits determination of BMC (Price R et al; ACPSEM 6: 128- 137, 1983 and ACPSEM 11: 36-43, 1988), and (as a bonus) reveals a pattern (suitable for FT analysis) of the radiographic shadows of the 3-D trabecular network projected onto the image plane. Hemiplegia is associated with excessive bone loss in the paralysed (hemi) forearm, and is a model for the study of immobilisation osteoporosis. Thus, by comparing hemiplegia-induced changes in BMC and trabecular structure, derived from the same in vivo radiographic image, it is possible to compare directly the effects of disease on both bone quantity and quality, using the image of the non-paralysed (non-hemi) arm as a control. Seventy-four patients with hemiplegia of duration 3.6±3.6 (Mean±SD) years were studied cross-sectionally for radiographic BMC of their normal and paralysed UD forearms in AP view, each arm in duplicate. Methods
Fourier analysis of non-Blazhko ab-type RR Lyrae stars observed with the Kepler space telescope
Nemec, J M; Benko, J M; Moskalik, P; Kolenberg, K; Szabo, R; Kurtz, D W; Bryson, S; Guggenberger, E; Chadid, M; Jeon, Y -B; Kunder, A; Layden, A C; Kinemuchi, K; Kiss, L L; Poretti, E; Christensen-Dalsgaard, J; Kjeldsen, H; Caldwell, D; Ripepi, V; Derekas, A; Nuspl, J; Mullally, F; Thompson, S E; Borucki, W J
2011-01-01
Nineteen of the ~40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. In this paper we present the results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on ~18400 long-cadence observations per star (and ~150000 short-cadence observations for FN Lyr and for AW Dra) are derived. None of the stars shows the recently discovered `period-doubling' effect seen in Blazhko variables; however, KIC 7021124 has been found to pulsate simultaneously in the fundamental and second overtone modes with a period ratio P2/P0 ~ 0.59305 and is similar to the double-mode star V350 Lyr. Period change rates are derived from O-C diagrams spanning, in some cases, over 100 years; these are compared with high-precision periods derived from the Kepler data alone. Extant Fourier correlations by Kovacs, Jurcsik et al. (with minor transformations from the V to t...
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. PMID:27257614
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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.
Weighted Fourier and Fourier-Stieltjes Algebras
Amin Mahmoodi
2010-01-01
Let $G$ be a locally compact group and $omega$ be a symmetric weight function on $G$. We define a co-product $Gamma_omega$ on the weighted algebra $L^infty(G, omega^{-1})$ of essentially $omega$-bounded Borel measurable functions on $G$ and show that $L^infty(G, omega^{-1})$ becomes a Kac algebra with natural co-inverse $kappa_omega$ and Haar weight $phi_omega$. We use the machinery of Kac algebras to introduce the weighted Fourier and Fourier-Stieltjes algebra $ A(G,omega^{-1})$ and $ B(G,o...
Rummel, Julia L; McKenna, Amy M; Marshall, Alan G; Eyler, John R; Powell, David H
2010-03-01
Direct Analysis in Real Time (DART) is an ambient ionization technique for mass spectrometry that provides rapid and sensitive analyses with little or no sample preparation. DART has been reported primarily for mass analyzers of low to moderate resolving power such as quadrupole ion traps and time-of-flight (TOF) mass spectrometers. In the current work, a custom-built DART source has been successfully coupled to two different Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometers for the first time. Comparison of spectra of the isobaric compounds, diisopropyl methylphosphonate and theophylline, acquired by 4.7 T FT-ICR MS and TOF MS, demonstrates that the TOF resolving power can be insufficient for compositionally complex samples. 9.4 T FT-ICR MS yielded the highest mass resolving power yet reported with DART ionization for 1,2-benzanthracene and 9,10-diphenylanthracene. Polycyclic aromatic hydrocarbons exhibit a spatial dependence in ionization mechanisms between the DART source and the mass spectrometer. The feasibility of analyzing a variety of samples was established with the introduction and analysis of food products and crude oil samples. DART FT-ICR MS provides complex sample analysis that is rapid, highly selective and information-rich, but limited to relatively low-mass analytes.
基于分数阶傅里叶变换的振动信号分析%Vibration Signal Analysis Based on Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
高宇; 黄宜坚
2012-01-01
通过仿真实验验证了分数阶傅里叶变换可以抑制高斯噪声,检测出chirp信号.通过机械振动实验进一步验证了分数阶傅里叶变换不仅可以分析平稳振动信号,而且分析非平稳振动信号比传统傅里叶变换更客观地表达出信号的频谱,提取出非平稳成分.%Simulation results verify that the fractional fourier transform can suppress gaussian noise and detect the chirp signal. Mechanical vibration experiments further prove that the fractional fourier transform not only analyses stationary signals, but also is more objective to show the spectral characteristics of the signal than that by the traditional fourier transform for analysis of nonstationary signals, and extract non-stationary components.
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T. Ge
1995-01-01
Full Text Available A semianalytical algorithm is proposed for the solutions and their stability of a piecewise nonlinear system. The conventional harmonic balance method is modified by the introduction of Toeplitz Jacobian matrices (TJM and by the alternative applications of fast Fourier transformation (FFT and its inverse. The TJM/FFT method substantially reduces the amount of computation and circumvents the necessary numerical differentiation for the Jacobian. An arc-length algorithm and a branch switching procedure are incorporated so that the secondary branches can be independently traced. Oscillators with piecewise nonlinear characteristics are taken as illustrative examples. Flip, fold, and Hopf bifurcations are of interest.
Wulstein, Devynn M; Regan, Kathryn E; Robertson-Anderson, Rae M; McGorty, Ryan
2016-09-01
Using light-sheet microscopy combined with digital Fourier methods we probe the dynamics of colloidal samples and DNA molecules. This combination, referred to as selective-plane illumination differential dynamic microscopy (SPIDDM), has the benefit of optical sectioning to study, with minimal photobleaching, thick samples allowing us to measure the diffusivity of colloidal particles at high volume fractions. Further, SPIDDM exploits the inherent spatially-varying thickness of Gaussian light-sheets. Where the excitation sheet is most focused, we capture high spatial frequency dynamics as the signal-to-background is high. In thicker regions, we capture the slower dynamics as diffusion out of the sheet takes longer.
Tudor, A. M.; Melia, C. D.; Davies, M. C.; Hendra, P. J.; Church, S.; Domb, A. J.; Langer, R.
Fourier transform Raman spectroscopy was used to characterise a homologous series of aliphatic poly(anhydrides), poly[ bis( p-carboxyphenoxy) alkane anhydrides] and a selection of co-polymers of sebacic/ [bis( p-carboxyphenoxy) propane anhydride] P(SA-CPP). The techniqe is compared to conventional infrared for characterisation work, highlighting the advantage of small sample requirement and minimal sample preparation necessary for acquisition of spectral information. It is possible to differentiate between aromatic and aliphatic anhydride bonding, and in conjunction with other diagnostic bands to monitor the change in individual monomer composition within a co-polymer mixture.
DEFF Research Database (Denmark)
Nørbygaard, Thomas; Berg, Rolf W.
2004-01-01
Fourier transform (FT) Raman spectroscopy is applied to a range of phthalate ester plasticizers in pure form as well as in poly(vinyl chloride) (PVC) samples. It is found that phthalate esters as a group can be identified by a set of six characteristic Raman bands. FT-Raman spectra of 22 phthalate...... esters are given. It is demonstrated that the presence of phthalate esters in PVC products is readily detectable by FT-Raman spectroscopy. By use of proper ref. samples quant. detn. of the phthalate ester content becomes possible as well....
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Energy Technology Data Exchange (ETDEWEB)
Santiago Buey, C. de
2011-07-01
This study focuses on the use of Fourier descriptors to evaluate and quantify two specific fabric characteristics of geological materials: anisotropy of particles or voids morphologies and particle orientation. To this end, a theoretical section of a rock was created, made of ellipses and rectangles of different axes ratios and different orientations. The Fourier descriptors method was applied to calculate the anisotropy and orientation of each particle and, finally, a rose diagram was constructed to represent the particles orientations distribution and to observe the presence or not of any preferred orientation. (Author) 15 refs.
Abdulla, Hussain A N; Sleighter, Rachel L; Hatcher, Patrick G
2013-04-16
Two-dimensional (2D) correlation analysis was applied to 20 Fourier transform ion cyclotron resonance mass spectra (FTICR-MS) of ultrafiltered dissolved organic matter samples from a salinity transect of the lower Chesapeake Bay. We were able to investigate the chemical changes in the dissolved organic matter pool at the molecular level and classify the individual peaks based on their biogeochemical reactivity. The power of this technique is its ability to be used on either the presence/absence of the individual peaks or their normalized magnitudes. The presence or absence of the peaks are utilized to identify the reactivity and correlation between peaks that plot in different regions of the van Krevelen diagram, whereas the normalized magnitudes are used to correlate the changes among individual peaks. One of the promising advantages of 2D correlation of FTICR-MS data is the ability to associate the variations of the individual peaks with the changes in the functional groups that are measured by other spectroscopic techniques. This approach takes us one step further from identifying molecular formulas to proposing chemical structures. PMID:23472832
Klein, Thomas; Wieser, Wolfgang; Biedermann, Benjamin R; Eigenwillig, Christoph M; Palte, Gesa; Huber, Robert
2008-12-01
We demonstrate a Raman-pumped Fourier-domain mode-locked (FDML) fiber laser and optical coherence tomography imaging with this source. The wavelength sweep range of only 30 nm centered around 1550 nm results in limited axial resolution, hence a nonbiological sample is imaged. An output power of 1.9 mW was achieved at a sweep rate of 66 kHz and a maximum ranging depth of ~2.5 cm. Roll-off characteristics are found to be similar to FDML lasers with semiconductor optical amplifiers as gain media. The application of Raman gain also enables unperturbed cavity ring-down experiments in FDML lasers for the first time, providing direct access to the photon lifetime in the laser cavity. Good agreement with nonswept cw operation is proof of the stationary operation of FDML lasers. PMID:19037436
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Felipe Andrade Medeiros
2003-12-01
this study, we performed Fourier analysis of retinal nerve fiber layer (RNFL thickness measurements obtained with scanning laser polarimetry and evaluated the ability of this method to detect localized nerve fiber layer defects in glaucomatous patients. METHODS: The study included 40 eyes of 40 glaucomatous patients with localized RNFL defects identified by slit-lamp biomicroscopy or RNFL photography and 43 eyes of 43 normal patients. The patients were submitted to RNFL thickness measurements using the GDx® - Nerve Fiber Analyzer. Fourier analysis was applied to the polarimetry data. Fourier coefficients and GDx parameters were compared between the two groups. A linear discriminant function was developed to identify and combine the most useful Fourier coefficients to separate the two groups. ROC curves were obtained for each measurement and sensitivity values (at fixed specificities were calculated. RESULTS: The combination of Fourier coefficients resulted in a sensitivity of 80% for a specificity set at higher than 90%. For the same specificity, the GDx parameters had sensitivities ranging from 15% to 48%. The area under the ROC curve (AUC for the combination of Fourier coefficients was 0.90, significantly higher than the AUC for the parameter The Number (0.76. CONCLUSION: Fourier analysis of RNFL polarimetry data had a better diagnostic performance than standard GDx parameters to identify localized retinal nerve fiber layer defects in glaucomatous patients.
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....
Photonic crystal biosensor in spatial fourier domain
Hallynck, Elewout; Bienstman, Peter
2011-01-01
We propose a photonic crystal biosensor, operating at a single wavelength, based on analysis of resonant guided modes in the spatial Fourier domain. Sensitivities of 65 degrees per RIU and more have been simulated.
Li, Yin-long
2016-01-01
The objective of this study was to investigate the spectra characteristics (SC) at wavelengths of 400~1000 nm and 2.5~15.5 μm of pure moxa stick (MS) during its 25-minute burning process using new spectral imaging techniques. Spectral images were collected for the burning pure MS at 5, 10, 15, 20, and 25 min using hyperspectral imaging (HSI) and Fourier transform infrared spectroscopy (FTIR) for the first time. The results showed that, at wavelengths of 400~1000 nm, the spectral range of the cross section of MS burning was 750~980 nm; the peak position was 860 nm. At wavelengths of 2.5~15.5 μm, the spectral range of the cross section of MS burning was 3.0~4.0 μm; the peak position was approximately 3.5 μm. The radiation spectra of MS burning include litter red and amount of infrared (but mainly near infrared) wavelengths. The temperature, blood perfusion, and oxygen saturation increase of Shenshu (BL23) after moxibustion radiation were observed too. According to mechanism of photobiological effects and moxibustion biological effects, it was inferred that moxibustion effects should be linked with moxibustion SC. This study provided new data and means for physical properties of moxibustion research.
Melin, A M; Perromat, A; Deleris, G
2001-09-01
We investigated the sensitivity of rat heart microsomes to free radical attack using Fourier transform infrared (FT-IR) spectroscopy. This physico-chemical method seemed a valuable technique: quite sensitive to changes in the vibrational spectra. The spectral variations observed between normal and treated rats were in great part due to reactive oxygen species that led to changes in protein conformation involving beta-sheets, aggregation of proteins, and modification of protein synthesis. Carrageenan-induced inflammation slightly enhanced the total lipid content; rearrangement of acyl chains and accumulation of cholesterol esters and phospholipids also occurred in the treated rats. Carbon tetrachloride induced a decrease in both lipid and protein contents. The level of glucidic substrates was diminished with carbon tetrachloride and enhanced with carrageenan; these changes were due to metabolic interactions between cell components and drugs. FT-IR spectroscopy provided an accurate means to monitor, in rat heart, the in vivo effects of inflammatory and peroxidative damages, to discriminate and classify the affected cells, and to correlate the findings with known physiological and biochemical data in close relationship with metabolic disruptions induced by the two xenobiotics.
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Eryi Hu
2015-01-01
Full Text Available The phase error caused by the speed mismatch issue is researched in the line-scan images capturing 3D profile measurement. The experimental system is constructed by a line-scan CCD camera, an object moving device, a digital fringe pattern projector, and a personal computer. In the experiment procedure, the detected object is moving relative to the image capturing system by using a motorized translation stage in a stable velocity. The digital fringe pattern is projected onto the detected object, and then the deformed patterns are captured and recorded in the computer. The object surface profile can be calculated by the Fourier transform profilometry. However, the moving speed mismatch error will still exist in most of the engineering application occasion even after an image system calibration. When the moving speed of the detected object is faster than the expected value, the captured image will be compressed in the moving direction of the detected object. In order to overcome this kind of measurement error, an image recovering algorithm is proposed to reconstruct the original compressed image. Thus, the phase values can be extracted much more accurately by the reconstructed images. And then, the phase error distribution caused by the speed mismatch is analyzed by the simulation and experimental methods.
Valtchanov, Ivan; Polehampton, Edward; Benielli, Dominique; Fulton, Trevor; Imhof, Peter; Konopczynski, Tomasz; Lim, Tanya; Lu, Nanyao; Marchili, Nicola; Naylor, David; Swinyard, Bruce
2014-01-01
We present a method to derive the relative pointing offsets for SPIRE Fourier-Transform Spectrometer (FTS) solar system object (SSO) calibration targets, which were observed regularly throughout the Herschel mission. We construct ratios of the spectra for all observations of a given source with respect to a reference. The reference observation is selected iteratively to be the one with the highest observed continuum. Assuming that any pointing offset leads to an overall shift of the continuum level, then these ratios represent the relative flux loss due to mispointing. The mispointing effects are more pronounced for a smaller beam, so we consider only the FTS short wavelength array (SSW, 958-1546 GHz) to derive a pointing correction. We obtain the relative pointing offset by comparing the ratio to a grid of expected losses for a model source at different distances from the centre of the beam, under the assumption that the SSW FTS beam can be well approximated by a Gaussian. In order to avoid dependency on the...
Courtiol, Alexandre; Ferdy, Jean Baptiste; Godelle, Bernard; Raymond, Michel; Claude, Julien
2010-05-01
Many studies use representations of human body outlines to study how individual characteristics, such as height and body mass, affect perception of body shape. These typically involve reality-based stimuli (e.g., pictures) or manipulated stimuli (e.g., drawings). These two classes of stimuli have important drawbacks that limit result interpretations. Realistic stimuli vary in terms of traits that are correlated, which makes it impossible to assess the effect of a single trait independently. In addition, manipulated stimuli usually do not represent realistic morphologies. We describe and examine a method based on elliptic Fourier descriptors to automatically predict and represent body outlines for a given set of predicted variables (e.g., sex, height, and body mass). We first estimate whether these predictive variables are significantly related to human outlines. We find that height and body mass significantly influence body shape. Unlike height, the effect of body mass on shape differs between sexes. Then, we show that we can easily build a regression model that creates hypothetical outlines for an arbitrary set of covariates. These statistically computed outlines are quite realistic and may be used as stimuli in future studies.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper demonstrates the application of step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy(FTIR-PAS) in non-destructively depth profiling of styrene-butadiene-styrene block copolymer/polyethylene terephthalate(SBS/PET) layered materials.The surface thicknesses of three layered samples were determined to be 1.2,4.3 and 9.4μm by using phase difference analysis,overcoming the spatial detection limits of FTIR.Combined with generalized two-dimensional(G2D) FTIR correlation analysis,the spatial origins of peaks in the SBS/PET spectrum are identified with those having overlapping peaks between different layers are resolved.
Akyuz, Sevim; Akyuz, Tanil; Mukhamedshina, Nuranya M.; Mirsagatova, A. Adiba; Basaran, Sait; Cakan, Banu
2012-05-01
Ancient glass fragments excavated in the archaeological district Enez (Ancient Ainos)-Turkey were investigated by combined Instrumental Neutron Activation Analysis (INAA) and Fourier Transform Infrared (FTIR) spectrometry techniques. Multi-elemental contents of 15 glass fragments that belong to Hellenistic, Roman, Byzantine, and Ottoman Periods, were determined by INAA. The concentrations of twenty six elements (Na, K, Ca, Sc, Cr, Mn, Fe, Co, Cu, Zn, As, Rb, Sr, Sb, Cs, Ba, Ce, Sm, Eu, Tb, Yb, Lu, Hf, Ta, Au and Th), which might be present in the samples as flux, stabilizers, colorants or opacifiers, and impurities, were examined. Chemometric treatment of the INAA data was performed and principle component analysis revealed presence of 3 distinct groups. The thermal history of the glass samples was determined by FTIR spectrometry.
Sunthornvarabhas, Jackapon; Thumanu, Kanjana; Limpirat, Wanwisa; Kim, Hyun-Joong; Piyachomkwan, Kuakoon; Sriroth, Klanarong
2014-09-01
Electrospun nanofibers between starch and polyethylene oxide were successfully prepared to be used as a template for wound healing application. Material blending ratios and fabrication conditions were optimized to determine the ability to control material spatial for further development. A fourier Transform Infrared (FT-IR) mapping system and purposed modified image clustering analysis were adopted to evaluate the material homogeneity of a sheet of homogeneous composite nanofibers. The fabrication conditions and material blending ratios both have an influence on the material distribution and optimum points were observed from this technique. This study showed the possibility of using a quick and non-destructive technique and a modified image cluster analysis technique to evaluate the homogeneity of the electrospun nanofiber sheet.
Nakabayashi, Ryo; Tsugawa, Hiroshi; Kitajima, Mariko; Takayama, Hiromitsu; Saito, Kazuki
2015-01-01
In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS) is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis). To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs). The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine) and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline) identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis. PMID:26734034
Directory of Open Access Journals (Sweden)
Ryo eNakabayashi
2015-12-01
Full Text Available In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis. To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs. The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis.
Nakabayashi, Ryo; Tsugawa, Hiroshi; Kitajima, Mariko; Takayama, Hiromitsu; Saito, Kazuki
2015-01-01
In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS) is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography-Fourier transform ion cyclotron resonance-tandem mass spectrometry analysis (MS/MS boost analysis). To verify the MS/MS boost analysis, both quercetin and uniformly labeled (13)C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs). The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine) and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline) identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis. PMID:26734034
Fourier Transform Infrared Spectroscopy (FT-IR) was used to detect Salmonella typhimurium and Salmonella enteritidis foodborne bacteria and distinguish between live and dead cells of both serotypes. Bacteria were loaded individually on the ZnSe Attenuated Total Reflection (ATR) crystal surface and s...
Fourier transforms in radar and signal processing
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
Harmonic functions on groups and Fourier algebras
Chu, Cho-Ho
2002-01-01
This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
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Mohammad Mohadasi
2014-09-01
Full Text Available Study of phenotypic diversity among populations can help better understanding of diversification of species within ecosystems and intraspecific diversification in fishes. A geometric morphometric study was carried out using the Elliptic Fourier analysis to demonstrate the effect of habitat type on morphological features of shemaya (Alburnus chalcoides populations. Populations were sampled from three rivers and one lagoon, from the southern part of Caspian Sea. Significant differences in body shape were found among the populations. Differences in shapes of the riverine populations were minute compared to those of lagoon one in terms of size and shape. Shemaya is an anaderemus fish and its populations have a common origin, therefore, observed differences could be as result of environmental factors. In addition, this study suggest that the amount of curvature i.e. fusiform body shape of this species could be independent form environmental condition.
Analysis of the High-Resolution Fourier Spectrum of the ν6 Band of the cis-C2h2d2 Molecule
Konov, I. A.; Chertavskikh, Yu. V.; Fomchenko, A. L.; Aslapovskaya, Yu. S.; Zhdanovich, S. A.; Sydow, C.
2016-03-01
The spectrum of the ν6 band of the cis-ethylene-d2 molecule (cis-C2H2D2) is recorded with a Bruker IFS 125 HR Fourier spectrometer in the range 580-1210 cm-1 with resolution of 0.0021 cm-1. An analysis of the experimental spectrum allows more than 1500 transitions belonging to this band to be assigned that by more than 2.5 times greater than it has been known in the literature so far. The obtained experimental data are then used to determine the model parameters of the molecule (the effective Hamiltonian in the A-reduction and I'- representation). Strong resonance interaction with the band ν4 forbidden in absorption by the symmetry of a molecule is taken into account. 10 parameters of the Hamiltonian obtained by solving inverse spectroscopic problem reproduce 427 initial experimental energies (more than 1500 transitions) with accuracy close to the experimental uncertainty.
Habibi, Neda
2015-02-01
The preparation and characterization of functional biocompatible magnetite-cellulose nano-composite fibrous material is described. Magnetite-cellulose nano-composite was prepared by a combination of the solution-based formation of magnetic nano-particles and subsequent coating with amino celluloses. Characterization was accomplished using X-ray powder diffraction (XRD), fourier transformed infrared (FTIR) and field emission scanning electron microscopy (FESEM) analysis. The peaks of Fe3O4 in the XRD pattern of nanocomposite confirm existence of the nanoparticles in the amino cellulose matrix. Magnetite-cellulose particles exhibit an average diameter of roughly 33 nm as demonstrated by field emission scanning electron microscopy. Magnetite nanoparticles were irregular spheres dispersed in the cellulose matrix. The vibration corresponding to the Nsbnd CH3 functional group about 2850 cm-1 is assigned in the FTIR spectra. Functionalized magnetite-cellulose nano-composite polymers have a potential range of application as targeted drug delivery system in biomedical field.
