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Showing papers on "Fourier transform published in 1995"


Book
01 Jan 1995
TL;DR: In this article, the authors present a general approach and the Kernel Method for reduced interference in the representation of signal signals, which is based on the Wigner distribution and the characteristic function operator.
Abstract: 1. The Time and Frequency Description of Signals. 2. Instantaneous Frequency and the Complex Signal. 3. The Uncertainty Principle. 4. Densities and Characteristic Functions. 5. The Need for Time-Frequency Analysis. 6. Time-Frequency Distributions: Fundamental Ideas. 7. The Short-Time Fourier Transform. 8. The Wigner Distribution. 9. General Approach and the Kernel Method. 10. Characteristic Function Operator Method. 11. Kernel Design for Reduced Interference. 12. Some Distributions. 13. Further Developments. 14. Positive Distributions Satisfying the Marginals. 15. The Representation of Signals. 16. Density of a Single Variable. 17. Joint Representations for Arbitrary Variables. 18. Scale. 19. Joint Scale Representations. Bibliography. Index.

2,951 citations


Journal ArticleDOI
TL;DR: A new optical encoding method of images for security applications is proposed and it is shown that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.
Abstract: We propose a new optical encoding method of images for security applications. The encoded image is obtained by random-phase encoding in both the input and the Fourier planes. We analyze the statistical properties of this technique and show that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.

2,361 citations


BookDOI
26 Dec 1995
TL;DR: In this article, the authors present an algebraic version of elementary mathematics proofs without words, including the concept of special numbers and the notion of numbers without words in elementary algebra.
Abstract: Numbers and Elementary Mathematics Proofs without words Constants Special numbers Number theory Series and products Algebra Elementary algebra Polynomials Vector algebra Linear and matrix algebra Abstract algebra Discrete Mathematics Set theory Combinatorics Graphs Combinatorial design theory Difference equations Geometry Euclidean geometry Coordinate systems in the plane Plane symmetries or isometries Other transformations of the plane Lines Polygons Surfaces of revolution: the torus Quadrics Spherical geometry and trigonometry Conics Special plane curves Coordinate systems in space Space symmetries or isometries Other transformations of space Direction angles and direction cosines Planes Lines in space Polyhedra Cylinders Cones Differential geometry Analysis Differential calculus Differential forms Integration Table of indefinite integrals Table of definite integrals Ordinary differential equations Partial differential equations Integral equations Tensor analysis Orthogonal coordinate systems Interval analysis Real analysis Generalized functions Complex analysis Special Functions Ceiling and floor functions Exponentiation Logarithmic functions Exponential function Trigonometric functions Circular functions and planar triangles Tables of trigonometric functions Angle conversion Inverse circular functions Hyperbolic functions Inverse hyperbolic functions Gudermannian function Orthogonal polynomials Gamma function Beta function Error functions Fresnel integrals Sine, cosine, and exponential integrals Polylogarithms Hypergeometric functions Legendre functions Bessel functions Elliptic integrals Jacobian elliptic functions Clebsch-Gordan coefficients Integral transforms: Preliminaries Fourier integral transform Discrete Fourier transform (DFT) Fast Fourier transform (FFT) Multidimensional Fourier transforms Laplace transform Hankel transform Hartley transform Mellin transform Hilbert transform Z-Transform Tables of transforms Probability and Statistics Probability theory Classical probability problems Probability distributions Queuing theory Markov chains Random number generation Control charts and reliability Statistics Confidence intervals Tests of hypotheses Linear regression Analysis of variance (ANOVA) Sample size Contingency tables Probability tables Scientific Computing Basic numerical analysis Numerical linear algebra Numerical integration and differentiation Mathematical Formulae from the Sciences Acoustics Astrophysics Atmospheric physics Atomic physics Basic mechanics Beam dynamics Classical mechanics Coordinate systems - Astronomical Coordinate systems - Terrestrial Earthquake engineering Electromagnetic transmission Electrostatics and magnetism Electronic circuits Epidemiology Finance Fluid mechanics Fuzzy logic Human body Image processing matrices Macroeconomics Modeling physical systems Optics Population genetics Quantum mechanics Quaternions Relativistic mechanics Solid mechanics Statistical mechanics Thermodynamics Miscellaneous Calendar computations Cellular automata Communication theory Control theory Computer languages Cryptography Discrete dynamical systems and chaos Electronic resources Elliptic curves Financial formulae Game theory Knot theory Lattices Moments of inertia Music Operations research Recreational mathematics Risk analysis and decision rules Signal processing Symbolic logic Units Voting power Greek alphabet Braille code Morse code List of References List of Figures List of Notation Index

656 citations


Journal ArticleDOI
TL;DR: This survey presents a unified and essentially self-contained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the average-case analysis of algorithms using the Mellin transform, a close relative of the integral transforms of Laplace and Fourier.