International Nuclear Information System (INIS)
This work presents a low cost, simple and new methodology for direct determination uranium in different matrices uranium: organic phase (UO2(NO3)2.2TBP - uranyl nitrate complex) and aqueous phase (UO2(NO3)2 - NTU - uranyl nitrate), based on Fourier Transform Infrared spectroscopy (FTIR) using KBr pellets technique. The analytical validation is essential to define if a developed methodology is completely adjusted to the objectives that it is destined and is considered one of the main instruments of quality control. The parameters used in the validation process were: selectivity, linearity, limits of detection (LD) and quantitation (LQ), precision (repeatability and intermediate precision), accuracy and robustness. The method for uranium in organic phase (UO2(NO3)2.2TBP in hexane/embedded in KBr) was linear (r=0.9989) over the range of 1.0 g L-1a 14.3 g L-1, LD were 92.1 mg L-1 and LQ 113.1 mg L-1, precision (RSD < 1.6% and p-value < 0.05), accurate (recovery of 100.1% - 102.9%). The method for uranium aqueous phase (UO2(NO3)2/embedded in KBr) was linear (r=0.9964) over the range of 5.4 g L-1 a 51.2 g L-1, LD were 835 mg L-1 and LQ 958 mg L-1, precision (RSD < 1.0% and p-value < 0.05), accurate (recovery of 99.1% - 102.0%). The FTIR method is robust regarding most of the variables analyzed, as the difference between results obtained under nominal and modified conditions were lower than the critical value for all analytical parameters studied. Some process samples were analyzed in FTIR and compared with gravimetric and x ray fluorescence (XRF) analyses showing similar results in all three methods. The statistical tests (Student-t and Fischer) showed that the techniques are equivalent. (author)
Vakil, Ashkan
2011-01-01
Using numerical simulations, here we demonstrate that a single sheet of graphene with properly designed inhomogeneous, nonuniform conductivity distributions can act as a convex lens for focusing and collimating the transverse-magnetic (TM) surface Plasmon polariton (SPP) surface wave propagating along the graphene. Consequently, we show that the graphene can act as a platform capable of obtaining spatial Fourier transform of infra-red (IR) SPP signals. This may lead to rebirth of the field of Fourier Optics on a one-atom-thick structure.
DEFF Research Database (Denmark)
Batina, N.; Reyna-Cordova, A.; Trinidad-Reyes, Y.;
2005-01-01
of oxidation state was compared to surface morphology data by AFM previously reported. The reported results emphasize the advantage of complementary techniques (AFM/FTIR microscopy) in the analysis of petroleum thin films that should be considered during analysis and interpretation of this type of data....
Bilinear Fourier restriction theorems
Demeter, Ciprian
2012-01-01
We provide a general scheme for proving $L^p$ estimates for certain bilinear Fourier restrictions outside the locally $L^2$ setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood--Paley inequality.
Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens
2015-01-01
Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.
Generic Quantum Fourier Transforms
Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander
2003-01-01
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.
Sagar T. Cholake; Mykanth R. Mada; R. K. Singh Raman; Yu Bai; Xl Zhao; Sami Rizkalla; Sri Bandyopadhyay
2014-01-01
This article informs the essence of major work done by a number of researchers on the analysis of two-step curing mechanism of diglycidyl ether of bisphenol A (DGEBA) epoxy resin in presence of amine curing agents using near- and mid-IR technology. Various peaks used as a marker for resin formation are discussed and their implementation is comprehensively studied. In addition to this, a wide range of information about the importance of reference peaks in both near-IR (NIR) and mid-IR (MIR) re...
Energy Technology Data Exchange (ETDEWEB)
Akyuz, Sevim, E-mail: s.akyuz@iku.edu.tr [Physics Department, Science and Letters Faculty, Istanbul Kultur University, Atakoy Campus, Bakirkoy 34156, Istanbul (Turkey); Akyuz, Tanil [Physics Department, Science and Letters Faculty, Istanbul Kultur University, Atakoy Campus, Bakirkoy 34156, Istanbul (Turkey); Mukhamedshina, Nuranya M.; Mirsagatova, A. Adiba [Institute of Nuclear Physics, Uzbek Academy of Sciences, 702132, Ulugbek, Tashkent (Uzbekistan); Basaran, Sait; Cakan, Banu [Department of Restoration and Conservation of Artefacts, Letters Faculty, Istanbul University, Vezneciler, Istanbul (Turkey)
2012-05-15
Ancient glass fragments excavated in the archaeological district Enez (Ancient Ainos)-Turkey were investigated by combined Instrumental Neutron Activation Analysis (INAA) and Fourier Transform Infrared (FTIR) spectrometry techniques. Multi-elemental contents of 15 glass fragments that belong to Hellenistic, Roman, Byzantine, and Ottoman Periods, were determined by INAA. The concentrations of twenty six elements (Na, K, Ca, Sc, Cr, Mn, Fe, Co, Cu, Zn, As, Rb, Sr, Sb, Cs, Ba, Ce, Sm, Eu, Tb, Yb, Lu, Hf, Ta, Au and Th), which might be present in the samples as flux, stabilizers, colorants or opacifiers, and impurities, were examined. Chemometric treatment of the INAA data was performed and principle component analysis revealed presence of 3 distinct groups. The thermal history of the glass samples was determined by FTIR spectrometry. - Highlights: Black-Right-Pointing-Pointer INAA was performed to determine elemental compositions of ancient glass fragments. Black-Right-Pointing-Pointer Basic, coloring/discoloring elements and impurities have been determined. Black-Right-Pointing-Pointer PCA discriminated the glasses depending on their chronological order. Black-Right-Pointing-Pointer The thermal history of the glass samples was determined by FTIR spectrometry.
Gudi, Gennadi; Krähmer, Andrea; Krüger, Hans; Schulz, Hartwig
2015-10-01
Sage (Salvia officinalis L.) is cultivated worldwide for its aromatic leaves, which are used as herbal spice, and for phytopharmaceutical applications. Fast analytical strategies for essential oil analysis, performed directly on plant material, would reduce the delay between sampling and analytical results. This would enhance product quality by improving technical control of cultivation. The attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) method described here provides a reliable calibration model for quantification of essential oil components [EOCs; R(2) = 0.96; root-mean-square error of cross-validation (RMSECV) = 0.249 mL 100 g(-1) of dry matter (DM); and range = 1.115-5.280 mL 100 g(-1) of DM] and main constituents [e.g., α-thujone/β-thujone; R(2) = 0.97/0.86; RMSECV = 0.0581/0.0856 mL 100 g(-1) of DM; and range = 0.010-1.252/0.005-0.893 mL 100 g(-1) of DM] directly on dried intact leaves of sage. Except for drying, no further sample preparation is required for ATR-FTIR, and the measurement time of less than 5 min per sample contrasts with the most common alternative of hydrodistillation followed by gas chromatography analysis, which can take several hours per sample.
Somogyi, Árpád; Thissen, Roland; Orthous-Daunay, Francois-Régis; Vuitton, Véronique
2016-01-01
It is an important but also a challenging analytical problem to understand the chemical composition and structure of prebiotic organic matter that is present in extraterrestrial materials. Its formation, evolution and content in the building blocks ("seeds") for more complex molecules, such as proteins and DNA, are key questions in the field of exobiology. Ultrahigh resolution mass spectrometry is one of the best analytical techniques that can be applied because it provides reliable information on the chemical composition and structure of individual components of complex organic mixtures. Prebiotic organic material is delivered to Earth by meteorites or generated in laboratories in simulation (model) experiments that mimic space or atmospheric conditions. Recent representative examples for ultrahigh resolution mass spectrometry studies using Fourier-transform (FT) mass spectrometers such as Orbitrap and ion cyclotron resonance (ICR) mass spectrometers are shown and discussed in the present article, including: (i) the analysis of organic matter of meteorites; (ii) modeling atmospheric processes in ICR cells; and (iii) the structural analysis of laboratory made tholins that might be present in the atmosphere and surface of Saturn's largest moon, Titan. PMID:27023520
Institute of Scientific and Technical Information of China (English)
Wang Wei; Liu Yingrong; Liu Zelong; Tian Songbai
2015-01-01
Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) has become a powerful tool for ana-lyzing the detailed composition of petroleum samples. However, the correlation between the numerous peaks obtained by FT-ICR MS and bulk properties of petroleum samples is still a challenge. In this study, the internal standard method was applied for the quantitative analysis of four straight-run vacuum gas oils (VGO) by atmospheric pressure photoionization (APPI) FT-ICR MS. The heteroatom class distribution of these VGO samples turned to be different when the concentration changed. Linear relationship between the normalized abundance and the concentration of VGO samples was identiifed for the total aromatic compounds, aromatic hydrocarbons, S1 and N1 species. The differences of the response factors were also discussed. The sulfur contents of a series of crude oils were proved to be linear with the FT-ICR MS data calibrated by the response factor of S1 species. This study demonstrated the feasibility of the internal standard method in quantitative analysis with APPI FT-ICR MS, and the bulk properties of petroleum samples could be correlated directly with the FT-ICR MS data.
Somogyi, Árpád; Thissen, Roland; Orthous-Daunay, Francois-Régis; Vuitton, Véronique
2016-01-01
It is an important but also a challenging analytical problem to understand the chemical composition and structure of prebiotic organic matter that is present in extraterrestrial materials. Its formation, evolution and content in the building blocks ("seeds") for more complex molecules, such as proteins and DNA, are key questions in the field of exobiology. Ultrahigh resolution mass spectrometry is one of the best analytical techniques that can be applied because it provides reliable information on the chemical composition and structure of individual components of complex organic mixtures. Prebiotic organic material is delivered to Earth by meteorites or generated in laboratories in simulation (model) experiments that mimic space or atmospheric conditions. Recent representative examples for ultrahigh resolution mass spectrometry studies using Fourier-transform (FT) mass spectrometers such as Orbitrap and ion cyclotron resonance (ICR) mass spectrometers are shown and discussed in the present article, including: (i) the analysis of organic matter of meteorites; (ii) modeling atmospheric processes in ICR cells; and (iii) the structural analysis of laboratory made tholins that might be present in the atmosphere and surface of Saturn's largest moon, Titan.
Directory of Open Access Journals (Sweden)
Árpád Somogyi
2016-03-01
Full Text Available It is an important but also a challenging analytical problem to understand the chemical composition and structure of prebiotic organic matter that is present in extraterrestrial materials. Its formation, evolution and content in the building blocks (“seeds” for more complex molecules, such as proteins and DNA, are key questions in the field of exobiology. Ultrahigh resolution mass spectrometry is one of the best analytical techniques that can be applied because it provides reliable information on the chemical composition and structure of individual components of complex organic mixtures. Prebiotic organic material is delivered to Earth by meteorites or generated in laboratories in simulation (model experiments that mimic space or atmospheric conditions. Recent representative examples for ultrahigh resolution mass spectrometry studies using Fourier-transform (FT mass spectrometers such as Orbitrap and ion cyclotron resonance (ICR mass spectrometers are shown and discussed in the present article, including: (i the analysis of organic matter of meteorites; (ii modeling atmospheric processes in ICR cells; and (iii the structural analysis of laboratory made tholins that might be present in the atmosphere and surface of Saturn’s largest moon, Titan.
International Nuclear Information System (INIS)
Ancient glass fragments excavated in the archaeological district Enez (Ancient Ainos)–Turkey were investigated by combined Instrumental Neutron Activation Analysis (INAA) and Fourier Transform Infrared (FTIR) spectrometry techniques. Multi-elemental contents of 15 glass fragments that belong to Hellenistic, Roman, Byzantine, and Ottoman Periods, were determined by INAA. The concentrations of twenty six elements (Na, K, Ca, Sc, Cr, Mn, Fe, Co, Cu, Zn, As, Rb, Sr, Sb, Cs, Ba, Ce, Sm, Eu, Tb, Yb, Lu, Hf, Ta, Au and Th), which might be present in the samples as flux, stabilizers, colorants or opacifiers, and impurities, were examined. Chemometric treatment of the INAA data was performed and principle component analysis revealed presence of 3 distinct groups. The thermal history of the glass samples was determined by FTIR spectrometry. - Highlights: ► INAA was performed to determine elemental compositions of ancient glass fragments. ► Basic, coloring/discoloring elements and impurities have been determined. ► PCA discriminated the glasses depending on their chronological order. ► The thermal history of the glass samples was determined by FTIR spectrometry.
Directory of Open Access Journals (Sweden)
Siong Fong Sim
2012-11-01
Full Text Available A computational approach was used to analyze the FTIR spectra of a wide range of treated and untreated lignocellulosic biomass (coconut husk, banana trunk, sago hampas, rice husk, and empty fruit bunch. The biomass was treated with strong sulphuric acid and NaOH, respectively. A total of 87 spectra were obtained in which the absorption bands were de-convoluted automatically, generating a peak table of 87 rows and 60 columns. Square roots were taken of the peak values, with further standardization prior to Principal Component Analysis (PCA for data exploration. In a scores plot, the treated and untreated biomass were distinguishable along the two main axes, PC1 and PC2. Examining the absorption bands corresponding to lignocellulosic components indicated that the acid pretreatment had resulted in dissolution and degradation of hemicelluloses and lignin, confirmed typically by disappearance of bands. The alkali treatment however was not as rigorous as the acid treatment, as some characteristic bands of hemicelluloses and lignin were enhanced, suggesting condensation of the degraded polysaccharides. The computer-assisted analysis of the FTIR spectra allowed efficient and simultaneous comparisons of lignocellulosic compositions present in various treated and untreated biomass. This represents an improvement relative to the conventional methods, since a large dataset can be handled efficiently and individual peaks can be examined.
On the Replica Fourier Transform
Carlucci, D. M.; De Dominicis, C.
1997-01-01
The Replica Fourier Transform introduced previously is related to the standard definition of Fourier transforms over a group. Its use is illustrated by block-diagonalizing the eigenvalue equation of a four-replica Parisi matrix.
Schaub, Tanner M; Hendrickson, Christopher L; Qian, Kuangnan; Quinn, John P; Marshall, Alan G
2003-05-01
We report the first field desorption ionization broadband high-resolution (m/Deltam(50%) approximately 65 000) mass spectra. We have interfaced a field ionization/field desorption source to a home-built 9.4-T FT-ICR mass spectrometer. The instrumental configuration employs convenient sample introduction (in-source liquid injection) and external ion accumulation. We demonstrate the utility of this configuration by generating high-resolution positive-ion mass spectra of C(60) and a midboiling crude oil distillate. The latter contains species not accessible by common soft-ionization methods, for example, low-voltage electron ionization, electrospray ionization, and matrix-assisted laser desorption/ionization. The present work demonstrates significant advantages of FI/FD FT-ICR MS for analysis of nonpolar molecules in complex mixtures.
Directory of Open Access Journals (Sweden)
Sagar T. Cholake
2014-05-01
Full Text Available This article informs the essence of major work done by a number of researchers on the analysis of two-step curing mechanism of diglycidyl ether of bisphenol A (DGEBA epoxy resin in presence of amine curing agents using near- and mid-IR technology. Various peaks used as a marker for resin formation are discussed and their implementation is comprehensively studied. In addition to this, a wide range of information about the importance of reference peaks in both near-IR (NIR and mid-IR (MIR regions are congregated and their accuracy is audited. Also discrepancies observed by researchers in epoxy conversion (α in NIR and MIR regions are reviewed to highlight the comparative advantages of both regions, one over the other.Defence Science Journal, Vol. 64, No. 3, May 2014, pp. 314-321, DOI:http://dx.doi.org/10.14429/dsj.64.7326
Fourier transforms principles and applications
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.
Institute of Scientific and Technical Information of China (English)
Javid Ali; Bashir Ahmad; Said Hassan; Muhammad Siddique; Farrah Gul; Shafaat Ullah
2015-01-01
Objective: To compare the proximate composition, mineral contents, antimicrobial, phytochemical and Fourier transforms infrared (FTIR) spectroscopy analysis of bark, stem and seed of Hippophae rhamnoides. Methods: Proximate composition was determined according to the described methods. Mineral analysis was carried out by atomic absorption spectroscopy and flame photometer. Antimicrobial activities were evaluated according to the agar well diffusion method. Phytochemical qualitative analysis was carried out according to the described methods and functional groups were determined by FTIR Prestige-21 Shimadzu Japan. Results:The proximate analysis showed high content of protein and fiber in stem and bark. High content of Na (900 mg/L) and K (670 mg/L) was found in bark powder, while in seed, high contents of Ca (800 mg/L), Mg (725 mg/L), Fe (250 mg/L) Zn (90 mg/L) and Mn (65 mg/L) were found compared to stem and bark. Phenols, flavonoids and tannins showed high contents in stem and bark of all extracts. The bark aqueous extract showed high zone of inhibition against Staphylococcus aureus (21 mm) and Escherichia coli (20 mm), while methanol extract of stem showed high zone of inhibition (14 mm and 13 mm) against Enterococcus faecalis and Escherichia coli respectively. The aqueous extract of bark documented high zone of inhibition against Aspergillus niger (21 mm) and Aspergillus parasiticus (20 mm). FTIR spectra revealed the presence of OH, C-O and C=O functional groups. Conclusions:The study concludes that bark, stem and seed extracts will be useful guideline for the new syntheses of feed, food supplements and herb drugs with various combination, which can be used for the treatment of many diseases at global level especially in tropical regions as well as the male nutrition problems in these areas.
Directory of Open Access Journals (Sweden)
Javid Ali
2015-06-01
Full Text Available Objective: To compare the proximate composition, mineral contents, antimicrobial, phytochemical and Fourier transforms infrared (FTIR spectroscopy analysis of bark, stem and seed of Hippophae rhamnoides. Methods: Proximate composition was determined according to the described methods. Mineral analysis was carried out by atomic absorption spectroscopy and flame photometer. Antimicrobial activities were evaluated according to the agar well diffusion method. Phytochemical qualitative analysis was carried out according to the described methods and functional groups were determined by FTIR Prestige-21 Shimadzu Japan. Results: The proximate analysis showed high content of protein and fiber in stem and bark. High content of Na (900 mg/L and K (670 mg/L was found in bark powder, while in seed, high contents of Ca (800 mg/L, Mg (725 mg/L, Fe (250 mg/L Zn (90 mg/L and Mn (65 mg/L were found compared to stem and bark. Phenols, flavonoids and tannins showed high contents in stem and bark of all extracts. The bark aqueous extract showed high zone of inhibition against Staphylococcus aureus (21 mm and Escherichia coli (20 mm, while methanol extract of stem showed high zone of inhibition (14 mm and 13 mm against Enterococcus faecalis and Escherichia coli respectively. The aqueous extract of bark documented high zone of inhibition against Aspergillus niger (21 mm and Aspergillus parasiticus (20 mm. FTIR spectra revealed the presence of OH, C-O and C=O functional groups. Conclusions: The study concludes that bark, stem and seed extracts will be useful guideline for the new syntheses of feed, food supplements and herb drugs with various combination, which can be used for the treatment of many diseases at global level especially in tropical regions as well as the male nutrition problems in these areas.
Sravan Kumar, S; Manoj, P; Giridhar, P
2015-12-01
FTIR analysis for five selected green leafy vegetables (GLVs) viz., Hibiscus cannabinus L., (kenaf), H. sabdariffa L., (roselle), Basella alba L., (vine spinach), B. rubra L. (malabar spinach) and Rumex vesicarius L., (sorrel) confirmed the presence of free alcohol, intermolecular bonded alcohol, intramolecular bonded alcohol, alkane, aromatic compounds, imine or oxime or ketone or alkene, phenol and amine stretching. The chlorophyll content was higher in native leaves of B. alba (2.96 g/kg) than defatted samples (1.11 g/kg). Total phenolic content (TPC) in H. sabdariffa native methanol extractives is more (17.6 g/kg) than defatted leaves (9.67 g/kg). Native B. rubra methanol extractives exhibited highest total flavonoid content (TFC) (21.59 g/kg), while that of R. vesicarius was lowest (3.21 g/kg). In general, antioxidant activities showed a significant reduction in retention of antioxidants in both native and defatted GLVs samples of ethanol and methanol extractives. Methanol extractives showed significantly stronger antioxidant activity probably due to greater solubility of phenolics and destruction of cellular components. PMID:26604386
Ushenko, Alexander G.; Dubolazov, Alexander V.; Ushenko, Vladimir A.; Novakovskaya, Olga Y.
2016-07-01
The optical model of formation of polarization structure of laser radiation scattered by polycrystalline networks of human skin in Fourier plane was elaborated. The results of investigation of the values of statistical (statistical moments of the 1st to 4th order) parameters of polarization-inhomogeneous images of skin surface in Fourier plane were presented. The diagnostic criteria of pathological process in human skin and its severity degree differentiation were determined.
International Nuclear Information System (INIS)
Purpose: Motion artifacts are common in patient 4DCT, leading to an illdefined tumor volume with variation up to 110% or setting up a poor foundation with low imaging fidelity for tumor motion study. We developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of corresponding 1D respiratory wave-function (1DRW) surrogate used for 4DCT reconstruction. Methods: Fast Fourier Transformation (FFT) was applied to analyze 1DRW periodicity, defined as the sum of the 5 largest Fourier coefficients, ranging in 0–1. Distortional motion artifacts of cine-scan 4DCT at the junctions of adjacent couchposition scans around the diaphragm were identified in 3 categories: incomplete, overlapping and duplicate. To quantify these artifacts, the discontinuity of the diaphragm at the junctions was measured in distance and averaged along 6 directions in 3 orthogonal views. Mean and sum artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase. To make the APJ inter-patient comparable, patientspecific motion was removed from APJ by dividing patient-specific diaphragmatic velocity (displacement divided by the mean period, from FFT analysis of the 1DRW) and the normalized APJ was defined as motion artifact severity (MAS). Twenty-five patients with free-breathing 10-phase 4DCT and corresponding 1DRW surrogate datasets were studied. Results: A mild correlation of 0.56 was found between 1DRW periodicity and 4DCT artifact severity. Higher MAS tends to appear around mid inhalation and mid exhalation and the lowest MAS tends to be around full exhalation. The breathing periodicity of >0.8 possesses minimal motion artifacts. Conclusion: The 1D-4D correlation provides a fast means to estimate 4DCT image quality. Using 1DRW signal, we can retrospectively screen out high-quality 4DCT images for clinical research (periodicity>0.8) and prospectively identify poor
Energy Technology Data Exchange (ETDEWEB)
Caraveo, M; McNamara, J; Rimner, A; Yorke, E; Li, G [Memorial Sloan Kettering Cancer Center, New York, NY (United States); Wei, J [City College of New York, New York, NY (United States)
2014-06-15
Purpose: Motion artifacts are common in patient 4DCT, leading to an illdefined tumor volume with variation up to 110% or setting up a poor foundation with low imaging fidelity for tumor motion study. We developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of corresponding 1D respiratory wave-function (1DRW) surrogate used for 4DCT reconstruction. Methods: Fast Fourier Transformation (FFT) was applied to analyze 1DRW periodicity, defined as the sum of the 5 largest Fourier coefficients, ranging in 0–1. Distortional motion artifacts of cine-scan 4DCT at the junctions of adjacent couchposition scans around the diaphragm were identified in 3 categories: incomplete, overlapping and duplicate. To quantify these artifacts, the discontinuity of the diaphragm at the junctions was measured in distance and averaged along 6 directions in 3 orthogonal views. Mean and sum artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase. To make the APJ inter-patient comparable, patientspecific motion was removed from APJ by dividing patient-specific diaphragmatic velocity (displacement divided by the mean period, from FFT analysis of the 1DRW) and the normalized APJ was defined as motion artifact severity (MAS). Twenty-five patients with free-breathing 10-phase 4DCT and corresponding 1DRW surrogate datasets were studied. Results: A mild correlation of 0.56 was found between 1DRW periodicity and 4DCT artifact severity. Higher MAS tends to appear around mid inhalation and mid exhalation and the lowest MAS tends to be around full exhalation. The breathing periodicity of >0.8 possesses minimal motion artifacts. Conclusion: The 1D-4D correlation provides a fast means to estimate 4DCT image quality. Using 1DRW signal, we can retrospectively screen out high-quality 4DCT images for clinical research (periodicity>0.8) and prospectively identify poor
International Nuclear Information System (INIS)
For many years, the IAEA has fostered the more widespread use of stable isotope techniques to assess body composition in different population groups to address priority areas in public health nutrition in Member States. The objective is to support national and regional nutrition projects through both the IAEA's technical cooperation programme and its coordinated research projects. In particular, during the last few years, the increased access to analyses of deuterium enrichment by Fourier transform infrared (FTIR) spectrometry has increased the application of this technique in Africa, Asia and Latin America. This publication was developed by an international group of experts to provide practical, hands-on guidance in the use of this technique in settings where the analysis of deuterium enrichment in saliva samples will be made by FTIR. It is targeted at new users of this technique, for example nutritionists, analytical chemists and other professionals. More detailed information on the theoretical background and the practical application of state of the art methodologies to monitor changes in body composition can be found in an IAEA publication entitled Assessment of Body Composition and Total Energy Expenditure in Humans by Stable Isotope Techniques (IAEA Human Health Series No. 3)
Guo, Yizhen; Lv, Beiran; Wang, Jingjuan; Liu, Yang; Sun, Suqin; Xiao, Yao; Lu, Lina; Xiang, Li; Yang, Yanfang; Qu, Lei; Meng, Qinghong
2016-01-01
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.
International Nuclear Information System (INIS)
The potential of electrospray ionization (ESI) Fourier transform ion cyclotron mass spectrometry (FTICR-MS) to assist in the structural characterization of monomeric and dimeric derivatives of the macrophage colony stimulating factor B (rhM-CSF B) was assessed. Mass spectrometric analysis of the 49 kDa protein required the use of sustained off-resonance irradiation (SORI) in-trap cleanup to reduce adduction. High resolution mass spectra were acquired for a fully reduced and a fully S-cyanylated monomeric derivative (∼25 kDa). Mass accuracy for monomeric derivatives was better than 5 ppm, after applying a new calibration method (i.e., DeCAL) which eliminates space charge effects upon high accuracy mass measurements. This high mass accuracy allowed the direct determination of the exact number of incorporated cyanyl groups. Collisionally induced dissociation using SORI yielded b- and y-fragment ions within the N- and C-terminal regions for the monomeric derivatives, but obtaining information on other regions required proteolytic digestion, or potentially the use of alternative dissociation methods
International Nuclear Information System (INIS)
Isotope-coded reagents have been developed for labeling of amino acids, phenols and fatty acids, but not for alcohols. In this work, a simple reaction based on direct N-alkylpyridinium isotope quaternization (NAPIQ) was developed for mild derivatization of cholesterol and fatty alcohols. Different from the conventional quaternary reagents with cations on themselves, two simple and charge-neutral reagents: pyridine and d5-pyridine directly attached N-cationic tag onto the target compounds in the presence of trifluoromethanesulfonic anhydride (Tf2O) without tedious sample preparation. The derivatization completed in 5 min and achieved charge labeling of the target compounds, which significantly improved the detection limits of analytes by 103-folds in further analysis by matrix-assisted laser desorption/ionization Fourier transform mass spectrometry (MALDI-FTMS). The use of commercially available d0/d5-pyridine pairs facilitated isotope-coded chemical derivatization and avoided the use of isotope-labeled internal standards; the excess pyridine did not affect the signals of analytes. Utility of the NAPIQ method was examined in the identification of cholesterol and fatty alcohols in small amount of human hair sample (0/d5 pairs, especially when isotope-labeled internal standards are unavailable.
Institute of Scientific and Technical Information of China (English)
Umer Daood; Chan Swee Heng; Jennifer Neo Chiew Lian; Amr S Fawzy
2015-01-01
To modify two-step experimental etch-and-rinse dentin adhesive with different concentrations of riboflavin and to study its effect on the bond strength, degree of conversion, along with resin infiltration within the demineralized dentin substrate, an experimental adhesive-system was modified with different concentrations of riboflavin (m/m, 0, 1%, 3%, 5%and 10%). Dentin surfaces were etched with 37%phosphoric acid, bonded with respective adhesives, restored with restorative composite–resin, and sectioned into resin–dentin slabs and beams to be stored for 24 h or 9 months in artificial saliva. Micro-tensile bond testing was performed with scanning electron microscopy to analyse the failure of debonded beams. The degree of conversion was evaluated with Fourier transform infrared spectroscopy (FTIR) at different time points along with micro-Raman spectroscopy analysis. Data was analyzed with one-way and two-way analysis of variance followed by Tukey’s for pair-wise comparison. Modification with 1%and 3%riboflavin increased the micro-tensile bond strength compared to the control at 24 h and 9-month storage with no significant differences in degree of conversion (P,0.05). The most predominant failure mode was the mixed fracture among all specimens except 10%riboflavin-modified adhesive specimens where cohesive failure was predominant. Raman analysis revealed that 1%and 3%riboflavin adhesives specimens showed relatively higher resin infiltration. The incorporation of riboflavin in the experimental two-step etch-and-rinse adhesive at 3%(m/m) improved the immediate bond strengths and bond durability after 9-month storage in artificial saliva without adversely affecting the degree of conversion of the adhesive monomers and resin infiltration.
Hackel, L.A.; Hermann, M.R.; Dane, C.B.; Tiszauer, D.H.
1995-12-12
A solid state laser is frequency tripled to 0.3 {micro}m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only about 1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power. 1 fig.
Energy Technology Data Exchange (ETDEWEB)
Krapez, J.C.; Spagnolo, L. [Politechnique di Bari (Italy); Friess, M. [Deutsches Luft- und Raumfahrtzentrum eV (DLR), Stuttgart (Germany); Maier, H.P. [Stuttgart Univ., MPA (Germany); Neuer, G. [Institut fur Kernenergetik und Energiesysteme, Universitat Stuttgart (Germany)
2003-07-01
The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximize the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid flash method). When the material presents a transverse gradient of conductivity, we propose, as a first approach, to perform the Fourier analysis over a sliding window corresponding to one period of the grid pattern. This method allowed us to quantify in situ the diffusivity decrease in a tensile composite sample due to the stress-induced density increase of transverse microcracks. We finally analysed a more rigorous method for transverse conductivity profile inversion. It is based on a perturbation method. The analytical expression of the 'transfer function' between the Fourier transform of the temperature contrast and the Fourier transform of conductivity was established. We validated the proposed inverse technique on simulated and noise-corrupted thermograms. The approach is robust and the simulated profiles are very well resolved. (authors)
Qu, Lei; Chen, Jian-bo; Zhou, Qun; Zhang, Gui-jun; Sun, Su-qin; Guo, Yi-zhen
2016-11-01
As a kind of expensive perfume and valuable herb, the commercial Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy and two-dimensional (2D) correlation analysis are employed to establish a simple and quick identification method for the authentic and adulterated ALR. In the conventional infrared spectra, the standard ALR has a strong peak at 1658 cm-1 referring to the conjugated carbonyl of resin, while this peak is absent in the adulterated samples. The position, intensity, and shape of the auto-peaks and cross-peaks of the authentic and adulterated ALR are much different in the synchronous 2D correlation spectra with thermal perturbation. In the range of 1700-1500 cm-1, the standard ALR has four obvious auto-peaks, while the strongest one is at 1659 cm-1. The adulterated sample w-1 has three obvious auto-peaks and the strongest one is at 1647 cm-1. The adulterated sample w-2 has three obvious auto-peaks and the strongest one is at 1519 cm-1. The adulterated sample w-3 has four obvious auto-peaks and the strongest one is at 1690 cm-1. The above auto-peaks confirm that the standard ALR contains a certain content of resin compounds, while the three counterfeits contain little or different resins. The results show the potential of FT-IR spectroscopy and 2D correlation analysis in the simple and quick identification of authentic and adulterated ALR.
Fourier Transform Spectrometer System
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.
Masked object registration in the Fourier domain.
Padfield, Dirk
2012-05-01
Registration is one of the most common tasks of image analysis and computer vision applications. The requirements of most registration algorithms include large capture range and fast computation so that the algorithms are robust to different scenarios and can be computed in a reasonable amount of time. For these purposes, registration in the Fourier domain using normalized cross-correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain so that all steps of translation registration can be computed efficiently using Fast Fourier Transforms. We provide algorithms and implementation details that demonstrate the correctness of our derivations. We also demonstrate how this masked FFT registration approach can be applied to improve the Fourier-Mellin algorithm that calculates translation, rotation, and scale in the Fourier domain. We demonstrate the computational efficiency, advantages, and correctness of our algorithm on a number of images from real-world applications. Our framework enables fast, global, parameter-free registration of images with masked regions.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hang, E-mail: hangwang@sjtu.edu.cn [Instrumental Analysis Center, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240 (China); Dai, Bona [Instrumental Analysis Center, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240 (China); Liu, Bin [Key Laboratory of Kidney Disease Pathogenesis and Intervention of Hubei Province, College of Medicine, Hubei Polytechnic University, Huangshi, Hubei 435003 (China); Lu, Han [Department of Anesthesiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine (SJTU-SM), 197, Rui Jin Er Road, Shanghai 200025 (China)
2015-07-02
Highlights: • Coumarins were used as new MALDI matrices. • Coumarins were used for MALDI-FT ICR MS detection of hydrophobic compounds. • DCA had improvement in detection sensitivity, stability, selectivity and reproducibility. • DCA was applied to sterols detection in yeast cells. - Abstract: Hydrophobic compounds with hydroxyl, aldehyde or ketone groups are generally difficult to detect using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), because these compounds have low proton affinity and are poorly ionized by MALDI. Herein, coumarins have been used as new matrices for MALDI-MS analysis of a variety of hydrophobic compounds with low ionization efficiency, including steroids, coenzyme Q10, a cyclic lipopeptide and cholesterol oleate. Five coumarins, including coumarin, umbelliferone, esculetin, 7-hydroxycoumarin-3-carboxylic acid (HCA) and 6,7-dihydroxycoumarin-3-carboxylic acid (DCA), were compared with the conventional matrices of 2,5-dihydroxybenzoic acid (DHB) and α-cyano-4-hydroxycinnamic acid (CHCA). Coumarins with hydroxyl or carboxylic acid groups enabled detection. Taking DCA as an example, this matrix proved to be superior to DHB or CHCA in detection sensitivity, stability, spot-to-spot and sample-to-sample reproducibility, and accuracy. DCA increased the stability of the target compounds and decreased the loss of water. The [M + Na]{sup +} peaks were observed for all target compounds by adding NaCl as an additive, and the [M − H{sub 2}O + H]{sup +} and [M + H]{sup +} peaks decreased. DCA was selected for the identification of sterols in yeast cells, and thirteen sterols were detected by Fourier transform ion cyclotron resonance (FT ICR) mass spectrometry. This work demonstrates the potential of DCA as a new matrix for detection of hydrophobic molecules by MALDI-MS and provides an alternative tool for screening sterols in antifungal research.
Alps, K; Kruzins, A; Tamanis, M; Ferber, R; Pazyuk, E A; Stolyarov, A V
2016-04-14
Fourier-transform A(1)Σ(+) - b(3)Π → X(1)Σ(+) laser-induced fluorescence spectra were recorded for the natural mixture of (39,41)K(85,87)Rb isotopologues produced in a heatpipe oven. Overall 4200 rovibronic term values of the spin-orbit coupled A(1)Σ(+) and b(3)Π states were determined with an uncertainty of about 0.01 cm(-1) in the energy range [10 850, 14 200] cm(-1) covering rotational quantum numbers J' ∈ [3, 280]. Direct deperturbation analysis of the A ∼ b complex performed within the framework of the A(1)Σ(+) ∼ b(3)ΠΩ=0,1,2 coupled-channel approach reproduced experimental data with a standard deviation of 0.004 cm(-1). Initial parameters of the internuclear potentials and spin-orbit coupling functions along with the relevant transition dipole moments were obtained by performing the quasi-relativistic electronic structure calculations. The mass-invariant molecular parameters obtained from the fit were used to predict energy and radiative properties of the A ∼ b complex for low J levels of (39)K(85)Rb as well as for (41)K(87)Rb isotopologues, allowing us to identify the most reasonable candidates for the stimulated Raman transitions between the initial uppermost vibrational levels of the a(3)Σ(+) and X(1)Σ(+) states, the intermediate levels of the A ∼ b complex, and the lowest absolute ground X(1)Σ(+)(v = 0, J = 0) state. PMID:27083724
International Nuclear Information System (INIS)
Flux distribution in central metabolic pathways of Desulfovibrio vulgaris Hildenborough was examined using 13C tracer experiments. Consistent with the current genome annotation and independent evidence from enzyme activity assays, the isotopomer results from both GC-MS and Fourier Transform-Ion Cyclotron Resonance mass spectrometry (FT-ICR MS) indicate the lack of oxidatively functional TCA cycle and an incomplete pentose phosphate pathway. Results from this study suggest that fluxes through both pathways are limited to biosynthesis. The data also indicate that >80 percent of the lactate was converted to acetate and the reactions involved are the primary route of energy production (NAD(P)H and ATP production). Independent of the TCA cycle, direct cleavage of acetyl-CoA to CO and 5,10-methyl-THF also leads to production of NADH and ATP. Although the genome annotation implicates a ferredoxin-dependent oxoglutarate synthase, isotopic evidence does not support flux through this reaction in either the oxidative or reductive mode; therefore, the TCA cycle is incomplete. FT-ICR MS was used to locate the labeled carbon distribution in aspartate and glutamate and confirmed the presence of an atypical enzyme for citrate formation suggested in previous reports (the citrate synthesized by this enzyme is the isotopic antipode of the citrate synthesized by the (S)-citrate synthase). These findings enable a better understanding of the relation between genome annotation and actual metabolic pathways in D. vulgaris, and also demonstrate FT-ICR MS as a powerful tool for isotopomer analysis, overcoming problems in both GC-MS and NMR spectroscopy
Ron, Izhar; Zaltsman, Amalia; Kendler, Shai
2013-12-01
On-site identification of organic compounds in the presence of interfering materials using a field-portable attenuated total reflection Fourier transform infrared (ATR FT-IR) spectrometer is presented. Identification is based on an algorithm that compares the analyte's infrared absorption spectrum with the reference spectra. The comparison is performed at several predetermined frequencies, and a similarity value (distance) between the measured and the reference spectra is calculated either at each frequency individually, or, alternatively, the average distance for all frequencies is calculated. The examined frequencies are selected to give the best contrast between the target materials of interest. In this study, the algorithm was optimized to identify three common chemical warfare agents (CWAs): O-ethyl S-[2-(diisopropylamino)ethyl] methylphosphonothioic acid (VX), sarin (GB), and sulfur mustard (bis(2-chloroethyl) sulfide) (HD), in the presence of field-related interfering materials (fuels, water, and dust). Receiver operating characteristics analysis was performed in order to determine the probabilities for detection (PD) and for false alerts (PF). Challenging the algorithm with a set of data that contains mixtures of CWAs and interfering materials resulted in PD of 90% and PF of 0%, 0%, and 1% for VX, GB, and HD, respectively, using the average distance approach, which was found to be much more effective than analyzing each frequency individually. This finding was validated for all possible combinations of 2-7 peaks per material. It is suggested that this algorithm provides a reliable mean for the identification of a predetermined set of target analytes and interfering materials.
International Nuclear Information System (INIS)
Highlights: • Coumarins were used as new MALDI matrices. • Coumarins were used for MALDI-FT ICR MS detection of hydrophobic compounds. • DCA had improvement in detection sensitivity, stability, selectivity and reproducibility. • DCA was applied to sterols detection in yeast cells. - Abstract: Hydrophobic compounds with hydroxyl, aldehyde or ketone groups are generally difficult to detect using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), because these compounds have low proton affinity and are poorly ionized by MALDI. Herein, coumarins have been used as new matrices for MALDI-MS analysis of a variety of hydrophobic compounds with low ionization efficiency, including steroids, coenzyme Q10, a cyclic lipopeptide and cholesterol oleate. Five coumarins, including coumarin, umbelliferone, esculetin, 7-hydroxycoumarin-3-carboxylic acid (HCA) and 6,7-dihydroxycoumarin-3-carboxylic acid (DCA), were compared with the conventional matrices of 2,5-dihydroxybenzoic acid (DHB) and α-cyano-4-hydroxycinnamic acid (CHCA). Coumarins with hydroxyl or carboxylic acid groups enabled detection. Taking DCA as an example, this matrix proved to be superior to DHB or CHCA in detection sensitivity, stability, spot-to-spot and sample-to-sample reproducibility, and accuracy. DCA increased the stability of the target compounds and decreased the loss of water. The [M + Na]+ peaks were observed for all target compounds by adding NaCl as an additive, and the [M − H2O + H]+ and [M + H]+ peaks decreased. DCA was selected for the identification of sterols in yeast cells, and thirteen sterols were detected by Fourier transform ion cyclotron resonance (FT ICR) mass spectrometry. This work demonstrates the potential of DCA as a new matrix for detection of hydrophobic molecules by MALDI-MS and provides an alternative tool for screening sterols in antifungal research
Energy Technology Data Exchange (ETDEWEB)
Wang Hang; Wang Haoyang; Zhang Li; Zhang Jing [Shanghai Mass Spectrometry Center, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 200032 (China); Guo Yinlong, E-mail: ylguo@sioc.ac.cn [Shanghai Mass Spectrometry Center, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 200032 (China)
2011-03-25
Isotope-coded reagents have been developed for labeling of amino acids, phenols and fatty acids, but not for alcohols. In this work, a simple reaction based on direct N-alkylpyridinium isotope quaternization (NAPIQ) was developed for mild derivatization of cholesterol and fatty alcohols. Different from the conventional quaternary reagents with cations on themselves, two simple and charge-neutral reagents: pyridine and d{sub 5}-pyridine directly attached N-cationic tag onto the target compounds in the presence of trifluoromethanesulfonic anhydride (Tf{sub 2}O) without tedious sample preparation. The derivatization completed in 5 min and achieved charge labeling of the target compounds, which significantly improved the detection limits of analytes by 10{sup 3}-folds in further analysis by matrix-assisted laser desorption/ionization Fourier transform mass spectrometry (MALDI-FTMS). The use of commercially available d{sub 0}/d{sub 5}-pyridine pairs facilitated isotope-coded chemical derivatization and avoided the use of isotope-labeled internal standards; the excess pyridine did not affect the signals of analytes. Utility of the NAPIQ method was examined in the identification of cholesterol and fatty alcohols in small amount of human hair sample (<0.5 mg). The fluctuation of total cholesterol in human body was profiled during time by quantitatively comparing the different segments of a single strand of hair. This study combines the direct pyridinium quaternization with MALDI-FTMS, which offers a perspective and an alternative tool for the identification and quantification of substances in biological matrix by comparing d{sub 0}/d{sub 5} pairs, especially when isotope-labeled internal standards are unavailable.
Projective Fourier duality and Weyl quantization
Energy Technology Data Exchange (ETDEWEB)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs.
Learning DNF Expressions from Fourier Spectrum
Feldman, Vitaly
2012-01-01
Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a product distribution. Kalai, Samorodnitsky and Teng (2009) showed that in this setting a DNF expression can be efficiently approximated from its "heavy" low-degree Fourier coefficients alone. This is in contrast to previous approaches where boosting was used and thus Fourier coefficients of the target function modified by various distributions were needed. This property is crucial for learning of DNF expressions over smoothed product distributions, a learning model introduced by Kalai et al. (2009) and inspired by the seminal smoothed analysis model of Spielman and Teng (2001). We give a new, simple algorithm for approximating any polynomial-size DNF expression from its "heavy" low-degree Fourier coefficients alone. Our algorithm greatly simplifies the proof of learnability o...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Applying Quaternion Fourier Transforms for Enhancing Color Images
Directory of Open Access Journals (Sweden)
M.I. Khalil
2012-03-01
Full Text Available The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.
Fourier-Laguerre transform, convolution and wavelets on the ball
McEwen, J D
2013-01-01
We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as convolution with a shifted Dirac delta function. We review the exact Fourier-Laguerre wavelet transform on the ball, coined flaglets, and show that flaglets constitute a tight frame.
P. Neelakantan; S. Sharma; H. Shemesh; P.R. Wesselink
2015-01-01
Introduction There is a lack of evidence on the chemical interaction between sealers and dentin. The influence of irrigation on the chemical interaction between root canal sealers and dentin was analyzed by using Fourier transform infrared spectroscopy (FTIRS) and measurement of dislocation resistan
Kamleh, A.; Barrett, M. P.; Wildridge, D.; Burchmore, R. J. S.; Scheltema, R. A.; Watson, D. G.
2008-01-01
It was shown that coupling hydrophilic interaction chromatography (HILIC) to Orbitrap Fourier transform mass spectrometery (FT-MS) provided an excellent tool for metabolic profiling, principally due to rapid elution of lipids in advance of most metabolites entering the mass spectrometer. We used in
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...
Reconstruction in Fourier space
Burden, A.; Percival, W. J.; Howlett, C.
2015-10-01
We present a fast iterative fast Fourier transform (FFT) based reconstruction algorithm that allows for non-parallel redshift-space distortions (RSDs). We test our algorithm on both N-body dark matter simulations and mock distributions of galaxies designed to replicate galaxy survey conditions. We compare solenoidal and irrotational components of the redshift distortion and show that an approximation of this distortion leads to a better estimate of the real-space potential (and therefore faster convergence) than ignoring the RSD when estimating the displacement field. Our iterative reconstruction scheme converges in two iterations for the mock samples corresponding to Baryon Oscillation Spectroscopic Survey CMASS Data Release 11 when we start with an approximation of the RSD. The scheme takes six iterations when the initial estimate, measured from the redshift-space overdensity, has no RSD correction. Slower convergence would be expected for surveys covering a larger angle on the sky. We show that this FFT based method provides a better estimate of the real-space displacement field than a configuration space method that uses finite difference routines to compute the potential for the same grid resolution. Finally, we show that a lognormal transform of the overdensity, used as a proxy for the linear overdensity, is beneficial in estimating the full displacement field from a dense sample of tracers. However, the lognormal transform of the overdensity does not perform well when estimating the displacements from sparser simulations with a more realistic galaxy density.
Explicit Fourier wavefield operators
Ferguson, R. J.; Margrave, G. F.
2006-04-01
Explicit wavefield extrapolators are based on direct analytic mathematical formulae that express the output as an extrapolation operator acting on the input, while implicit methods usually require the calculation of the numerical inverse of a matrix to obtain the output. Typically, explicit methods are faster than implicit methods, and they often give more insight into the physics of the wave propagation, but they often suffer from instability. Four different explicit extrapolators based on Fourier theory are presented and analysed. They are: PS (ordinary phase shift), GPSPI (generalized phase shift plus interpolation), NSPS (non-stationary phase shift) and SNPS (symmetric non-stationary phase shift). A formal proof is given that NSPS in a direction orthogonal to the velocity gradient is the mathematical adjoint process to GPSPI in the opposite direction. This motivates the construction of SNPS that combines NSPS and GPSPI in a symmetric fashion. This symmetry (under interchange of input and output lateral coordinates) is required by reciprocity arguments. PS and SNPS are symmetric while NSPS and GPSPI are not. A numerical stability study using SVD (singular value decomposition) shows that all of these extrapolators can become unstable for strong lateral velocity gradients. Unstable operators allow amplitudes to grow non-physically in a recursion. Stability is enhanced by introducing a small (~3 per cent) imaginary component to the velocities. This causes a numerical attenuation that tends to stabilize the operators but does not address the cause of the instability. For the velocity model studied (a very challenging case) GPSPI and NSPS have exactly the same instability while SNPS is always more stable. Instability manifests in a complicated way as a function of extrapolation step size, frequency, velocity gradient, and strength of numerical attenuation. The SNPS operator can be stabilized over a wide range of conditions with considerably less attenuation than is
Vibration analysis of reciprocating cutter based on Fourier series%基于傅里叶级数的往复式切割器振动分析
Institute of Scientific and Technical Information of China (English)
严帅
2013-01-01
本文对曲柄连杆往复式切割器工作特性进行了分析，利用傅里叶级数将切割器周期激励分解为简谐收敛级数，以特征值为插值结点对傅里叶级数的待定系数进行了求解，并利用叠加原理求出切割器振动系统的稳态响应。%This paper analyzed the characteristics of the crank and connecting rod reciprocating cutter, decomposed the cutter periodic excitation into the harmonic convergenc series using the Fourier series, undetermined coefficients of Fourier series are solved with the eigenvalues for the interpolation nodes, and by using the principle of superposition to calculate the steady-state vibration response of system.
Hosono, Satsuki; Qi, Wei; Sato, Shun; Suzuki, Yo; Fujiwara, Masaru; Hiramatsu, Hiroyuki; Suzuki, Satoru; Abeygunawardhana, P. K. W.; Wada, Kenji; Nishiyama, Akira; Ishimaru, Ichiro
2015-03-01
For simultaneous measurement of multi-components on-site like factories, the ultra-compact (diameter: 9[mm], length: 45[mm], weight: 200[g]) one-shot ATR (Attenuated Total Reflection) Fourier spectroscopic imager was proposed. Because the proposed one-shot Fourier spectroscopic imaging is based on spatial-phase-shift interferometer, interferograms could be obtained with simple optical configurations. We introduced the transmission-type relativeinclined phase-shifter, that was constructed with a cuboid prism and a wedge prism, onto the optical Fourier transform plane of infinity corrected optical systems. And also, small light-sources and cameras in the mid-infrared light region, whose size are several millimeter on a side, are essential components for the ultra-compact spectroscopic configuration. We selected the Graphite light source (light source area: 1.7×1.7[mm], maker: Hawkeye technologies) whose radiation factor was high. Fortunately, in these days we could apply the cost-effective 2-dimensional light receiving device for smartphone (e.g. product name: LEPTON, maker: FLIR, price: around 400USD). In the case of alcoholic drinks factory, conventionally workers measure glucose and ethanol concentrations by bringing liquid solution back to laboratories every day. The high portable spectroscopy will make it possible to measure multi-components simultaneously on manufacturing scene. But we found experimentally that absorption spectrum of glucose and water and ethanol were overlapped each other in near infrared light region. But for mid-infrared light region, we could distinguish specific absorption peaks of glucose (@10.5[μm]) and ethanol (@11.5[μm]) independently from water absorption. We obtained standard curve between absorption (@9.6[μm]) and ethanol concentration with high correlation coefficient 0.98 successfully by ATR imaging-type 2-dimensional Fourier spectroscopy (wavelength resolution: 0.057[μm]) with the graphite light source (maker: Hawkeye
Institute of Scientific and Technical Information of China (English)
杨天鸣; 马雯婷; 付海燕; 郑岸冰; 吴燕
2012-01-01
采用粉末X-射线衍射法对7个不同厂家的银杏叶片进行分析,获得了各样品的粉末X-射线衍射Fourier指纹图谱.根据银杏叶提取物的粉末X-射线衍射Fourier图谱的几何拓扑图形和32个特征共有峰,研究了银杏叶片的粉末X-射线衍射Fourier指纹图谱的图形几何拓扑规律,并计算了其特征共有峰的比例,为银杏叶片的质量鉴定提供了参考依据.%Powder X-ray diffraction analysis was used to analyze tablets of Ginkgo biloba L. from different manufacturers. The powder X-ray diffraction Fourier fingerprint patterns of these samples were obtained. Based on the geometry topology of powder X-ray diffraction Fourier fingerprint pattern and 32 characteristic peaks of the extract of Ginkgo biloba L. , the geometry topology law of powder X-ray diffraction Fourier fingerprint pattern of the tablets of Ginkgo biloba L. was studied,and the proportions of characteristic peaks were calculated. It could be used as reference for the quality identification of the tablets of Ginkgo biloba L..
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Embolic Doppler ultrasound signal detection via fractional Fourier transform.
Gençer, Merve; Bilgin, Gökhan; Aydın, Nizamettin
2013-01-01
Computerized analysis of Doppler ultrasound signals can aid early detection of asymptomatic circulating emboli. For analysis, physicians use informative features extracted from Doppler ultrasound signals. Time -frequency analysis methods are useful tools to exploit the transient like signals such as Embolic signals. Detection of discriminative features would be the first step toward automated analysis of embolic Doppler ultrasound signals. The most problematic part of setting up emboli detection system is to differentiate embolic signals from confusing similar wave-like patterns such as Doppler speckle and artifacts caused by tissue movement, probe tapping, speaking etc. In this study, discrete version of fractional Fourier transform is presented as a solution in the detection of emboli in digitized Doppler ultrasound signals. An accurate set of parameters are extracted using short time Fourier transform and fractional Fourier transform and the results are compared to reveal detection quality. Experimental results prove the efficiency of fractional Fourier transform in which discriminative features becomes more evident.
Directory of Open Access Journals (Sweden)
Mariele Regina Pinheiro
2011-03-01
Full Text Available Este trabalho foi realizado utilizando dados coletados em uma Floresta de Transição, em uma área pertencente à Fazenda Maracaí no Noroeste de Sinop, MT, com dados micrometeorológicos obtidos com o sistema de correlação de vórtices turbulentos (Eddy Covarience instalado numa torre de 40 metros. Teve como objetivo principal estudar as potencialidades da análise de Fourier aplicada a dados de fluxo de Calor Latente (LE, Calor Sensível (H e Temperatura (T. Para os cálculos foram feitas médias de 3 em 3 horas para cada mês, ao longo do período de 1999 a 2005, para as variáveis estudadas. Os períodos dominantes encontrados foram de 24; 12; 4 e 3,4 horas. Os dois primeiros são atribuíveis ao movimento de rotação da Terra, ou seja, à periodicidade dia/noite. Quanto aos dois períodos menores, há indícios que estão relacionados com a dinâmica de abertura dos estômatos. Assim sendo, os resultados deste trabalho indicam que os fatores que influenciam predominantemente as variáveis microclimatológicas durante o dia (freqüências entre 10-5 a 10-4 Hz são a radiação solar e a dinâmica de abertura dos estômatos, um resultado que destaca as potencialidades da aplicação do método de Fourier no estudo da dinâmica de microclimas em ecossistemas.In this work, we employed data collected in a transition forest, on the Maracaí farm, northwest of Sinop, MT, Brazil. The data was obtained by the eddy covariance method, using equipment installed on a 42m high tower. Its main purpose was to study the potentialities of Fourier analysis applied to data of latent (H and sensible (Le heat flux and the air temperature (T. We investigated the main frequencies presented by the data, and obtained mean values for the variables corresponding to every 3 hours, between 1999 and 2005. The main periods obtained with the Fourier method were 24; 12; 4 and 3.4 hours. The first two are attributed to the solar radiation and to the Earth rotation. The
DEFF Research Database (Denmark)
Renfrow, MB; Mackay, CL; Chalmers, MJ;
2007-01-01
IgA nephropathy (IgAN) is the most common form of primary glomerulonephritis. In IgAN, IgA1 molecules with incompletely galactosylated O-linked glycans in the hinge region (HR) are present in mesangial immunodeposits and in circulating immune complexes. It is not known whether the galactose...... deficiency in IgA1 proteins occurs randomly or preferentially at specific sites. We have previously demonstrated the first direct localization of multiple O-glycosylation sites on a single IgA1 myeloma protein by use of activated ion-electron capture dissociation (AI-ECD) Fourier transform ion cyclotron...
Fourier transform resampling: Theory and application
International Nuclear Information System (INIS)
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)
Marr, Greg C.
2003-01-01
The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.
Fourier modal method and its applications in computational nanophotonics
Kim, Hwi
2012-01-01
Most available books on computational electrodynamics are focused on FDTD, FEM, or other specific technique developed in microwave engineering. In contrast, Fourier Modal Method and Its Applications in Computational Nanophotonics is a complete guide to the principles and detailed mathematics of the up-to-date Fourier modal method of optical analysis. It takes readers through the implementation of MATLAB(R) codes for practical modeling of well-known and promising nanophotonic structures. The authors also address the limitations of the Fourier modal method. Features Provides a comprehensive guid
Yang, Fan; Voelkel, Jacob E; Dearden, David V
2012-06-01
We demonstrate a technique for determining molecular collision cross sections via measuring the variation of Fourier transform ion cyclotron resonance (FTICR) line width with background damping gas pressure, under conditions where the length of the FTICR transient is pressure limited. Key features of our method include monoisotopic isolation of ions, the pulsed introduction of damping gas to a constant pressure using a pulsed leak valve, short excitation events to minimize collisions during the excitation, and proper choice of damping gas (Xe is superior to He). The measurements are reproducible within a few percent, which is sufficient for distinguishing between many structural possibilities and is comparable to the uncertainty in cross sections calculated from computed molecular structures. These techniques complement drift ion mobility measurements obtained on dedicated instruments. They do not require a specialized instrument, but should be easily performed on any FTICR mass spectrometer equipped with a pulsed leak valve.
Parametric Spectral Correlations of Disordered Systems in the Fourier Domain
Guarneri, I.; Zyczkowski, K.; Zakrzewski, J.; Molinari, L.; Casati, G.
1995-01-01
A Fourier analysis of parametric level dynamics for random matrices periodically depending on a phase is developed. We demonstrate both theoretically and numerically that under very general conditions the correlation $C(\\varphi )$ of level velocities is singular at $\\varphi =0$ for any symmetry class; the singularity is revealed by algebraic tails in Fourier transforms, and is milder, the stronger the level repulsion in the chosen ensemble. The singularity is strictly connected with the diver...
Institute of Scientific and Technical Information of China (English)
周业勤; 龙敏
2015-01-01
According to the properties of fractional Fourier transform, a kind of fractional Fourier transform image encryp-tion algorithm is analyzed. The key is not sensitive and the deciphering diagram is of great distortion, when with the naked eye on results chart to judge and extract the image data for comparison. Theoretical analysis and experimental results show that the algorithm is not sensitive to the key when the fractional Fourier transform is directly applied to image encryption. The introduction of RGB mapping to realize the cipher image display and transmission, result a great distortion in pixels.%从分数阶傅里叶变换的性质出发，对一类分数阶傅里叶变换图像加密算法进行分析。对原有算法结果图进行肉眼判断，提取图像中间结果数据进行对比分析，可知算法的密钥具有不敏感性，并且解密图具有很大失真。对分数傅里叶变换进行理论上的分析和讨论。分析及实验结果表明，直接使用分数阶傅里叶变换进行加密的算法对密钥并不敏感，存在安全隐患。为实现密文图像的显示和传输而引入的RGB映射将导致解密图像像素值失真。
Field Experiment and Result Analysis of Fourier Telescopy%傅里叶望远镜外场实验与结果分析
Institute of Scientific and Technical Information of China (English)
董磊; 刘欣悦; 陈宝刚; 林旭东; 卫沛峰
2011-01-01
为了分析外场环境因素对傅里叶望远镜成像质量的影响和验证成像过程不受下行链路大气扰动影响的特点,开展了傅里叶望远镜外场实验研究.外场实验在室内实验的发射光学系统的基础上增加了主镜、次镜和会聚透镜组对目标散射光进行3次会聚仿真实际系统的成像过程,同时将目标与主镜、主镜与次镜分别拉开100 m距离验证成像系统不受下行链路大气扰动影响的特点.实验利用胶片打印的2种不同的卫星图片作为目标,获得了Strehl值分别为0.44、0.39的无大气扰动的外场重构图像和Strehl值分别为0.43、0.38的含大气扰动的外场重构图像.通过比较外场重构图像与室内重构图像的Strehl值,得出发射光学系统中光束的振动对成像有较大影响.分析发现无大气扰动外场重构图像与含大气扰动外场重构图像的Strehl值相近,从而验证傅里叶望远镜成像过程不受下行链路大气扰动的影响.%In order to study effects of outdoor factors to Fourier telescopy imaging and validate properties of imaging immune to down-link atmospheric turbulence, outdoor experiments were developed. Under the ground of lab experiments, outdoor experiments added primary mirror, secondary mirror and condense lens to simulate the real system imaging. The distance between object and primary mirror and the distance between primary mirror and secondary mirror was put away 100m, separately, to validate the property of Fourier telescopy imaging immune to atmospheric turbulence. Using 2 different satellite films as objects, the outdoor reconstructed images were gotten with the Strehl value 0. 44 and 0. 39 without turbulence, separately, and Strehl value 0. 43 and 0. 38 with turbulence, separately. Compared the reconstructed images of outdoor with lab, the conclusion was gained that libration had obvious effect on imaging. The result that the Strehl value of outdoor imaging was similar to lab
Jung, In-Keun; Park, Sang-Chul; Bin, Sung-Ah; Roh, Young Sup; Lee, John Hwan; Kim, Boo-Min
2016-03-01
The Maillard reaction has been well researched and used in the food industry and the fields of environmental science and organic chemistry. Here, we induced the Maillard reaction inside human hair and analyzed its effects by using Fourier transform infrared spectroscopy with a focal-plane array (FTIR-FPA) detector. We used arginine (A), glycine (G), and D-xylose (X) to generate the Maillard reaction by dissolving them in purified water and heating it to 150 °C. This label-free process generated a complex compound (named AGX after its ingredients) with a monomer structure, which was determined by using nuclear magnetic resonance (NMR) and FTIR-FPA. This compound was stable in hair and substantially increased its tensile strength. To our knowledge, we are the first to report the formation of this monomer in human hair, and our study provides insights into a new method that could be used to improve the condition of damaged or aging hair. PMID:26905862
Kumar, Dinesh; Singh, Surjan; Rai, K. N.
2016-06-01
In this paper, the temperature distribution in a finite biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions is studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bio-heat transfer in biological tissues. The analytical solution obtained for all the three models using Laplace transform technique and results are compared. The effect of the variability of different parameters such as relaxation time, metabolic heat source, spatial heat source, different type boundary conditions on temperature distribution in different type of the tissues like muscle, tumor, fat, dermis and subcutaneous based on three models are analyzed and discussed in detail. The result obtained in three models is compared with experimental observation of Stolwijk and Hardy (Pflug Arch 291:129-162, 1966). It has been observe that the DPL bio-heat transfer model provides better result in comparison of other two models. The value of metabolic and spatial heat source in boundary condition of first, second and third kind for different type of thermal therapies are evaluated.
Quinten, M.; Houta, F.; Fries, T.
2015-06-01
Thin film thickness determination with a reflectometer suffers from two problems. One problem is the leakage in the Fast Fourier Transform caused by the fact that the two variables wavenumber 1/λ and optical thickness nṡd are not really independent, since the refractive index n of the film material itself depends upon the wavenumber. This causes uncertainties in the thickness determination in the order of up to 5% for highly refractive materials like semiconductors. We present a simple but effective improvement of this contribution of the leakage that reduces the uncertainty to less than 2% for highly refractive materials. Another problem that mainly affects thin films below about 2 μm arises if one uses measuring heads collimators or even microscope headers to obtain high lateral resolutions in the thickness determination. The use of a header introduces angles of incidence different from the default angle α = 0° in reflectometry. Then, the measured reflectance becomes polarization-dependent and the angle must be explicitly considered in the evaluation algorithm. For a microscope header however, all angles between 0° and the angle of aperture must be considered. We will present a solution that allows to reduce the work for each header on taking into account the polarization of the reflected light and a corresponding effective angle αeff.
Walker, Amanda M; Yu, Peiqiang; Christensen, Colleen R; Christensen, David A; McKinnon, John J
2009-08-12
The objectives of this study were to use Fourier transform infrared microspectroscopy (FTIRM) to determine structural makeup (features) of cereal grain endosperm tissue and to reveal and identify differences in protein and carbohydrate structural makeup between different cereal types (corn vs barley) and between different varieties within a grain (barley CDC Bold, CDC Dolly, Harrington, and Valier). Another objective was to investigate how these structural features relate to rumen degradation kinetics. The items assessed included (1) structural differences in protein amide I to nonstructural carbohydrate (NSC, starch) intensity and ratio within cellular dimensions; (2) molecular structural differences in the secondary structure profile of protein, alpha-helix, beta-sheet, and their ratio; (3) structural differences in NSC to amide I ratio profile. From the results, it was observed that (1) comparison between grain types [corn (cv. Pioneer 39P78) vs barley (cv. Harrington)] showed significant differences in structural makeup in terms of NSC, amide I to NSC ratio, and rumen degradation kinetics (degradation ratio, effective degradability of dry matter, protein and NSC) (P makeup in terms of amide I, NSC, amide I to NSC ratio, alpha-helix and beta-sheet protein structures, and rumen degradation kinetics (effective degradability of dry matter, protein, and NSC) (P makeup differences between cereal types and between different varieties within a type of grain could be revealed. These structural makeup differences were related to the rate and extent of rumen degradation.
Energy Technology Data Exchange (ETDEWEB)
Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan,Richard; Hazen, Terry C.; Keasling, Jay D.
2007-03-15
Flux distribution in central metabolic pathways ofDesulfovibrio vulgaris Hildenborough was examined using 13C tracerexperiments. Consistent with the current genome annotation andindependent evidence from enzyme activity assays, the isotopomer resultsfrom both GC-MS and Fourier Transform-Ion Cyclotron Resonance massspectrometry (FT-ICR MS) indicate the lack of oxidatively functional TCAcycle and an incomplete pentose phosphate pathway. Results from thisstudy suggest that fluxes through both pathways are limited tobiosynthesis. The data also indicate that>80 percent of the lactatewas converted to acetate and the reactions involved are the primary routeof energy production (NAD(P)H and ATP production). Independent of the TCAcycle, direct cleavage of acetyl-CoA to CO and 5,10-methyl-THF also leadsto production of NADH and ATP. Although the genome annotation implicatesa ferredoxin-dependentoxoglutarate synthase, isotopic evidence does notsupport flux through this reaction in either the oxidative or reductivemode; therefore, the TCA cycle is incomplete. FT-ICR MS was used tolocate the labeled carbon distribution in aspartate and glutamate andconfirmed the presence of an atypical enzyme for citrate formationsuggested in previous reports (the citrate synthesized by this enzyme isthe isotopic antipode of the citrate synthesized by the (S)-citratesynthase). These findings enable a better understanding of the relationbetween genome annotation and actual metabolic pathways in D. vulgaris,and also demonstrate FT-ICR MS as a powerful tool for isotopomeranalysis, overcoming problems in both GC-MS and NMRspectroscopy.
Zumbühl, Stefan; Scherrer, Nadim C; Eggenberger, Urs
2014-01-01
The interpretation of standard Fourier transform infrared spectra (FT-IR) on oil-based paint samples often suffers from interfering bands of the different compounds, namely, binder, oxidative aging products, carboxylates formed during aging, and several pigments and fillers. The distinction of the aging products such as ketone and carboxylic acid functional groups pose the next problem, as these interfere with the triglyceride esters of the oil. A sample preparation and derivatization technique using gaseous sulfur tetrafluoride (SF4), was thus developed with the aim to discriminate overlapping signals and achieve a signal enhancement on superposed compounds. Of particular interest in this context is the signal elimination of the broad carboxylate bands of the typical reaction products developing during the aging processes in oil-based paints, as well as signal interference originating from several typical pigments in this spectral range. Furthermore, it is possible to distinguish the different carbonyl-containing functional groups upon selective alteration. The derivatization treatment can be applied to both microsamples and polished cross sections. It increases the selectivity of the infrared spectroscopy technique in a fundamental manner and permits the identification and two-dimensional (2D) localization of binder components in aged paint samples at the micrometer scale. The combination of SF4 derivatization with high-resolution 2D FT-IR focal plane array (FPA) imaging delivers considerable advances to the study of micro-morphological processes involving organic compounds.
Fourier spectra from exoplanets with polar caps and ocean glint
Visser, P M
2015-01-01
The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coeffici...
Methods of theme presentation "The Fourier transform of impulse functions"
Directory of Open Access Journals (Sweden)
Faniya Ahmetova
2016-09-01
Full Text Available The paper considers the Fourier transform of impulse functions, which is the mathematical basis of the tasks associated with the theory of reception and signal conversion in optoelectronic system. The method of calculating of two functions convolution, its Fourier image and the image of the Fourier-Bessel axisymmetric functions are demonstrated in details. A table, which summarizes the analytical expression for the shifted impulse functions and records their Fourier transforms, is provided. A wide range of examples of solving tasks, containing the graphic illustration, is analyzed. A structured approach to the presentation of the material, which combines basic theoretical information and analysis of typical tasks, will help second-year students of optoelectronic specialty in their independent work and homework.
Fourier transform infrared spectroscopy for Mars science
Anderson, Mark S.; Andringa, Jason M.; Carlson, Robert W.; Conrad, Pamela; Hartford, Wayne; Shafer, Michael; Soto, Alejandro; Tsapin, Alexandre I.; Dybwad, Jens Peter; Wadsworth, Winthrop; Hand, Kevin
2005-03-01
Presented here is a Fourier transform infrared spectrometer (FTIR) for field studies that serves as a prototype for future Mars science applications. Infrared spectroscopy provides chemical information that is relevant to a number of Mars science questions. This includes mineralogical analysis, nitrogen compound recognition, truth testing of remote sensing measurements, and the ability to detect organic compounds. The challenges and scientific opportunities are given for the in situ FTIR analysis of Mars soil and rock samples. Various FTIR sampling techniques are assessed and compared to other analytical instrumentation. The prototype instrument presented is capable of providing field analysis in a Mars analog Antarctic environment. FTIR analysis of endolithic microbial communities in Antarctic rocks and a Mars meteor are given as analytical examples.
Picollo, Marcello; Bartolozzi, Giovanni; Cucci, Costanza; Galeotti, Monica; Marchiafava, Veronica; Pizzo, Benedetto
2014-01-01
This study was completed within the framework of two research projects dealing with the conservation of contemporary artworks. The first is the Seventh Framework Project (FP7) of the European Union, Preservation of Plastic ARTefacts in Museum Collections (POPART), spanning years 2008-2012, and the second is the Italian project funded by the Tuscan Region, Preventive Conservation of Contemporary Art (Conservazione Preventiva dell'Arte Contemporanea (COPAC)), spanning 2011-2013. Both of these programs pointed out the great importance of having noninvasive and portable analytical techniques that can be used to investigate and characterize modern and contemporary artworks, especially those consisting of synthetic polymers. Indeed, despite the extensive presence of plastics in museum collections, there is still a lack of analytical tools for identifying, characterizing, and setting up adequate conservation strategies for these materials. In this work, the potentials of in situ and noninvasive Fourier transform infrared (FT-IR) spectroscopy, implemented by means of portable devices that operate in reflection mode, are investigated with a view to applying the results in large-scale surveys of plastic objects in museums. To this end, an essential prerequisite are the reliability of spectral data acquired in situ and the availability of spectral databases acquired from reference materials. A collection of polymeric samples, which are available commercially as ResinKit, was analyzed to create a reference spectral archive. All the spectra were recorded using three FT-IR configurations: transmission (trans), attenuated total reflection (ATR), and total reflection (TR). A comparative evaluation of the data acquired using the three instrumental configurations is presented, together with an evaluation of the similarity percentages and a discussion of the critical cases.
Motion-corrected Fourier ptychography
Bian, Liheng; Guo, Kaikai; Suo, Jinli; Yang, Changhuei; Chen, Feng; Dai, Qionghai
2016-01-01
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample's Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released...
Slice Fourier transform and convolutions
Cnudde, Lander; De Bie, Hendrik
2015-01-01
Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel function of this integral transform is constructed using the Mehler formula. An explicit expression for the integral transform is obtained and allows for the study of its properties. In the second part, two kinds of corresponding convolutions are examined:...
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
Institute of Scientific and Technical Information of China (English)
王祝文; 向旻; 刘菁华; 王晓丽; 张雪昂; 杨闯
2012-01-01
目前,阵列声波测井信号处理大多在时间域或频率域中进行.但是,单纯的时间域或频率域方法有很大的局限性.为了打破这些局限性,笔者将分数阶Fourier变换方法用于阵列声波测井信号的分析之中,研究了不同性质储集层中信号幅度随分数阶Fourier变换阶数变化的规律.实验结果表明:在干层,幅度呈“1”型分布；在水层,幅度呈“Y”型分布,“Y”的两支开口较小,在阶数大于0.3的区域中,幅度较大；在油层,幅度呈“Y”型分布,“Y”的两支开口较大,在阶数大于0.6的区域中,幅度较大.因此,分数阶Fourier变换在提取阵列声波测井蕴含的储集层流体性质信息方面具有很好的前景.%As we knew, most of the process techniques for array acoustic logging data still use the analysis methods only in either time domain or frequency domain, but these methods all have obvious limitation for signal analysis. In order to break these limitations, the authors used the fratal Fourier for analysing the array acoustic logging signals and researching the law of signal amplitude variation with the order of the fratal Fourier transform variation in different kinds of reservoirs. As the results, in the dry formation, amplitude shows "1" type distribution; In water formation, amplitude shows "Y" type distribution, two branch of "Y" open narrow and in area of order greater than 0. 3, amplitude is larger; In oil formation, amplitude shows "Y" type distribution, two branch of "Y" open wide and in area of order greater than 0. 6, amplitude is larger. So the fratal Fourier transform have very good prospect for extracting the reservoir liquid properties information embedded in the array acoustic logging data.
Logarithm of the Discrete Fourier Transform
Directory of Open Access Journals (Sweden)
Michael Aristidou
2007-01-01
Full Text Available The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.
Logarithm of the Discrete Fourier Transform
Michael Aristidou; Jason Hanson
2007-01-01
The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.
Aperture scanning Fourier ptychographic microscopy
Ou, Xiaoze; Chung, Jaebum; Horstmeyer, Roarke; Yang, Changhuei
2016-01-01
Fourier ptychographic microscopy (FPM) is implemented through aperture scanning by an LCOS spatial light modulator at the back focal plane of the objective lens. This FPM configuration enables the capturing of the complex scattered field for a 3D sample both in the transmissive mode and the reflective mode. We further show that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density. This implementation expands the scope of application for FPM and can be beneficial for areas such as tissue imaging and wafer inspection. PMID:27570705
Fourier-transform optical microsystems
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.
JPL Fourier transform ultraviolet spectrometer
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Novel Micro Fourier Transform Spectrometers
Institute of Scientific and Technical Information of China (English)
KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun
2008-01-01
The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.
Fourier-Transform Infrared Spectrometer
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
Compact Fourier transform spectrometer without moving parts
Huang, Chu-Yu; Estroff, B.; Wang, Wei-Chih
2012-04-01
Fourier transform spectroscopy (FTS) is a potent analytical tool for chemical and biological analysis, but is limited by system size, expense, and robustness. To make FTS technology more accessible, we present a compact, inexpensive FTS system based on a novel liquid crystal (LC) interferometer. This design is unique because the optical path difference (OPD) is controlled by voltage applied to the LC cell. The OPD is further improved by reflecting the polarized incident light through the LC several times before reaching the second polarizer and measurement. This paper presents the theoretical model and numerical simulations for the liquid crystal Fourier transform spectrometer (LCFTS), and experimental results from the prototype. Based on the experimental results, the LCFTS performs in accordance with the theoretical predictions, achieving a maximum OPD of 210μm and a resolution of 1nm at a wavelength of 630nm. The instrumental response refresh rate is just under 1 second. Absorbance measurements were conducted for single and mixed solutions of deionized water and isopropyl alcohol, demonstrating agreement with a commercial system and literature values. We also present the LCFTS transmission spectra for varying concentrations of potassium permanganate to show system sensitivity.
Faye; Kou; Farrenq; Guelachvili
1999-10-01
The extension of high-resolution observation of the electronic emission spectrum of (14)N(2) toward the infrared domain is presented. To date, rotational analysis of the widely investigated spectrum of the N(2) molecule was done in a spectral domain ranging from 2500 cm(-1) to the UV. We have recorded for the first time the infrared part of the (14)N(2) spectrum from 1250 to 2250 cm(-1), using the Fourier transform spectrometer of Laboratoire de Photophysique Moléculaire (LPPM) at an unapodized resolution of 0.0043 cm(-1). A complete rotational analysis is performed for the (1 --> 0), (2 --> 1), (0 <-- 1), (1 <-- 2) bands of the B(3)Pi(g)-W(3)Delta(u) system, not included in any previous analysis. Spectroscopic parameters for the v = 0, v = 1, v = 2 levels of the B(3)Pi(g) and the W(3)Delta(u) states, consistent with those previously reported but with improved accuracy, are obtained from the experimental wavenumbers by a nonlinear least-squares procedure. Copyright 1999 Academic Press.
Faye, A.; Kou, Q.; Farrenq, R.; Guelachvili, G.
1999-10-01
The extension of high-resolution observation of the electronic emission spectrum of 14N2 toward the infrared domain is presented. To date, rotational analysis of the widely investigated spectrum of the N2 molecule was done in a spectral domain ranging from 2500 cm-1 to the UV. We have recorded for the first time the infrared part of the 14N2 spectrum from 1250 to 2250 cm-1, using the Fourier transform spectrometer of Laboratoire de Photophysique Moléculaire (LPPM) at an unapodized resolution of 0.0043 cm-1. A complete rotational analysis is performed for the (1 → 0), (2 → 1), (0 ← 1), (1 ← 2) bands of the B3Πg-W3Δu system, not included in any previous analysis. Spectroscopic parameters for the v = 0, v = 1, v = 2 levels of the B3Πg and the W3Δu states, consistent with those previously reported but with improved accuracy, are obtained from the experimental wavenumbers by a nonlinear least-squares procedure.
Carlesi, Serena; Ricci, Marilena; Cucci, Costanza; La Nasa, Jacopo; Lofrumento, Cristiana; Picollo, Marcello; Becucci, Maurizio
2015-07-01
This work explores the application of chemometric techniques to the analysis of lipidic paint binders (i.e., drying oils) by means of Raman and near-infrared spectroscopy. These binders have been widely used by artists throughout history, both individually and in mixtures. We prepared various model samples of the pure binders (linseed, poppy seed, and walnut oils) obtained from different manufacturers. These model samples were left to dry and then characterized by Raman and reflectance near-infrared spectroscopy. Multivariate analysis was performed by applying principal component analysis (PCA) on the first derivative of the corresponding Raman spectra (1800-750 cm(-1)), near-infrared spectra (6000-3900 cm(-1)), and their combination to test whether spectral differences could enable samples to be distinguished on the basis of their composition. The vibrational bands we found most useful to discriminate between the different products we studied are the fundamental ν(C=C) stretching and methylenic stretching and bending combination bands. The results of the multivariate analysis demonstrated the potential of chemometric approaches for characterizing and identifying drying oils, and also for gaining a deeper insight into the aging process. Comparison with high-performance liquid chromatography data was conducted to check the PCA results. PMID:26036244
Institute of Scientific and Technical Information of China (English)
任重; 董明; 吴立远; 任明; 司文荣
2013-01-01
为了分析冲击电压下GIS腔体内局部放电信号的特征,将一种时频变换理论即二次型短时傅立叶变换应用于局放脉冲序列的分析,得到信号在时频平面的能量分布和变化规律.通过对含噪声局放脉冲序列时频变换的仿真研究,有效地提取了放电脉冲.另外,在实验室对220 kV GIS母线段进行了尖刺缺陷模型的安装和冲击耐压下局放检测,对实测数据进行了时频分析,验证了二次型短时傅里叶变换在局放信号处理中的有效性,得到了信号时频谱图在不同长度窗函数处理下的变化规律.%In order to analyze the characteristics of signals of partial discharge (PD) in GIS under the impulse voltage, a kind of time-frequency transform theory called the quadratic short-time Fourier transform was applied in analysis of the PD pulse sequence to get the distribution of energy and variation law of signals in the time-frequency plane. In this research, the time-frequency transform of a kind of typical PD pulse sequence containing noise was simulated, which showed that PD pulse could be extracted efficiently. Besides, a kind of spikes defect model was installed in the bus segment of 220 kV GIS and the PD of GIS under impulse voltage was detected. By time-frequency analysis of experiment data, it can be found that the theory of quadratic short-time Fourier transform can be applied in analysis of PD signals efficiently and the variation law of time-frequency spectrogram was affected by the length of window function.
American Society for Testing and Materials. Philadelphia
2004-01-01
1.1 This test method covers determining the concentrations of refrigerant-114, other carbon-containing and fluorine-containing compounds, hydrocarbons, and partially or completely substituted halohydrocarbons that may be impurities in uranium hexafluoride. The two options are outlined for this test method. They are designated as Part A and Part B. 1.1.1 To provide instructions for performing Fourier-Transform Infrared (FTIR) spectroscopic analysis for the possible presence of Refrigerant-114 impurity in a gaseous sample of uranium hexafluoride, collected in a "2S" container or equivalent at room temperature. The all gas procedure applies to the analysis of possible Refrigerant-114 impurity in uranium hexafluoride, and to the gas manifold system used for FTIR applications. The pressure and temperatures must be controlled to maintain a gaseous sample. The concentration units are in mole percent. This is Part A. 1.2 Part B involves a high pressure liquid sample of uranium hexafluoride. This method can be appli...
Triebel, S; Sproll, C; Reusch, H; Godelmann, R; Lachenmeier, D W
2007-09-01
So-called energy drinks with very high amounts of taurine (up to 4000 mg/l are usually granted by certificates of exemption) are increasingly offered on the market. To control the currently valid maximum limits of taurine in energy drinks, a simple and rapid analytical method is required to use it routinely in food monitoring. In this article, we describe a fast and efficient analytical method (FTIR-spectroscopy) that is able to reliably characterize and quantify taurine in energy drinks. The determination of taurine in energy drinks by FTIR was compared with amino acid analyzer (ion chromatography with ninhydrin-postcolumn derivatization). During analysis of 80 energy drinks, a median concentration of 3180 mg/l was found in alcohol-free products, 314 mg/l in energy drinks with spirits, 151 mg/l in beer-containing drinks and 305 mg/l in beverages with wine. Risk analysis of these products is difficult due to the lack of valid toxicological information about taurine and its interferences with other ingredients of energy drinks (for example caffeine and alcohol). So far, the high taurine concentrations of energy drinks in comparison to the rest of the diet are scientifically doubtful, as the advertised physiological effects and the value of supplemented taurine are unproven. PMID:17051421
An introduction to non-harmonic Fourier series
Young, Robert M
2001-01-01
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
Dynamics of Fourier domain mode-locked lasers.
Slepneva, S; Kelleher, B; O'Shaughnessy, B; Hegarty, S P; Vladimirov, A G; Huyet, G
2013-08-12
An analysis of the dynamical features in the output of a Fourier Domain Mode Locked laser is presented. An experimental study of the wavelength sweep-direction asymmetry in the output of such devices is undertaken. A mathematical model based on a set of delay differential equations is developed and shown to agree well with experiment. PMID:23938841
The Fourier Transform on Quantum Euclidean Space
Directory of Open Access Journals (Sweden)
Kevin Coulembier
2011-05-01
Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
The multiple-parameter fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
LANG Jun; TAO Ran; RAN QiWen; WANG Yue
2008-01-01
The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in frac-tional operator. A new source for the multiplicity of the weight-type fractional Fou-rier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters MN,∈ZM. Therefore a generalized frac-tional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
On Fourier Series of Fuzzy-Valued Functions
Directory of Open Access Journals (Sweden)
Uğur Kadak
2014-01-01
Full Text Available Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh’s Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We derive uniform convergence of a fuzzy-valued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist.
Note on Redshift Distortion in Fourier Space
Institute of Scientific and Technical Information of China (English)
Yan-Chuan Cai; Jun Pan
2007-01-01
We explore features of redshift distortion in Fourier analysis of N-body simulations.The phases of the Fourier modes of dark matter density fluctuation are generally shifted by the peculiar motion along the line of sight, the induced phase shift is stochastic and has a probability distribution function (PDF) that is symmetric about the peak at zero shift and whose exact shape depends on the wave vector, except on very large scales where phases are invariant by linear perturbation theory. Analysis of the phase shifts motivates our phenomenological models for the bispectrum in redshift space. Comparison with simulations shows that our toy models are very successful in modeling bispectrum of equilateral and isosceles triangles at large scales. In the second part we compare the monopole of the power spectrum and bispectrum in the radial and plane-parallel distortion to test the plane-parallel approximation.We confirm the results of Scoccimarro that difference of power spectrum is at the level of 10%, and, in the reduced bispectrum, the difference is as small as a few percent. However, on the plane perpendicular to the line of sight of kz = 0, the difference in power spectrum between the radial and plane-parallel approximation can be more than ～ 10%, and even worse on very small scales. Such difference is prominent for bispectrum, especially for configurations of tilted triangles. Non-Gaussian signals under the radial distortion on small scales are systematically biased downside than are in the plane-parallel approximation, with amplitudes depending on the opening angle of the sample point to the observer. This observation gives warning to the practice of using the power spectrum and bispectrum measured on the kz = 0 plane as estimates of the real space statistics.
Energy Technology Data Exchange (ETDEWEB)
Lee, Chong-Yong; Fleming, Barry D.; Zhang Jie; Guo Sixuan [School of Chemistry, Monash University, Clayton, Victoria 3800 (Australia); Elton, Darrell M. [Department of Electronic Engineering, La Trobe University, Bundoora, Victoria 3086 (Australia); Bond, Alan M., E-mail: alan.bond@sci.monash.edu.au [School of Chemistry, Monash University, Clayton, Victoria 3800 (Australia)
2009-10-12
A systematic approach to quantifying the electrode kinetics of surface-confined proteins and identifying the impact of surface heterogeneity is presented. The evaluation approach is based on analysis of individual harmonics derived from Fourier transformed large-amplitude ac voltammetry, and their peak current magnitude, I{sub p}(n{omega}t) versus frequency, f, relationships. Effectively, variability in the time-scale of each harmonic is expected, and advantage is taken of the fact that each individual harmonic displays a different level of sensitivity with respect to the kinetic evaluation. The data strategy protocols have been examined for the azurin Cu(II)/Cu(I) process when this metalloprotein is immobilized on gold electrodes modified alkanethiols having different chain lengths, using both pure and mixed thiol systems. I{sub p}(n{omega}t) versusf relationships also offer the advantage of the ability to detect and allow for the ohmic IR{sub u} drop effect and allow analyses that are independent of protein surface coverage. Estimation of an electron transfer rate is achievable from this form of analysis. However, experimentally observed waveshapes for each individual harmonic are consistently broader than that deduced theoretically on the basis of their rate constants because of kinetic and/or thermodynamic dispersion. In the mixed thiol systems, and with use of the ac method, kinetic discrimination is achieved for fast processes. This systematic study based on a model protein indicates that a more comprehensive level of evaluation of electrode kinetics can be derived from analysis of the ac harmonics available in large-amplitude ac voltammetry, by initially using I{sub p}(n{omega}t)-f data to evaluate the electrode kinetics followed by waveshape analysis to detect heterogeneity effects that give rise to kinetic or thermodynamic dispersion.
Guo, Tao; Feng, Wei-Hong; Liu, Xiao-Qian; Gao, Hui-Min; Wang, Zhi-Min; Gao, Liang-Liang
2016-05-10
The granule of Chinese medicine (GCM) is prepared by water-soluble extract of single yinpian (WESY) of herbal medicine, and used as a drug ingredient for clinical formulation. The WESY content or corresponding yinpian amount is the most important parameter in evaluating the quality of GCM. Low WESY content reflects poor GCM. Classical quantitative methods, such as HPLC, cannot fully detect the adulteration by adding characteristic ingredients and less WESY production. GCM is composed of WESY and a high content of specific excipient. The WESY content in the GCM may be indirectly analyzed using mid-infrared spectroscopy (MIR). In this paper, a quantitative method to evaluate the quality of Danshen (Salvia miltiorrhiza) granule (DG) was developed using MIR combined with chemometrics. Appropriate characteristic quantitative regions (CQR) were extracted by selecting the spectral regions corresponding to altered excipient content in DG. The best model of dextrin content determination in DG with low RMSEC of 1.97, low RMSEP of 2.07, and excellent RPD of 5.03 (>5.0) was obtained using partial least-squares (PLS) regression, and validated using accepted values of precision and recovery. The results suggest that FT-MIR combined with PLS is a rapid and valuable analytical tool to determine the WESY in DG based on excipient content. The model enabling indirect calculation of WESY content in GCM represents a reference standard for rapid analysis of other WESYs in GCM industry. PMID:26859611
Energy Technology Data Exchange (ETDEWEB)
Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan,Richard; Hazen, Terry C.; Keasling, Jay D.
2006-07-11
It has been proposed that during growth under anaerobic oroxygen-limited conditions Shewanella oneidensis MR-1 uses theserine-isocitrate lyase pathway common to many methylotrophic anaerobes,in which formaldehyde produced from pyruvate is condensed with glycine toform serine. The serine is then transformed through hydroxypyruvate andglycerate to enter central metabolism at phosphoglycerate. To examine itsuse of the serine-isocitrate lyase pathway under anaerobic conditions, wegrew S. oneidensis MR-1 on [1-13C]lactate as the sole carbon source witheither trimethylamine N-oxide (TMAO) or fumarate as an electron acceptor.Analysis of cellular metabolites indicates that a large percentage(>75 percent) of lactate was partially oxidized to either acetate orpyruvate. The 13C isotope distributions in amino acids and other keymetabolites indicate that, under anaerobic conditions, a complete serinepathway is not present, and lactate is oxidized via a highly reversibleserine degradation pathway. The labeling data also suggest significantactivity in the anaplerotic (malic enzyme and phosphoenolpyruvatecarboxylase) and glyoxylate shunt (isocitrate lyase and malate synthase)reactions. Although the tricarboxylic acid (TCA) cycle is often observedto be incomplete in many other anaerobes (absence of 2-oxoglutaratedehydrogenase activity), isotopic labeling supports the existence of acomplete TCA cycle in S. oneidensis MR-1 under TMAO reductioncondition.
Zhao, Gong-Bo; Saito, Shun; Wang, Dandan; Ross, Ashley J; Beutler, Florian; Grieb, Jan Niklas; Chuang, Chia-Hsun; Kitaura, Francisco-Shu; Rodriguez-Torres, Sergio; Percival, Will J; Brownstein, Joel R; Cuesta, Antonio J; Eisenstein, Daniel J; Gil-Marín, Héctor; Kneib, Jean-Paul; Nichol, Robert C; Olmstead, Matthew D; Prada, Francisco; Rossi, Graziano; Salazar-Albornoz, Salvador; Samushia, Lado; Sánchez, Ariel G; Thomas, Daniel; Tinker, Jeremy L; Tojeiro, Rita; Weinberg, David H; Zhu, Fangzhou
2016-01-01
We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release (DR)12 covering the redshift range of $0.20
Institute of Scientific and Technical Information of China (English)
蒋方明; 刘登瀛; 蔡睿贤
2001-01-01
This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the nonFourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.``
Ariosa, D.; Berger, H.; Schmauder, T.; Pavuna, D.; Margaritondo, G.; Christensen, S.; Kelley, R. J.; Onellion, M.
2001-04-01
We report on a distortion of Bi 2Sr 2Ca nCu n+1O 6+2n+x ( n=0,1) single crystals, perpendicular to the CuO 2 planes (the c-axis), for non-stoichiometric samples containing an excess of Bi. The distortion involves two parts: (a) symmetric displacements in the SrO and CuO 2 planes along the c-axis, and (b) an antisymmetric longitudinal compressive wave. The latter is revealed by observing odd harmonics in the X-ray diffraction (XRD) data. Such odd harmonics are typically extinguished for the I4/mmm space group of the exact stoichiometric phase. The antisymmetric compressive wave is reported for both BSCCO-2201 and BSCCO-2212 Bi excess samples, as well as for La-doped BSCCO-2201 samples. We have performed XRD model calculations for all samples studied, combined with Fourier analysis of the periodic c-axis modulation. The antisymmetric compressive wave was proven by reconstructing the atomic position profile from the intensity of odd XRD peaks caused by this commensurate modulation. Our results indicate preferential ordered substitution of Bi ions on nominally Sr ion positions. We also discuss implications for oxygen mobility, reversible sample doping, and electronic properties.
An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.
Eastman, M. P.; And Others
1986-01-01
Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.
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
Matrix Fourier transform with discontinuous coefficients
Yaremko, O.; Zhuravleva, E.
2013-01-01
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of mathematical physics.Multidimensional integral transformations with non-separated variables for problems with discontinuous coefficients are constructed in this work. The coefficient discontinuities focused on the of parallel hyperplanes. In this work explicit formul...
1-Convergence of Complex Double Fourier Series
Indian Academy of Sciences (India)
Kulwinder Kaur; S S Bhatia; Babu Ram
2003-11-01
It is proved that the complex double Fourier series of an integrable function (, ) with coefficients {} satisfying certain conditions, will converge in 1-norm. The conditions used here are the combinations of Tauberian condition of Hardy–Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.
On the $q$-Bessel Fourier transform
Dhaouadi, Lazhar
2013-01-01
In this work, we are interested by the $q$-Bessel Fourier transform with a new approach. Many important results of this $q$-integral transform are proved with a new constructive demonstrations and we establish in particular the associated $q$-Fourier-Neumen expansion which involves the $q$-little Jacobi polynomials.
Product Theorem for Quaternion Fourier Transform
Bahri, Mawardi
2014-01-01
In this paper we present the generalized convolution and correlation for the two-dim ensional discrete quaternion Fourier transform (DQFT). We provide several new properties of the generalizations. There results can be considered as the extension of correlation and convolution properties of real and complex Fourier transform to the DQFT domain.
Two modified discrete chirp Fourier transform schemes
Institute of Scientific and Technical Information of China (English)
樊平毅; 夏香根
2001-01-01
This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.
The invariance of current energy fourier spectrum of discrete real signals on finite intervals
Directory of Open Access Journals (Sweden)
Ponomarev V. A.
2014-02-01
Full Text Available Digital spectral analysis of signals based on DFT has a number of advantages. However, the transition from analog to digital methods and techniques is accompanied by a number of undesirable effects. Signals in each subject area usually have their own specifics. Therefore, it is necessary to study these effects in applications of spectral Fourier analysis. Such research is important for three reasons. Firstly, DFT properties are accurate, have their own specificity and significantly differ from the properties of the Fourier transform of continuous signals. Secondly, signals in each subject area have their own specificity. Thirdly, researchers often have prevailing knowledge in some particular domain, rather than in the field of digital signal processing techniques. As a result, in practice, some of the processes and effects arising in applications of digital spectral analysis, unfortunately, escape the attention of researchers which can result in erroneous conclusions. The paper deals with the problems of measuring Fourier spectrum of signals in the base of discrete exponential functions. Methods and algorithms of sliding measurements of energy Fourier spectrum of signals on finite intervals were described. The invariance of current energy Fourier spectrum to moving discrete real signals (which are not periodic were investigated. The authors identify a new effect of digital spectral analysis — the effect of non-invariance of the current energy Fourier spectrum. Theoretical and practical results of analysis of invariance of current energy Fourier spectrum of tonal components are shown. The conducted studies allow us: — to see in a new light the measurement results on finite intervals of current Fourier spectrum and the current energy Fourier spectra of signals; give a numerical estimate of the non-invariance of the current energy Fourier spectrum of real tonal components. — to increase the effectiveness of digital spectral analysis in its
Fourier transform approach in modulation technique of experimental measurements.
Khazimullin, M V; Lebedev, Yu A
2010-04-01
An application of Fourier transform approach in modulation technique of experimental studies is considered. This method has obvious advantages compared with traditional lock-in amplifiers technique--simple experimental setup, a quickly available information on all the required harmonics, high speed of data processing using fast Fourier transform algorithm. A computationally simple, fast and accurate Fourier coefficients interpolation (FCI) method has been implemented to obtain a useful information from harmonics of a multimode signal. Our analysis shows that in this case FCI method has a systematical error (bias) of a signal parameters estimation, which became essential for the short data sets. Hence, a new differential Fourier coefficients interpolation (DFCI) method has been suggested, which is less sensitive to a presence of several modes in a signal. The analysis has been confirmed by simulations and measurements of a quartz wedge birefringence by means of the photoelastic modulator. The obtained bias, noise level, and measuring speed are comparable and even better than in lock-in amplifier technique. Moreover, presented DFCI method is expected to be promised candidate for using in actively developing imaging systems based on the modulation technique requiring fast digital signal processing of large data sets.
The Fast Fourier Transform and its application to tidal oscillations
Directory of Open Access Journals (Sweden)
A. dos Santos Franco
1971-06-01
Full Text Available This paper proposes a new way of tidal spectral analysis based on the Cooley-Tukey algorithm, known as the Fast Fourier Transform. The Fast Fourier Transform analysis is used to compute both the harmonic constants of the tide and the power spectrum.The latter is obtained by means of a weighted sum. A new way is also derived to obtain the formula giving the number of the degrees of freedom,on which is based the confi dence interval corresponding to the noise spectrum.Este trabalho propõe um novo caminho para a analise espectral da maré baseada no algoritmo de Cooley-Tukey. A análise através da "Transformação Rápida de Fourier" (Fast Fourier Transform - FFT é empregada tanto para calcular as constantes harmônicas da maré quanto para a obtenção do espectro de energia. Este é calculado por meio de uma soma ponderada. Também é dada uma nova dedução da fórmula que exprime o número de graus de liberdade em que se baseia o intervalo de confiança correspondente ao espectro do ruído. O trabalho foi redigido em inglês a fim de facilitar o intercâmbio de informações.
From "Dirac combs" to Fourier-positivity
Giraud, Bertrand G
2015-01-01
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.
Institute of Scientific and Technical Information of China (English)
温芝元; 曹乐平
2013-01-01
Plant pests and diseases image recognition is one of the key technologies of digital agricultural information collection and processing. Usually, based on pest infestation-like plant, it is carried out according to the size, shape, color, texture, etc., or a combination of several parameters. Machine recognition of diseases and insect pests needs to use digitalized characteristics without overlapping. Multi-fractal analysis of Fourier transform spectra was adopted to investigate the possibility of extraction of damage pattern characteristics for Citrus reticulata Blanco var. Ponkan. First, images of the boundary of a damaged pattern are extracted with an improved watershed algorithm and region merging. Secondly, a Discrete Fourier Transform (DFT) was applied to the damaged fruit image. With reference to the boundary of a damaged pattern, a fruit image magnitude spectrum was extracted. Thirdly, a fruit image magnitude spectrum was multi-fractiously analyzed and the multi-fractal spectrum of DFT magnitude spectrum was quadratic fitted. Height, width, and centroid coordinate of a fitting parabolic section were chosen feature values to identify the diseases and insect damage of fruits, with these three feature values as inputs of a BP neural network identifying diseases and insect damage of Ponkan, and the accuracy was up to 92.67%. Finally, the amplitude spectrum of the Fourier transform was adopted for multifractal analysis and multi-fractal spectrum of a quadratic fit;fit parabola segment height, width, and centroid coordinates were regarded as pests’ Eigen values, and then used as input variables to establish a BP citrus pest identification neural network model for pest identification. Among 5 classes of pests, in 30 groups of test samples, such as Pezothrips Kellyanus, Oxycetonia Jucunda, Oraesia Emarginata, Polyphagotarsonemus Latus, Colletotrichum Gloeoporioides Penz, the highest recognition rate was for Oraesia Emarginata, that is 96.67%, Polyphagotarsonemus
Institute of Scientific and Technical Information of China (English)
王本庆; 李兴国
2009-01-01
现有很多LFM信号调频斜率的分析算法,但这些算法存在诸多不足,如计算复杂、搜索时间长,对多LFM信号有交叉项等.该文提出了基于双正交Fourier变换的新LFM信号调频斜率分析算法,其特点是信号在双正交基下展开,通过变换得到信号调频斜率密度谱.该算法不需要搜索,且特别适合对不同调频斜率组成的多LFM信号进行调频斜率分析.文中推导了连续双正交Fourier变换公式和离散变换公式,并讨论了算法的一些主要性质.%There are many analysis algorithms for frequency rate of LFM signal, but those algorithms have some drawbacks, such as highly computational complexity, long time for searching, and cross-term in multi-LFM signal. In this paper, a new analysis algorithm of frequency rate of LFM signal is presented based on Biorthogonal Fourier Transform (BFT), the signal is expanded with biorthogonal base function that could be got frequency rate density spectrum of the signal. This algorithm need no searching, and has better performance for detection different frequency rate of multi-LFM signal. This paper derives continual BFT formula and discrete transform formula and discusses its some main characters.
Indian Academy of Sciences (India)
Renu Singh; K N Uttam; M D Saksena; M N Deo
2009-11-01
The emission spectrum of InBr molecule has been recorded in the region 350–400 nm on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.06 cm-1 using microwave excitation technique. About 61 violet degraded and single headed bands have been recorded and are classified into two band systems, viz. $A^{3} _{0} –X^{1} \\sum^{+}$ and $B^{3} _{1} –X^{1} \\sum^{+}$. A few new bands have been observed and are fitted in the vibrational schemes of the two systems. Revised vibrational constants have been determined. The vibrational assignments have been confirmed by observing isotope effect due to InBr81 in the 30 bands of the $A^{3} _{0} –X^{1} \\sum^{+}$ system and 19 bands of the $B^{3} _{1} –X^{1} \\sum^{+}$ system. The analysis is further supported by calculating the Franck–Condon factor for InBr79 and InBr81 molecules. The following vibrational constants (in cm-1) have been determined from the analysis: $$ \\begin{array}{llll} \\text{A}^{3}_{0}-\\text{X}^{1}^{+} & \\text{system} & v_{00}=26599.1 & '_{\\text{e}} = 226.42, \\ '_{\\text{e}}x'_{\\text{e}}=1.24\\text{~cm}^{-1},\\\\ & & & ''_{\\text{e}} = 221.19, \\ ''_{\\text{e}}x''_{\\text{e}}=0.528\\text{~cm}^{-1}.\\\\ \\text{B}^{3}_{1}-\\text{X}^{1}^{+} & \\text{system} & v_{00}=27380.52 & '_{\\text{e}}=223.086, \\ '_{\\text{e}}x'_{\\text{e}}=1.446\\text{~cm}^{-1},\\\\ & & & ''_{\\text{e}}=221.19, \\ ''_{\\text{e}}x''_{\\text{e}}=0.528\\text{~cm}^{-1}. \\end{array} $$
Institute of Scientific and Technical Information of China (English)
曹岗; 丛晓东; 蔡皓; 蔡宝昌
2012-01-01
Objective; To identify crude and processed Atractylodes macrocephala samples with fourier transform infrared (FTIR) spectrometry. Methods; Based on the fingerprint infrared spectrum from 1 800 to 600 cm , crude and processed Atractylodes macrocephala samples were classified and studied using the method of clustering analysis. Results: There were tiny differences between the spectra of different origins, including the crude and processed Atractylodes macrocephala samples. These samples could be successfully classified by soft independent modeling of class analogy (SIMCA). Recognition rate and rejection rate of crude and processed Atractylodes macrocephala samples were up to 95%. When testing with the blind sample that was picked out from the chosen samples by the authors, the accuracy was up to 95% . Conclusion: In combination with clustering analysis, FTIR coupled with SIMCA method provides an effective way to rapidly evaluate the crude and processed Chinese medicines%目的:应用傅里叶变换红外光谱(FTIR)法测定了白术生品和炮制品.方法:以1800～600cm-1范围内的吸收峰和吸光度为指标,以红外光谱图为对象,应用SIMCA聚类分析法对二者进行了聚类分析.结果:红外光谱结合聚类分析法对白术生品和炮制品的聚类结果较理想,识别率和拒绝率达到95％以上,盲样检测正确率可达95％以上.结论:红外光谱与聚类分析法相结合可以快速的鉴别原药材和炮制品.
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Application of the least-squares inversion method: Fourier series versus waveform inversion
Min, Dong-Joo; Shin, Jungkyun; Shin, Changsoo
2015-11-01
We describe an implicit link between waveform inversion and Fourier series based on inversion methods such as gradient, Gauss-Newton, and full Newton methods. Fourier series have been widely used as a basic concept in studies on seismic data interpretation, and their coefficients are obtained in the classical Fourier analysis. We show that Fourier coefficients can also be obtained by inversion algorithms, and compare the method to seismic waveform inversion algorithms. In that case, Fourier coefficients correspond to model parameters (velocities, density or elastic constants), whereas cosine and sine functions correspond to components of the Jacobian matrix, that is, partial derivative wavefields in seismic inversion. In the classical Fourier analysis, optimal coefficients are determined by the sensitivity of a given function to sine and cosine functions. In the inversion method for Fourier series, Fourier coefficients are obtained by measuring the sensitivity of residuals between given functions and test functions (defined as the sum of weighted cosine and sine functions) to cosine and sine functions. The orthogonal property of cosine and sine functions makes the full or approximate Hessian matrix become a diagonal matrix in the inversion for Fourier series. In seismic waveform inversion, the Hessian matrix may or may not be a diagonal matrix, because partial derivative wavefields correlate with each other to some extent, making them semi-orthogonal. At the high-frequency limits, however, the Hessian matrix can be approximated by either a diagonal matrix or a diagonally-dominant matrix. Since we usually deal with relatively low frequencies in seismic waveform inversion, it is not diagonally dominant and thus it is prohibitively expensive to compute the full or approximate Hessian matrix. By interpreting Fourier series with the inversion algorithms, we note that the Fourier series can be computed at an iteration step using any inversion algorithms such as the
Fourier time spectral method for subsonic and transonic flows
Zhan, Lei; Liu, Feng; Papamoschou, Dimitri
2016-06-01
The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.
Optical scatter imaging using digital Fourier microscopy
Seet, K Y T; Meredith, P; Zvyagin, A V
2007-01-01
An approach reported recently by Alexandrov et al. on optical scatter imaging, termed digital Fourier microscopy (DFM), represents an adaptation of digital Fourier holography to selective imaging of biological matter. Holographic mode of recording of the sample optical scatter enables reconstruction of the sample image. Form-factor of the sample constituents provides a basis for discrimination of these constituents implemented via flexible digital Fourier filtering at the post processing stage. Like in the dark-field microscopy, the DFM image contrast appears to improve due to the suppressed optical scatter from extended sample structures. In this paper, we present theoretical and experimental study of DFM using biological phantom that contains polymorphic scatterers.
利用傅里叶变换红外光谱法分析燕麦片的品质%Analysis of Oatmeal Quality by Fourier ransform Infrared Spectroscopy
Institute of Scientific and Technical Information of China (English)
周旭章; 彭昕; 张慧恩; 蔡艳
2011-01-01
In order to establish a fast nondestructive method for analysis of oatmeal quality, qualities of eight brands of oatmeal from Ningbo supermarkets were analyzed by Fourier transform infrared spectroscopy ( FTIR). Results showed that the comparison of infrared spectrum and characteristic absorption peaks of different brands of oatmeal could determine the contents and composition of nutritional ingredients in oatmeals; second derivative spectrum which could identify overlapped peaks in conventional IR spectrum and increase resolution had been used to achieve more accurate and finer analysis. FTIR combined with two - dimensional correlation infrared spectrum was applied to study the thermal stability of oatmeal through mini - heating process. In conclusion, FTIR could provide a fast nondestructive method for analysis of oatmeal quality.%为了建立一种快速、无损的鉴定市场所销售的燕麦片的品质鉴定分析方法,对宁波市超市所销售的品牌1～品牌8的燕麦片商品进行了抽样,采取傅里叶变换红外光谱法(FTIR)进行定性分析.结果表明,通过红外光谱图和特征峰之间的比较,可以分析出燕麦中含有的营养成分及其含量高低;结合二阶导数谱能把红外图谱中重叠的峰区分开来,增大谱图的分辨率,使分析更加精细准确;利用热微扰法测定燕麦红外光谱及其二维相关红外光谱可以判断燕麦的热稳定性.因此,傅里叶变换红外光谱法是一种快速、无损的鉴定燕麦片品质的分析方法.
Content adaptive sparse illumination for Fourier ptychography
Bian, Liheng; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-01-01
Fourier Ptychography (FP) is a recently proposed technique for large field of view and high resolution imaging. Specifically, FP captures a set of low resolution images under angularly varying illuminations and stitches them together in Fourier domain. One of FP's main disadvantages is its long capturing process due to the requisite large number of incident illumination angles. In this letter, utilizing the sparsity of natural images in Fourier domain, we propose a highly efficient method termed as AFP, which applies content adaptive sparse illumination for Fourier ptychography by capturing the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework with both simulations and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP by around 30%-60%.
Electronically-Scanned Fourier-Transform Spectrometer
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
郑建斌; 张红权; 高鸿
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new method of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new me- thod of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Fractional Fourier transform of Lorentz beams
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan
2009-01-01
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
Shift sampling theory of Fourier transform computation
Institute of Scientific and Technical Information of China (English)
柴玉璞
1997-01-01
The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.
Quaternion Fourier and Linear Canonical Inversion Theorems
Hu, Xiao Xiao; Kou, Kit Ian
2016-01-01
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In addition, understanding the QFT paves the way for understanding other integral transform, such as the Quaternion Fractional Fourier transform (QFRFT), Quaternion linear canonical transform (QLCT) and Quaternion Wigner-Ville distribution. The aim of this pa...
Fourier theory of linear gain media
Hâgenvik, Hans Olaf; Malema, Markus E.; Skaar, Johannes
2015-04-01
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane-wave component (plane-wave limit). For gain media, we demonstrate that these two limits generally do not commute; for example, one order may lead to a diverging field, while the other order leads to a finite field. Moreover, the plane-wave limit may be dependent on whether it is realized with a finite-support excitation or Gaussian excitation, eventually of infinite widths. We consider wave propagation in gain media by a Fourier-Laplace integral in space and time, and demonstrate how the correct monochromatic limit or plane-wave limit can be taken, by deforming the integration surface in complex frequency-complex wave-number space. We also give the most general criterion for absolute instabilities. The general theory is applied in several cases, and is used to predict media with novel properties. In particular, we show the existence of isotropic media which in principle exhibit simultaneous refraction, meaning that they refract positively and negatively at the same time.
Fourier theory of linear gain media
Hågenvik, Hans Olaf; Skaar, Johannes
2014-01-01
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane wave component (plane wave limit), separately. For gain media, we demonstrate that these two limits generally do not commute; for example, one order may lead to a diverging field, while the other order leads to a finite field. Moreover, the plane wave limit may be dependent on whether it is realized with a rect function excitation or gaussian excitation of infinite widths. We consider wave propagation in gain media by a Fourier--Laplace integral in time and space, and demonstrate how the correct monochromatic limit or plane wave limit can be taken, by deforming the integration surface in complex frequency--complex wavenumber space. We also give the most general criterion for absolute instabilities. The general theory is applied in several cases, and is used to predict media with novel properties. In particular, we show the existence of isotrop...
Institute of Scientific and Technical Information of China (English)
汤南; 陈鸿鹏; 郑军华; 赵仲留; 林坚涛
2012-01-01
OBJECTIVE To establish the X-ray diffraction Fourier fingerprint pattern of Nervilia fordii (Hance) Schltr. and analyze the similarity of different origination. METHODS Powder X-ray diffraction was used. The X-ray diffraction Fourier fingerprint pattern was established by analyzing eight samples of Nervilia fordii (Hance) Schltr. RESULTS The X-ray diffraction Fourier fingerprint pattern, the characteristic diffraction peaks and the similarity of Nervilia fordii (Hance) Schltr were obtained and calculated. CONCLUSION The method is specific, it can be used for identification of Nervilia fordii (Hance) Schltr.%目的:建立青天葵X-射线衍射Fourier(傅立叶)指纹图谱,并对不同产地该药材进行相似度分析.方法:应用粉末X-射线衍射法,通过对8批青天葵药材进行分析,建立青天葵X-射线衍射Fourier指纹图谱,并进行相似度评价 结果:获得了青天葵X-射线衍射Fourier指纹图谱、特征标记峰值和相似度.结论:X-射线衍射Fourier指纹图谱专属性强,可用于中药青天葵的鉴定.
Kok, S.J.; Wold, C.A.; Hankemeier, Th.; Schoenmakers, P.J.
2003-01-01
Two commercial liquid chromatography-Fourier-transform infrared spectroscopy interfaces (LC-FTIR), viz. a flow cell and a solvent-elimination interface have been assessed for use in size-exclusion chromatography (SEC) with respect to their chromatographic integrity (i.e. peak asymmetry, chromatograp
The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.
King, Roy W.; Williams, Kathryn R.
1989-01-01
Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)
Institute of Scientific and Technical Information of China (English)
张涛; 朱熀秋; 孙晓东; 杨泽斌
2013-01-01
To optimize the permanent magnet rotor structure and reduce the rotor eddy current loss, the rotor eddy current loss generated by slot effect of air-gap magnetic field in surface-mounted high-speed permanent magnet synchronous motor was analyzed. The magnetization models of permanent magnets were investigated to establish the eddy current loss mathematic models of permanent rotor. The air-gap magnetic field data samples were extracted based on the air-gap magnetic field static analysis. For permanent magnets with parallel magnetization or Halbach magnetization, the air-gap magnetic field space, time harmonics and the corresponding eddy current loss caused by air-gap permeance variation were investigated by double Fourier transforms. The eddy current loss was calculated by transient finite element analysis at non-load state. The results show that the permanent magnet rotor with Halbach magnetization mode can effectively reduce the high order harmonics, and the rotor eddy-current loss is 34% of that with parallel magnetization.%为了优化永磁转子结构,降低转子涡流损耗,分析了表面贴式高速永磁同步电机气隙磁场齿槽效应产生的转子涡流损耗.研究了表面贴式永磁同步电机转子永磁体磁化模式,建立了永磁同步电机转子涡流损耗数学模型,分析了永磁同步电机静态气隙磁场,提取气隙磁场样本数据.采用双重傅里叶变换,研究和比较了四极永磁同步电机永磁体在Halbach磁化和平行磁化时,由齿槽效应引起的气隙磁场时空谐波和对应的转子涡流损耗,并采用瞬态有限元法计算了空载时的转子涡流损耗.结果表明:永磁体采用Halbach磁化模式,能够有效降低气隙磁场高次谐波,转子涡流损耗约为平行磁化时的34％.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
Energy Technology Data Exchange (ETDEWEB)
Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)
1993-08-28
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
International Nuclear Information System (INIS)
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author)
Modeling the reconstructed BAO in Fourier space
Seo, Hee-Jong; Beutler, Florian; Ross, Ashley J.; Saito, Shun
2016-08-01
The density field reconstruction technique, which partially reverses the non-linear degradation of the Baryon acoustic oscillation (BAO) feature in the galaxy redshift surveys, has been successful in substantially improving the cosmology constraints from recent surveys such as Baryon Oscillation Spectroscopic Survey (BOSS). We estimate the efficiency of the method as a function of various reconstruction details. To directly quantify the BAO information in non-linear density fields before and after reconstruction, we calculate the cross-correlations (i.e. propagators) of the pre(post)-reconstructed density field with the initial linear field using a mock sample that mimics the clustering of the BOSS galaxies. The results directly provide the BAO damping as a function of wavenumber that can be implemented into the Fisher matrix analysis. We focus on investigating the dependence of the propagator on a choice of smoothing filters and on two major different conventions of the redshift-space density field reconstruction that have been used in literature. By estimating the BAO signal to noise for each case, we predict constraints on the angular diameter distance and Hubble parameter using the Fisher matrix analysis. We thus determine an optimal Gaussian smoothing filter scale for the signal-to-noise level of the BOSS CMASS. We also present appropriate BAO fitting models for different reconstruction methods based on the first- and second-order Lagrangian perturbation theory in Fourier space. Using the mock data, we show that the modified BAO fitting model can substantially improve the accuracy of the BAO position in the best fits as well as the goodness of the fits.
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species.
Institute of Scientific and Technical Information of China (English)
杨铭; 朱小玲; 梁国正
2016-01-01
,thermogravimetric (TG)analysis coupled with Fourier transform infrared spectroscopy(FTIR),are able to an-alyze materials not only qualitatively but also quantitatively.This method has obvious advantages in researching the thermal de-composition of many materials.However,the thermal decomposition processing of Kevlar fibers is rarely reported in the litera-ture,therefore,we firstly studied the pyrolysis behavior of Kevlar fibers with thermogravimetric analysis coupled with Fourier transform infrared spectroscopy at the temperature of 30~800 ℃.We not only obtained the processing of the Kevlar fibers'ther-mal decomposition with great details but also the products of every stage.Experimental results exhibited that the decomposition of Kevlar fibers has experienced three stages:100~240,240~420 and 420~800 ℃.The weight loss of Kevlar fibers was quite slow before 500 ℃.The third stage was the main stage of the decomposition,and the amount of residue finally reached to a mass percent of 56.21%.FTIR analysis illustrated that free water released from Kevlar fibers at the first stage,followed by the dehy-dration and depolymerization which made polymer chains short.Finally the fiber fragments further reacted and produced the ga-ses of small molecular mass,and the main products were water,ammonia,carbon monoxide and carbon dioxide.Generation rate of water was increased;the emission of ammonia was at the same rate;carbon monoxide was only produced at the temperature of 515~630 ℃,then turned into carbon dioxide.The release of carbon dioxide was on rise because of the conversion process of car-bon monoxide,and then dropped to a certain value.
Multiparty Quantum Secret Sharing Using Quantum Fourier Transform
Institute of Scientific and Technical Information of China (English)
HUANG Da-Zu; CHEN Zhi-Gang; GUO Ying
2009-01-01
A (n, n )-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform.In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert.Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant.Security analysis shows that our scheme is secure.Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.
Physics of the Blues: Music, Fourier and Wave - Particle Duality
Energy Technology Data Exchange (ETDEWEB)
Gibson, J. Murray (ANL)
2003-10-15
Art and science are intimately connected. There is probably no art that reveals this more than music. Music can be used as a tool to teach physics and engineering to non-scientists, illustrating such diverse concepts as Fourier analysis and quantum mechanics. This colloquium is aimed in reverse, to explain some interesting aspects of music to physicists. Topics include: What determines the frequency of notes on a musical scale? What is harmony and why would Fourier care? Where did the blues come from? (We' re talking the 'physics of the blues', and not 'the blues of physics' - that's another colloquium). Is there a musical particle? The presentation will be accompanied by live keyboard demonstrations. The presenter will attempt to draw tenuous connections between the subject of his talk and his day job as Director of the Advanced Photon Source at Argonne National Laboratory.
Energy Technology Data Exchange (ETDEWEB)
Weissgerber, Wilfried
2013-05-01
The book under consideration covers the basics and calculation methods of the Laplace-transformation for the regulation technology, Fourier transformation for the signal theory, the quadrupole theory for the communications engineering and balancing processes for linear networks. The book is dedicated to the students of engineering and natural sciences, electrical engineering, technical informatics and physics at higher institutes of applied sciences, technical colleges, universities and universities of cooperative education.
Glasser, L.
1987-01-01
This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…
Mawardi Bahri
2013-01-01
In this paper we introduce convolution theorem for the Fourier transform (FT) of two complex functions. We show that the correlation theorem for the FT can be derived using properties of convolution. We develop this idea to derive the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternion functions.
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}.
Illustrative EDOF topics in Fourier optics
George, Nicholas; Chen, Xi; Chi, Wanli
2011-10-01
In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF camera systems. They are at the level of final examination problems that have been made solvable by a student or professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits, four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
Adaptive optics implementation with a Fourier reconstructor.
Glazer, Oded; Ribak, Erez N; Mirkin, Leonid
2007-02-01
Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.
Electro-optic imaging Fourier transform spectrometer
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.
Fourier transforms and convolutions for the experimentalist
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
Fourier Series Approximations to J2-Bounded Equatorial Orbits
Directory of Open Access Journals (Sweden)
Wei Wang
2014-01-01
Full Text Available The current paper offers a comprehensive dynamical analysis and Fourier series approximations of J2-bounded equatorial orbits. The initial conditions of heterogeneous families of J2-perturbed equatorial orbits are determined first. Then the characteristics of two types of J2-bounded orbits, namely, pseudo-elliptic orbit and critical circular orbit, are studied. Due to the ambiguity of the closed-form solutions which comprise the elliptic integrals and Jacobian elliptic functions, showing little physical insight into the problem, a new scheme, termed Fourier series expansion, is adopted for approximation herein. Based on least-squares fitting to the coefficients, the solutions are expressed with arbitrary high-order Fourier series, since the radius and the flight time vary periodically as a function of the polar angle. As a consequence, the solutions can be written in terms of elementary functions such as cosines, rather than complex mathematical functions. Simulations enhance the proposed approximation method, showing bounded and negligible deviations. The approximation results show a promising prospect in preliminary orbits design, determination, and transfers for low-altitude spacecrafts.
Design of high-resolution Fourier transform lens
Zhang, Lei; Zhong, Xing; Jin, Guang
2007-12-01
With the development of optical information processing, high-resolution Fourier transform lens has often been used in holographic data storage system, spatial filtering and observation of particles. This paper studies the optical design method of high-resolution Fourier transform optical lenses system, which could be used in particles observation and holographic data storage system. According to Fourier transform relation between object and its frequency plane and the theory of geometrical optics, the system with working wavelength 532nm and resolution 3μm was designed based on ZEMAX. A multi-configuration method was adopted to optimize the system's lenses. In the optical system, a diaphragm was placed at the system's spectrum plane and the system demanded a low vacuum to cut down the influences of atmosphere and other particles. The result of finite element analysis indicated that the influences of vacuum pumping to optics spacing and mirror surface shape very minor, and the imaging quality not being affected. This system has many advantages, such as simple structure, good image quality and a high resolution of 3μm. So it has a wide application prospect and can be used both in holographic data storage system and particles observation.
Parametric spectral correlations of disordered systems in the Fourier domain
Guarneri, I; Zakrzewski, J A; Molinari, L; Casati, G; Guarneri, I; Zyczkowski, K; Zakrzewski, J; Molinari, L; Casati, G
1995-01-01
A Fourier analysis of parametric level dynamics for random matrices periodically depending on a phase is developed. We demonstrate both theoretically and numerically that under very general conditions the correlation C(\\varphi ) of level velocities is singular at \\varphi =0 for any symmetry class; the singularity is revealed by algebraic tails in Fourier transforms, and is milder, the stronger the level repulsion in the chosen ensemble. The singularity is strictly connected with the divergence of the 2nd moments of level derivatives of appropriate order, and its type is specified to leading terms for Gaussian, stationary ensembles of GOE, GUE, GSE types, and for the Gaussian ensemble of Periodic Banded Random Matrices, in which a breaking of symmetry occurs. In the latter case, we examine the behaviour of correlations in the diffusive regime and in the localized one as well, finding a singularity like that of pure GUE cases. In all the considered ensembles we study the statistics of the Fourier coefficients o...
Institute of Scientific and Technical Information of China (English)
王盛锋; 刘云霞; 高丽丽; 韩亚; 黄金生; Hilman; 刘荣乐; 汪洪
2014-01-01
锌导致玉米植株生长受抑,利用FTIR技术研究发现缺锌植株中碳水化合物、脂类、蛋白质及核酸组分发生变化,农大108植株中各组分变化受缺锌影响较大,品种农大108可能较郑单958对缺锌更为敏感。%[Objectives]Fourier transform infrared spectroscopy ( FTIR) is a structural analysis technique based on the vibrations of functional group and polar bond in chemical components. The objective of this study was to reveal the component changes in different organs of maize plants with and without zinc( Zn) application using FTIR. It would provide some physiological evidences of maize plants subjected to Zn deficiency stress.[Methods]Two maize cultivars, Nongda108 and Zhengdan958, were chosen as tested crops. Hydroponic culture experiments were conducted with 0 and 1. 0 μmol/L Zn treatments. The plant shoot and root biomass were weighted. Dry plant samples were digested with HNO3 -HClO4 ( 3:1 ) for Zn determination by atomic absorption spectrophotometer. Root samples were stored in FAA solution ( 70% alcohol:38% formaldehyde:acetic acid = 90 :5:5 parts by volume) prior to measurements. The root systems were then digitized with the EsponV700 scanner at 300 dpi resolution for further analysis. The total root length and root volume were measured with WinRHIZO root analysis software ( Regent Instruments Inc. , Canada) . Dry samples of roots, stems and leaves were ground to through 0. 2 mm sieve. A potassium bromide tablet method was used to detect spectral characteristics of different plant parts with FTIR (VERTEX 70, Bruker) and data were collected and analyzed by the OPUS 6. 5 software. [Results]The results show that Zn concentrations in maize plants without Zn application are below the critical level of 20 μg/g, and the Zn deficiency stress significantly decreases shoot dry matter weight, root surface, root volume and total root length. The shoot biomass and root length of maize cultivar, Nongda108, are less than those
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
Fourier-Bessel heat kernel estimates
Malecki, Jacek; Serafin, Grzegorz; Zorawik, Tomasz
2015-01-01
We provide sharp two-sided estimates of the Fourier-Bessel heat kernel and we give sharp two-sided estimates of the transition probability density for the Bessel process in (0,1) killed at 1 and killed or reflected at 0.
Fourier transforms on an amalgam type space
Liflyand, E
2012-01-01
We introduce an amalgam type space, a subspace of $L^1(\\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Ultrafast Fourier-transform parallel processor
Energy Technology Data Exchange (ETDEWEB)
Greenberg, W.L.
1980-04-01
A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.
Directional Uncertainty Principle for Quaternion Fourier Transform
Hitzer, Eckhard
2013-01-01
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.
Fourier theory and C∗-algebras
Bédos, Erik; Conti, Roberto
2016-07-01
We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.
Institute of Scientific and Technical Information of China (English)
胡亮; 徐鹏; 崔贺; 谢文加; 王勤美
2013-01-01
关性有统计学意义(r=0.361,P＜ 0.01).飞秒LASIK术后中度近视组RJ0与CJ0 (r=0.393,P＜ 0.01),RJ0与TJ0(r=0.596,P＜ 0.01),RJ45与TJ0(r=0.396,P＜0.01)相关性均有统计学意义.结论:①鹰视酷眼准分子激光行OUP-SBK或飞秒LASIK手术矫正中高度近视患者的顺规散光具有较高的准确性；②手术对顺规散光患者垂轴成分的矫正准确性高于对斜轴散光成分的矫正准确性；③手术矫正中高度近视患者的顺规散光准确性相近.%Objective:To evaluate the accuracy of Cool Excimer Laser System for myopic astigmatism in One Use-Plus Sub-Bowman's keratomileusis (OUP-SBK) and Femtosecond Laser In Situ Keratomileusis (FSLASIK) with Fourier Analysis and develop a customized nomogram for astigmatic patients.Methods:Retrospectively reviewed the charts of 542 eyes (OUP-SBK:318 eyes; FS-LASIK:224 eyes),who had excimer laser surgery in Eye Hospital of Wenzhou Medical College during Jan 2012 to March 2012,with an inclusion criteria as:WTR astigmatism ≥-0.5 D,myopia ＞-3 D.The moderate and high myopia groups were divided respectively according to baseline myopia.Preoperative and 3 to 6 months postoperative examinations included:refraction,corneal topography,pachymetry,best spectacles corrected visual acuity (BSCVA).Fourier Analysis was used to transform preoperative astigmatism to TJ0 and TJ45; preoperative corneal astigmatism to CJ0 and CJ45;postoperative residual astigmatism to RJ0 and RJ45.Group t test and Pearson test were used for statistical analysis.Results:① Residual Astigmatism.OUP-SBK moderate myopia group:RJ0=(0.012 ± 0.161)D,RJ45=-(0.012 ± 0.128)D; OUP-SBK high myopia group:RJ0=(0.026 ± 0.239)D,RJ45=(-0.029 ± 0.194)D,the difference between moderate and high myopia group was not statistically significant (P=0.697,0.402).Femtosecond LASIK moderate myopia group:RJ0=(0.053 ± 0.248)D,RJ45=(-0.039 ± 0.186)D; femtosecond LASIK high myopia group:RJ0=(0.042 ± 0.267)D,RJ45=(0.044 ± 0.261)D,the difference between
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne
2011-10-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
Beam profile for the Herschel-SPIRE Fourier transform spectrometer.
Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D
2013-06-01
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile.
Digital Backpropagation in the Nonlinear Fourier Domain
Wahls, Sander; Prilepsky, Jaroslaw E; Poor, H Vincent; Turitsyn, Sergei K
2015-01-01
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\\"odinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the ...
X-ray Fourier ptychographic microscopy
Simons, H; Guigay, J P; Detlefs, C
2016-01-01
Following the recent developement of Fourier ptychographic microscopy (FPM) in the visible range by Zheng et al. (2013), we propose an adaptation for hard x-rays. FPM employs ptychographic reconstruction to merge a series of low-resolution, wide field of view images into a high-resolution image. In the x-ray range this opens the possibility to overcome the limited numerical aperture of existing x-ray lenses. Furthermore, digital wave front correction (DWC) may be used to charaterize and correct lens imperfections. Given the diffraction limit achievable with x-ray lenses (below 100 nm), x-ray Fourier ptychographic microscopy (XFPM) should be able to reach resolutions in the 10 nm range.
Miniaturization of holographic Fourier-transform spectrometers.
Agladze, Nikolay I; Sievers, Albert J
2004-12-20
Wave propagation equations in the stationary-phase approximation have been used to identify the theoretical bounds of a miniature holographic Fourier-transform spectrometer (HFTS). It is demonstrated that the HFTS throughput can be larger than for a scanning Fourier-transform spectrometer. Given room- or a higher-temperature constraint, a small HFTS has the potential to outperform a small multichannel dispersive spectrograph with the same resolving power because of the size dependence of the signal-to-noise ratio. These predictions are used to analyze the performance of a miniature HFTS made from simple optical components covering a broad spectral range from the UV to the near IR. The importance of specific primary aberrations in limiting the HFTS performance has been both identified and verified. PMID:15646777
High order generalized permutational fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Ran Qi-Wen; Yuan Lin; Tan Li-Ying; Ma Jing; Wang Qi
2004-01-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT),is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +∞,M = 4k (k is a natural number), and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
High order generalized permutational fractional Fourier transforms
Ran, Qi-Wen; Yuan, Lin; Tan, Li-Ying; Ma, Jing; Wang, Qi
2004-02-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +infty, M = 4k (k is a natural number) and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
Fourier Transform Infrared Spectroscopic Studies in Flotation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Fourier transform infrared (FTIR) spectroscopy has been extensively employed in flotation research.The work done by the author and co-workers has been reported.A comparison has been made among the different FTIR spectroscopic techniques,e.g.,transmission FTIR spectroscopy,diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy,and attenuated total reflectance (ATR) FTIR spectroscopy.FTIR spectroscopy has been used to study the mechanism of interaction between the collector and the surfaces of different minerals,the mechanism of action of the depressant in improving the selectivity of flotation,and the mechanism of adsorption of the polymeric modifying reagent on mineral surfaces.The interaction between particles in mineral suspension has also been studied by FTIR spectroscopy.
Institute of Scientific and Technical Information of China (English)
高鸿启; 沈学举; 甘厚吉
2011-01-01
In order to limit the influence of background noise on correlation spot on the output correlation plane , the Fourier spectrum of the matched filter function and the background noise were compared, and the amplitude of the matched filter was nonlinearly modulated based on the exponent function relying on the Founer spectrum of the background noise. It enables the filter to reduce the transmittance in the area of the intense noise Fourier spectrum relative to the transmittance for input image Fourier spectrum. The signal-to-noise ratio on the output correlation plane was improved and the detection of the correlation spots was realized. The results of computer simulation show that the correlation peak value reduces 2. 28 times and the signal-to-noise ratio increases 3 times when m changes into 1. 2 from 0. The results of simulation and experiment show that the anti-noise capability of exponent type space matched filter is imprved obviously.%光学相关识别过程中,为减小输入场景中背景噪音对输出相关点的影响,通过分析背景噪音和目标图像的傅里叶谱,在匹配滤波函数中引入一由背景噪音傅里叶谱确定的指数函数,通过指数函数对匹配滤波函数振幅进行非线性调制,使设计的指数型空间匹配滤波器对背景噪音谱透过率小于目标图像谱透过率,从而增加输出相关平面上的信噪比,以实现相关点的正确探测.模拟结果表明当参量m由0增加到1.2时,相关峰值下降2.28倍,信噪比增加3倍.模拟和实验结果均表明:与纯相位匹配滤波器相比其抗噪能力得到明显改善.
Fractional Fourier Transform of Cantor Sets
Institute of Scientific and Technical Information of China (English)
LIAO Tian-ne; GAO Qiong
2005-01-01
@@ A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.
Fourier-transform spectroscopy instrumentation engineering
Saptari, Vidi
2003-01-01
Many applications today require the Fourier-transform (FT) spectrometer to perform close to its limitations, such as taking many quantitative measurements in the visible and in the near infrared wavelength regions. In such cases, the instrument should not be considered as a perfect ""black box."" Knowing where the limitations of performance arise and which components must be improved are crucial to obtaining repeatable and accurate results. One of the objectives of this book is to help the user identify the instrument's bottleneck.
Fourier Spectra of Binomial APN Functions
Bracken, Carl; Markin, Nadya; McGuire, Gary
2008-01-01
In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting BCH code. Furthermore, for fields of odd degree, our results provide an alternative proof of the APN property of the functions.
An Imaging Fourier Transform Spectrometer for NGST
Graham, J R
1999-01-01
Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for tremendous scientific return in many fields of astrophysical inquiry. We describe the operation and quantify the advantages of an IFTS for space applications. The conceptual design of the Integral Field Infrared Spectrograph (IFIRS) is a wide field (5'.3 x 5'.3) four-port imaging Michelson interferometer.
Turbulence on a Fractal Fourier set
Lanotte, Alessandra Sabina; Biferale, Luca; Malapaka, Shiva Kumar; Toschi, Federico
2015-01-01
The dynamical effects of mode reduction in Fourier space for three dimensional turbulent flows is studied. We present fully resolved numerical simulations of the Navier-Stokes equations with Fourier modes constrained to live on a fractal set of dimension D. The robustness of the energy cascade and vortex stretching mechanisms are tested at changing D, from the standard three dimensional case to a strongly decimated case for D = 2.5, where only about $3\\%$ of the Fourier modes interact. While the direct energy cascade persist, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the co-dimension of the fractal set, $E(k)\\sim k^{- 5/3 + 3 -D }$, explains the results. At small scales, the intermittent behaviour due to the vorticity production is strongly modified by the fractal decimation, leading to an almost Gaussian statistics already at D ~ 2.98. These effects are connected to a genuine modification in the triad-to-tri...
Institute of Scientific and Technical Information of China (English)
杨彦利; 苗长云; 伉大俪
2012-01-01
Based on elliptic Fourier descriptors, vibration signals measured from the same section of the orbit by a couple of sensor mounted in radial direction 90°apart are analyzed in data fusion. The theoretical expression of filtered orbit is derived. The full spectrum, the holospectrum, and the vector spectrum are compared, a general theoretical framework for these three kinds spectrum is proposed, and a numerical method to obtain these three kinds spectrum by one Fourier transform is designed. The vector ellipse spectrum which is synthesized by the full spectrum, the holospectrum, and the vector spectrum is proposed as a new method to analyze synchronous vibration signals. The comparison shows that the vector ellipse spectrum is simple and feasible.%基于椭圆Fourier描述子,对转子同一截面上相互垂直的两个传感器测取的同源振动信号进行融合分析.从理论上推导出滤波轴心轨迹的表达式.研究对比全谱、全息谱和矢谱,建立三种谱分析方法的统一理论框架,给出三种谱分析方法的理论表达式,并设计利用一次快速Fourier变换实现三种谱图的数值方法.在融合全谱、全息谱和矢谱三种谱分析方法的基础上,提出基于椭圆Fourier描述子的矢椭谱分析方法,用于分析转子的同源振动信号.应用对比验证了矢椭谱的简洁可行性.
The derivative-free Fourier shell identity for photoacoustics.
Baddour, Natalie
2016-01-01
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.
A Note on Fourier and the Greenhouse Effect
Postma, Joseph E.
2015-01-01
Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...
Analogue computer using fourier series for optical spectrometry
International Nuclear Information System (INIS)
The object of the present report is to describe an electronic unit designed for the automatic calculation of optical spectra, a calculation carried out, by a Fourier transformation of an interferogram recorded on magnetic tape. With this, apparatus it is possible to calculate 20 points simultaneously and its theoretical resolving power is only limited by the duration of the interferogram. The practical limit due to the technique adopted is 5 x 106. Its general characteristics are the following: - Signal analysis for frequencies of between 3 and 10 Kc/s - No automatic progression of the analysis frequency 0.01 c/s - Simultaneous calculation of 5 spectra and of 4 circuits per spectrum - Compensation of the changes in the unrolling speed of the spectrum magnetic band for differences of between ± 10 per cent (response time 200 μs max.) - Choice of the origin frequency with an accuracy of 0.01 c/s This description is preceded by a description of the spectrometric method using a Fourier transformation. (authors)
Some Applications of Fourier's Great Discovery for Beginners
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…
Optical image encryption based on multifractional Fourier transforms.
Zhu, B; Liu, S; Ran, Q
2000-08-15
We propose a new image encryption algorithm based on a generalized fractional Fourier transform, to which we refer as a multifractional Fourier transform. We encrypt the input image simply by performing the multifractional Fourier transform with two keys. Numerical simulation results are given to verify the algorithm, and an optical implementation setup is also suggested. PMID:18066153
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
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",…
Research progress on discretization of fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
TAO Ran; ZHANG Feng; WANG Yue
2008-01-01
As the fractional Fourier transform has attracted a considerable amount of atten-tion in the area of optics and signal processing,the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier trans-form.Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain,the discre-tization of the fractional Fourier transform has been investigated recently.A sum-mary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper.The discretizations include sampling in the fractional Fourier domain,discrete-time fractional Fourier transform,frac-tional Fourier series,discrete fractional Fourier transform (including 3 main types:linear combination-type;sampling-type;and eigen decomposition-type),and other discrete fractional signal transform.It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
Energy Technology Data Exchange (ETDEWEB)
DeKeyser, C.F. Jr.
1984-01-01
Use of isotope exchange kinetics for functional group determination in coal is investigated. Net exchange kinetics determined by time dependent Neutron Activation Analysis measurements (NAA) would be related to individual functional group exchange kinetics determined by Fourier Transform Infrared (FTIR) spectroscopy measurements. The work described herein can be grouped into three categories: 1) work relating to the FTIR spectroscopy of coal, 2) work relating to oxygen exchange in coal, and 3) work relating to measurements of O-18 by NAA. Methods are discussed for preparing IR observable samples of coal and ash, obtaining FTIR spectra of these samples, and reducing the spectral data to numerical form. Also included in this category is an investigation into the use of IR spectroscopic methods for the ultimate analysis of coals. An initial attempt at the observation of oxygen exchange in coal is described which includes two exchange schemes and the FTIR spectroscopic observation of their end products. A facile exchange between O-18 water and O-16 in coal was attempted with and without catalysts. Also, the design and construction of a fast pneumatic transfer system for the determination of O-18 is described.
Energy Technology Data Exchange (ETDEWEB)
Jouy, P.; Mougel, J.F. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-07-01
The object of the present report is to describe an electronic unit designed for the automatic calculation of optical spectra, a calculation carried out, by a Fourier transformation of an interferogram recorded on magnetic tape. With this, apparatus it is possible to calculate 20 points simultaneously and its theoretical resolving power is only limited by the duration of the interferogram. The practical limit due to the technique adopted is 5 x 10{sup 6}. Its general characteristics are the following: - Signal analysis for frequencies of between 3 and 10 Kc/s - No automatic progression of the analysis frequency 0.01 c/s - Simultaneous calculation of 5 spectra and of 4 circuits per spectrum - Compensation of the changes in the unrolling speed of the spectrum magnetic band for differences of between {+-} 10 per cent (response time 200 {mu}s max.) - Choice of the origin frequency with an accuracy of 0.01 c/s This description is preceded by a description of the spectrometric method using a Fourier transformation. (authors) [French] L'objet du present rapport est la description d'un ensemble electronique destine au calcul automatique des spectres optiques, calcul realise par transformation de Fourier d'un interferogramme enregistre sur bande magnetique. Cet appareil permet le calcul simultane de 20 points, et son pouvoir de resolution theorique n'est limite que par la duree de l'interferogramme. La limitation pratique due a la technique adoptee est de 5.10{sup 6}. Ses caracteristiques generales sont les suivantes: - Analyse de signaux dont les frequences sont comprises entre 3 et 10 Kc/s - Pas de progression automatique de la frequence d'analyse 0,01 c/s - Calcul simultane de 5 spectres et de 4 circuits par spectre - Compensation des variations de vitesse de defilement de la bande magnetique pour des ecarts compris entre {+-} 10 pour cent (temps de reponse 200 {mu}s max.) - Choix de la frequence origine a 0,01 c/s pres Cette description est
Fourier transform infrared spectroscopy of deuterated proteins
Marcano O., A.; Markushin, Y.; Melikechi, N.; Connolly, D.
2008-08-01
We report on Fourier transform spectra of deuterated proteins: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor II, monoclonal antibody to ovarian cancer antigen CA125 and Osteopontin. The spectra exhibit changes in the relative amplitude and spectral width of certain peaks. New peaks not present in the non-deuterated sample are also observed. Ways for improving the deuteration of proteins by varying the temperature and dilution time are discussed. We propose the use of deuterated proteins to increase the sensitivity of immunoassays aimed for early diagnostic of diseases most notably cancer.
Gong, Ning-Bo; Lü, Li-Juan; Liu, Chao; Ma, Lin; Chen, Ruo-Yun; Lü, Yang
2010-05-01
The powder X-ray diffraction Fourier fingerprint pattern technique was used to develop a new quantitation method for the analysis of andrographolide and dehydroandrographolide. And the high performance liquid chromatography method was used to evaluate the quantity of andrographolide and dehydroandrographolide. The relationship of diffraction peak intensity and content of andrographolide and dehydroandrographolide was investigated. The powder X-ray diffraction Fourier fingerprint pattern analysis technique can be used to evaluate the quantity of andrographolide and dehydroandrographolide in the herb simultaneously.
Directory of Open Access Journals (Sweden)
Yajing Lou
2014-01-01
Full Text Available Background: Sulfur-fumigation may induce chemical transformation of traditional Chinese medicines leading to harmful effects following patient ingestion. For quality control, it is urgently needed to develop a reliable and efficient method for sulfur-fumigation identification. Materials and Methods: The spectrochemical identification of non-fumigated and sulfur-fumigated Fritillaria thunbergii Miq. was carried out to evaluate inorganic elements and organic components. The concentrations of 12 elements, including Zn, Mn, Cu, Fe, Li, Mg, Sr, Pb, As, Cd, Hg, and S of samples were determined by microwave digestion - inductively coupled plasma atomic emission spectrometry (ICP-AES. Meanwhile, Fourier transform infrared spectrometry (FTIR was used for the study of chemical group characteristic reactions after sulfur-fumigation. Results: The concentrations of Fe, Mg, Hg, and S elements showed significant differences between non-fumigated and sulfur-fumigated Fritillaria thunbergii Miq. The characteristic stretching vibrations of some groups in FTIR spectra, such as -OH, -S = O and -S-O, provided the identification basis for the discrimination of non-fumigated and sulfur-fumigated Fritillaria thunbergii Miq. Conclusion: The application of microwave digestion - ICP-AES was successfully used in combination with FTIR to authenticate and evaluate the quality of medicinal Fritillaria thunbergii Miq. Further applications of this technique should be explored.
Seeley, Kent W; Fertig, Alison R; Dufresne, Craig P; Pinho, Joao P C; Stevens, Stanley M
2014-04-14
The overproduction of reactive oxygen and nitrogen species (ROS and RNS) can have deleterious effects in the cell, including structural and possible activity-altering modifications to proteins. Peroxynitrite is one such RNS that can result in a specific protein modification, nitration of tyrosine residues to form nitrotyrosine, and to date, the identification of nitrotyrosine sites in proteins continues to be a major analytical challenge. We have developed a method by which 15N-labeled nitrotyrosine groups are generated on peptide or protein standards using stable isotope-labeled peroxynitrite (O15NOO-), and the resulting standard is mixed with representative samples in which nitrotyrosine formation is to be measured by mass spectrometry (MS). Nitropeptide MS/MS spectra are filtered using high mass accuracy Fourier transform MS (FTMS) detection of the nitrotyrosine immonium ion. Given that the nitropeptide pair is co-isolated for MS/MS fragmentation, the nitrotyrosine immonium ions (at m/z=181 or 182) can be used for relative quantitation with negligible isotopic interference at a mass resolution of greater than 50,000 (FWHM, full width at half-maximum). Furthermore, the standard potentially allows for the increased signal of nitrotyrosine-containing peptides, thus facilitating selection for MS/MS in a data-dependent mode of acquisition. We have evaluated the methodology in terms of nitrotyrosine site identification and relative quantitation using nitrated peptide and protein standards.
Kok, S J; Wold, C A; Hankemeier, Th; Schoenmakers, P J
2003-10-31
Two commercial liquid chromatography-Fourier-transform infrared spectroscopy interfaces (LC-FTIR), viz. a flow cell and a solvent-elimination interface have been assessed for use in size-exclusion chromatography (SEC) with respect to their chromatographic integrity (i.e. peak asymmetry, chromatographic resolution), quantitative and qualitative aspects. A polycarbonate/aliphatic polyester (PC/APE) blend and a polycarbonate-co-polydimethylsiloxane (PC-co-PDMS) copolymer were selected for the assessment. Both samples were successfully and selectively analyzed. The relatively large volume of the flow cell and the inherent deposition characteristics of the solvent-elimination interface led to a comparable decrease in the chromatographic resolution. The separation of oligomers was diminished in comparison with SEC-ultra-violet (UV). However, the peak asymmetry was not significantly affected by either interface. For both interfaces, a linear relationship was obtained for the FTIR response versus the injected concentration. The sensitivity was found to be higher for the solvent-elimination interface. For the current model compounds, the flow-cell interface detection limits are worse. However, the repeatability of flow-cell SEC-FTIR, evaluated by means of four SEC-FTIR analyses of polycarbonate, was considerably better than for solvent-elimination SEC-FTIR. This is probably due to the well-defined optical path length of the sample in the flow cell. By spectral subtraction, it was very well possible to obtain qualitative (functional group) information for compound identification also with flow-cell SEC-FTIR.
Unger, Miriam; Pfeifer, Frank; Siesler, Heinz W
2016-07-01
The main objective of this communication is to compare the performance of a miniaturized handheld near-infrared (NIR) spectrometer with a benchtop Fourier transform near-infrared (FT-NIR) spectrometer. Generally, NIR spectroscopy is an extremely powerful analytical tool to study hydrogen-bonding changes of amide functionalities in solid and liquid materials and therefore variable temperature NIR measurements of polyamide II (PAII) have been selected as a case study. The information content of the measurement data has been further enhanced by exploiting the potential of two-dimensional correlation spectroscopy (2D-COS) and the perturbation correlation moving window two-dimensional (PCMW2D) evaluation technique. The data provide valuable insights not only into the changes of the hydrogen-bonding structure and the recrystallization of the hydrocarbon segments of the investigated PAII but also in their sequential order. Furthermore, it has been demonstrated that the 2D-COS and PCMW2D results derived from the spectra measured with the miniaturized NIR instrument are equivalent to the information extracted from the data obtained with the high-performance FT-NIR instrument.
Institute of Scientific and Technical Information of China (English)
代秀迎; 郑建明; 陈斌
2011-01-01
In recent years, some incidents, which are from waste oils to trans fatty acids, were exposured frequently.There are a variety of problems about edible oils, and the traditional detecting method is difficult and time-consuming.The use of Fourier transform infrared spectroscopy in the study of edible oils is reviewed.This technique can characterise oils and fats and detect adulterations.At the same time, the application of spectroscopic data and chemometrics methods can rapidly determine trans- unsaturated fatty acids content, free fatty acids content, iodine value, average chain length or saponification number, as well as peroxide value.%近年来,食用植物油的问题越来越多,从地沟油到反式脂肪酸等一系列事件频繁曝光.而传统的检测方法费时费力,本文综述了傅立叶变换红外光谱在食用油分析上的应用.该技术可以对油脂进行分类和掺杂掺假检测,同时运用光谱数据和化学计量学方法还可以对食用油的反式不饱和脂肪酸含童、游离脂肪酸含童、碘值、皂化值及过氧化值等进行快速检测.
Leung Tang, Pik; Alqassim, Mohammad; Nic Daéid, Niamh; Berlouis, Leonard; Seelenbinder, John
2016-05-01
Concrete is by far the world's most common construction material. Modern concrete is a mixture of industrial pozzolanic cement formulations and aggregate fillers. The former acts as the glue or binder in the final inorganic composite; however, when exposed to a fire the degree of concrete damage is often difficult to evaluate nondestructively. Fourier transform infrared (FT-IR) spectroscopy through techniques such as transmission, attenuated total reflectance, and diffuse reflectance have been rarely used to evaluate thermally damaged concrete. In this paper, we report on a study assessing the thermal damage of concrete via the use of a nondestructive handheld FT-IR with a diffuse reflectance sample interface. In situ measurements can be made on actual damaged areas, without the need for sample preparation. Separate multivariate models were developed to determine the equivalent maximal temperature endured for three common industrial concrete formulations. The concrete mixtures were successfully modeled displaying high predictive power as well as good specificity. This has potential uses in forensic investigation and remediation services particularly for fires in buildings.
Directory of Open Access Journals (Sweden)
Vahid Bagheri
2014-11-01
Full Text Available This paper introduce a new data SONAR classification method based on Short-Time Fractional Fourier Transform (STFrFT analysis. The passive SONAR system receives the acoustic signals radiated by vessels and attempts to categorize them as a function of the similarities between vessels of the same class.Here, a time-frequency processing and feature extraction method is developed in order to improve the performance of a feedforwardneural network, which is used to classify five classes of vessels.Processing of time-varying signals in fractional fourier domain allows us to estimate the signal with higher concentration than conventional fourier domain, making the technique robust against additive noise, maintaining same computational complexity. With the purpose of dimension reduction and classification improvement, we use Linear Discriminant Analysis (LDA technique. The feasibility of the proposed technique (STFrFTLDA has been tested experimentally using a real database. The experimental results show the superiority of the proposed method
Fourier domain multispectral multiple scattering low coherence interferometry.
Matthews, Thomas E; Giacomelli, Michael G; Brown, William J; Wax, Adam
2013-12-01
We have implemented multispectral multiple scattering low coherence interferometry (ms2/LCI) with Fourier domain data collection. The ms2/LCI system is designed to localize features with spectroscopic contrast with millimeter resolution up to 1 cm deep in scattering samples by using photons that have undergone multiple low-angle (forward) scattering events. Fourier domain detection both increases the data acquisition speed of the system and gives access to rich spectroscopic information, compared to the previous single channel, time-domain implementation. Separate delivery and detection angular apertures reduce collection of the diffuse background signal in order to isolate localized spectral features from deeper in scattering samples than would be possible with traditional spectroscopic optical coherence tomography. Light from a supercontinuum source is used to acquire absorption spectra of chromophores in the visible range within a tissue-like scattering phantom. An intensity modulation and digital lock-in detection scheme is implemented to mitigate relative intensity and spectral noise inherent in supercontinuum sources. The technical parameters of the system and comparative analysis are presented.
Coherent Fourier scatterometry: tool for improved sensitivity in semiconductor metrology
Kumar, N.; El Gawhary, O.; Roy, S.; Kutchoukov, V. G.; Pereira, S. F.; Coene, W.; Urbach, H. P.
2012-03-01
Incoherent Optical Scatterometry (IOS) is a well-established metrology technique in the semiconductor industry to retrieve periodic grating structures with high accuracy from the signature of the diffracted optical far field. With shrinking dimensions in the lithography industry, finding possible improvements in wafer metrology is highly desirable. The grating is defined in terms of a finite number of geometrical shape parameters (height, side-wall angles, midCD etc.). In our method the illumination is a scanning focused spot from a spatially coherent source (laser) within a single period of the grating. We present a framework to study the increment in sensitivity of Coherent Fourier Scatterometry (CFS) with respect to the IOS. Under suitable conditions, there is a more than fourfold enhancement in sensitivity for grating shape parameters using CFS. The dependence of scanning positions on the sensitivity analysis is also highlighted. We further report the experimental implementation of a Coherent Fourier Scatterometer. The simulated and experimental far fields are compared and analyzed for the real noise in the experimental configuration.
The Fourier transform of tubular densities
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.
Resolution optimization with irregularly sampled Fourier data
International Nuclear Information System (INIS)
Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer–Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications. (paper)
Resolution optimization with irregularly sampled Fourier data
Ferrara, Matthew; Parker, Jason T.; Cheney, Margaret
2013-05-01
Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer-Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications.
Efficient single pixel imaging in Fourier space
Bian, Liheng; Suo, Jinli; Hu, Xuemei; Chen, Feng; Dai, Qionghai
2016-08-01
Single pixel imaging (SPI) is a novel technique capturing 2D images using a bucket detector with a high signal-to-noise ratio, wide spectrum range and low cost. Conventional SPI projects random illumination patterns to randomly and uniformly sample the entire scene’s information. Determined by Nyquist sampling theory, SPI needs either numerous projections or high computation cost to reconstruct the target scene, especially for high-resolution cases. To address this issue, we propose an efficient single pixel imaging technique (eSPI), which instead projects sinusoidal patterns for importance sampling of the target scene’s spatial spectrum in Fourier space. Specifically, utilizing the centrosymmetric conjugation and sparsity priors of natural images’ spatial spectra, eSPI sequentially projects two \\tfrac{π }{2}-phase-shifted sinusoidal patterns to obtain each Fourier coefficient in the most informative spatial frequency bands. eSPI can reduce requisite patterns by two orders of magnitude compared to conventional SPI, which helps a lot for fast and high-resolution SPI.
Turbulence on a Fractal Fourier Set.
Lanotte, Alessandra S; Benzi, Roberto; Malapaka, Shiva K; Toschi, Federico; Biferale, Luca
2015-12-31
A novel investigation of the nature of intermittency in incompressible, homogeneous, and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension D from the original three dimensional case to a strongly decimated system with D=2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set E(k)∼k(-5/3+3-D) explains the results. At small scales, the intermittency of the vorticity field is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D∼2.98. These effects must be connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism. PMID:26764993
基于快速傅里叶方法的地震前兆振幅谱分析%Analysis on earthquake precursor amplitude spectrum based on fast fourier method
Institute of Scientific and Technical Information of China (English)
戴勇; 高立新; 尹战军; 查斯; 杨彦明
2012-01-01
In this paper, the time series of geoelectrical resistivity, geomagnetism, earth deformation and gravity are processed with fast Fourier transform method, "FFT" for short. There are three main harmonics in daily mean data of the earth resistivity, recorded at Baochang and Wujiahe seismic stations. The harmonic with a period of approximately one year, has physical meaning. Different items in same geomagnetic station or same items in different geomagnetic stations, usually contain four main harmonics whose periods are 24, 12, 8 and 6 hours. Besides there exist tidal waves, there are different harmonics in the minute values recorded by horizontal pendulum tiltometer, water tube inclinometer, and gravimeter. It can be effective measuring the periods of noise precisely using FFT. But there are still many jobs to do in future, for example improving methods, the selection of data, explaining physical meaning of harmonic, etc.%利用FFT方法,对地电、地磁、形变及重力等前兆时间序列信号进行分析,结果显示,宝昌地震台及乌加河地震台地电两测向日均值时间序列存在3个主要谐波分量,其中周期近一年的分量物理意义明确.FFT方法在精确确定前兆时间序列中的干扰信息周期时具有较好的效果.
Institute of Scientific and Technical Information of China (English)
陈建君; 朱永; 刘波; 韦玮; 张洁; 王宁
2012-01-01
The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wavelength accuracy is approximately 1 ran and the sampling pcriod of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR.%提出了一种新型的基于可编程MEMS(micro-electro-mechanical systems)微镜的微型傅里叶变换红外光谱仪.该光谱仪采用可编程MEMS微镜和倾斜反射镜替代了传统傅里叶变换光谱仪的动镜系统.理论分析了该光谱仪的工作原理,并进行了计算机仿真,验证了该方法的可行性.结果表明,该光谱系统能够准确地还原光谱信息,其光谱分辨率在近红外区域小于5 nm,波长准确性约1nm,系统理论上的信号采集周期约50 ms.适合于利用阿达玛变换提高信噪比,可应用于微量物质检测.
[Using Fourier transform to calculate gas concentration in DOAS].
Liu, Qian-lin; Wang, Li-shi; Huang, Xin-jian; Wu, Yan-dan; Xiao, Ming-wei
2008-12-01
Being an analysis tool of high sensitivity, high resolution, multicomponents, real-time and fast monitoring, the differential optical absorption spectrometry (DOAS) is becoming a new method in atmosphere pollution monitoring. In the DOAS technique, many gases spectra have periodicity evidently, such as those from SO2, NO, NH3 and NO2. Aiming at three kinds of main air-polluted gases, i.e., SO2, NO and NO2 in atmosphere, the DOAS technique is used to monitor them, and Fourier transform is used to analyse the above-mentioned absorption spectra. Under the condition of Hanning Windows, Fourier transforma is used to process various gases spectra which have periodicity. In the process, the value of the characteristic frequency has a linearity relation to the gas concentration. So a new analysis method of DOAS is proposed, which is utilizing the relation between the value of the characteristic frequency and the gas concentration to deduce a linearity formula to calculate the gas concentration. So the value of the characteristic frequency can be used to get the gas concentration. For the gases with evident spectrum periodicity, such as SO2 and NO, this method is good. But for some gases with periodicity not evident, the error in the calculated concentration is beyond the allowable value. So in this method, the important process is frequency separation. It is also the main part in the future study. In a word, this method frees itself from the basic theory in the DOAS technique, cuts down on the process of the concentration calculation and the spectral analysis, and deserves further study. PMID:19248493
Institute of Scientific and Technical Information of China (English)
Chujun Zheng; Peng Han; Hongsen Chang
2006-01-01
@@ A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π,and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.
Two-dimensional fourier transform spectrometer
Energy Technology Data Exchange (ETDEWEB)
DeFlores, Lauren; Tokmakoff, Andrei
2016-10-25
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.
Phase information in coherent Fourier scatterometry
Kumar, N.; El Gawhary, O.; Roy, S.; Pereira, S. F.; Urbach, H. P.
2013-04-01
Incoherent Optical Scatterometry (IOS) is widely used in semiconductor industry in applications related to optical metrology particularly in grating reconstruction. Recently, Coherent Fourier Scatterometry (CFS) has emerged as a strong alternative to the traditional IOS under suitable condition. When available, phase information is an added advantage in CFS to complement the intensity data. Phase information in the scattered far field is dependent on the structure and the composition of the grating. We derive and discuss the phase information accessible through the CFS. Phase difference between the diffracted orders is computed and the polarization dependent phase sensitivity of the grating parameters are discussed. The results are rigorously simulated and an experimental implementation of CFS demonstrates the functionality of the method.
Fourier microscopy of single plasmonic scatterers
Sersic, Ivana; Koenderink, A Femius
2011-01-01
We report a new experimental technique for quantifying the angular distribution of light scattered by single plasmonic and metamaterial nanoscatterers, based on Fourier microscopy in a dark field confocal set up. This new set up is a necessary tool for quantifying the scattering properties of single plasmonic and meatamaterial building blocks, as well as small coupled clusters of such building blocks, which are expected to be the main ingredients of nano-antennas, light harvesting structures and transformation optics. We present a set of measurements on Au nanowires of different lengths and show how the radiation pattern of single Au nanowires evolve with wire length and as a function of driving polarization and wave vector.
Two-dimensional fourier transform spectrometer
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.
Model of computation for Fourier optical processors
Naughton, Thomas J.
2000-05-01
We present a novel and simple theoretical model of computation that captures what we believe are the most important characteristics of an optical Fourier transform processor. We use this abstract model to reason about the computational properties of the physical systems it describes. We define a grammar for our model's instruction language, and use it to write algorithms for well-known filtering and correlation techniques. We also suggest suitable computational complexity measures that could be used to analyze any coherent optical information processing technique, described with the language, for efficiency. Our choice of instruction language allows us to argue that algorithms describable with this model should have optical implementations that do not require a digital electronic computer to act as a master unit. Through simulation of a well known model of computation from computer theory we investigate the general-purpose capabilities of analog optical processors.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
Efficient Two-Comb Fourier Spectroscopy
Mandon, Julien; Picqué, Nathalie
2008-01-01
Molecular fingerprinting through absorption spectroscopy is a powerful analytical method. Wide spectral ranges are explored with Doppler-limited resolution. Fast data acquisition, accurate measurements of frequency, intensity, and line shape; time-resolved, selective spectra are achieved with excellent sensitivities. However, presently spectrometers are unable to provide all these features at once. Here we show that, based on frequency comb lasers, a spectrometer may overcome this difficulty. We have recorded two series of spectra with a 1.5 $\\mu$m Cr:YAG frequency comb. In the first series, we propose to use the comb structure to considerably improve the recording time and signal to noise ratio of Doppler-resolved spectra, (Fourier Transform (FT) of the beating signatures of two combs issued from the same initial laser). The second series demonstrates that under very simple experimental conditions, FT spectroscopists may record much more sensitive spectra than with the usual incoherent white light source. We...
Spectral/Fourier Domain Optical Coherence Tomography
de Boer, Johannes F.
Optical coherence tomography is a low-coherence interferometric method for imaging of biological tissue [1, 2]. For more than a decade after its inception between 1988 and 1991, the dominant implementation has been time domain OCT (TD-OCT), in which the length of a reference arm is rapidly scanned. The first spectral or Fourier domain OCT (SD/FD-OCT) implementation was reported in 1995 [3]. In SD-OCT the reference arm is kept stationary, and the depth information is obtained by a Fourier transform of the spectrally resolved interference fringes in the detection arm of a Michelson interferometer. This approach has provided a significant advantage in signal-to-noise ratio (SNR), which despite reports as early as 1997 [4, 5] has taken about half a decade to be recognized fully by the OCT community in 2003 [6-8]. The first demonstration of SD-OCT for in vivo retinal imaging in 2002 [9] was followed by a full realization of the sensitivity advantage by video rate in vivo retinal imaging [10], including high-speed 3-D volumetric imaging [11], ultrahigh-resolution video rate imaging [12, 13], and Doppler blood flow determination in the human retina [14, 15]. The superior sensitivity of SD-OCT, combined with the lack of need for a fast mechanical scanning mechanism, has opened up the possibility of much faster scanning without loss of image quality and provided a paradigm shift from point sampling to volumetric mapping of biological tissue in vivo. The technology has been particularly promising for ophthalmology [16, 17]. In this chapter, the principles and system design considerations of SD-OCT will be discussed in more detail.