603 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a method for extracting eigenvalues and eigen states of a given operator at any desired energy range, where correlation between distant eigenstates through a short-time filter is eliminated by diagonalization.
Abstract: In a previous paper we developed a method, Filter‐Diagonalization, for extracting eigenvalues and eigenstates of a given operator at any desired energy range. In essence, the method eliminates correlation between distant eigenstates through a short‐time filter while correlations between closely lying states are eliminated by diagonalization. Here we extend Filter‐Diagonalization. When used to extract eigenvalues for a given operator H, we show that all eigenvalue information is directly extracted from a short segment of the correlation functionC(t)=(ψ(0)‖e −iHt ‖ψ(0)), or alternately from a small number of residues (ψ(0)‖R n (H)‖ψ(0)), where ψ(0) is a random initial function and R n (H) is any desired polynomial expansion in H. The implications of this feature are twofold. First, in contrast to the previous version the wave packet needs only to be propagated once (to prepare C(t)), and eigenstates at all desired energy windows can then be extracted with negligible extra computation time (and negligible storage requirements). In a simulation presented here, accurate eigenvalues are extracted using propagation times which are only a 0.0041 fraction of the ‘‘natural’’ time, i.e., the time by which the relative phase of the two closest eigenstates reaches 2π. The second and more important feature is that the method is automatically suitable for extracting eigenvalues (or normal modes) using a short‐time segment of any signal C(t) which is a sum of (unknown) Fourier components (C(t)=∑ nd ne −ie nt ) regardless of its origin. In addition to its use for determining eigenvalues of known operators, the method may also be utilized to extract normal modes from classical‐dynamics simulations, eigenstates from real‐time Quantum Monte‐Carlo studies, frequencies from experimental optical or electrical signals, or be utilized in any other circumstance where a correlation function or general signal is only known for short times (or expensive to generate at long times).

502 citations


Journal ArticleDOI
TL;DR: The proposed chirplets are generalizations of wavelets related to each other by 2-D affine coordinate transformations in the time-frequency plane, as opposed to wavelets, which are related to Each other by 1-D affirmations in thetime domain only.
Abstract: We consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis. We propose the use of quadratic chirp functions (which we will call q-chirps for short), giving rise to a parameter space that includes both the time-frequency plane and the time-scale plane as 2-D subspaces. The parameter space contains a "time-frequency-scale volume" and thus encompasses both the short-time Fourier transform (as a slice along the time and frequency axes) and the wavelet transform (as a slice along the time and scale axes). In addition to time, frequency, and scale, there are two other coordinate axes within this transform space: shear in time (obtained through convolution with a q-chirp) and shear in frequency (obtained through multiplication by a q-chirp). Signals in this multidimensional space can be obtained by a new transform, which we call the "q-chirplet transform" or simply the "chirplet transform". The proposed chirplets are generalizations of wavelets related to each other by 2-D affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets, which are related to each other by 1-D affine coordinate transformations (translations and dilations) in the time domain only.

460 citations


Journal ArticleDOI
TL;DR: An experimental comparison of shape classification methods based on autoregressive modeling and Fourier descriptors of closed contours shows better performance of Fourier-based methods, especially for images containing noise.
Abstract: An experimental comparison of shape classification methods based on autoregressive modeling and Fourier descriptors of closed contours is carried out. The performance is evaluated using two independent sets of data: images of letters and airplanes. Silhouette contours are extracted from non-occluded 2D objects rotated, scaled, and translated in 3D space. Several versions of both types of methods are implemented and tested systematically. The comparison clearly shows better performance of Fourier-based methods, especially for images containing noise. >

415 citations


Journal ArticleDOI
TL;DR: An explicit approximation of the Fourier Transform of generalized functions of functions with singularities based on projecting such functions on a subspace of Multiresolution Analysis is obtained and a fast algorithm based on its evaluation is developed.

359 citations


Journal ArticleDOI
TL;DR: In this article, an exact polynomial expansion of the operator [E−(H+Γ)−1, Γ being a simple complex optical potential, was shown to converge uniformly in the real energy domain.
Abstract: The new recently introduced [J. Chem. Phys 102, 7390 (1995)] empirical recursion formula for the scattering solution is here proved to yield an exact polynomial expansion of the operator [E−(H+Γ)]−1, Γ being a simple complex optical potential. The expansion is energy separable and converges uniformly in the real energy domain. The scaling of the Hamiltonian is trivial and does not involve complex analysis. Formal use of the energy‐to‐time Fourier transform of the ABC (absorbing boundary conditions) Green’s function leads to a recursion polynomial expansion of the ABC time evolution operator that is global in time. Results at any energy and any time can be accumulated simultaneously from a single iterative procedure; no actual Fourier transform is needed since the expansion coefficients are known analytically. The approach can be also used to obtain a perturbation series for the Green’s function. The new iterative methods should be of a great use in the area of the reactive scattering calculations and o...

307 citations


Journal ArticleDOI
01 Jun 1995-Lethaia
TL;DR: Elliptic Fourier shape analysis is a powerful, though underutilized, biometric tool that is particularly suited for the description of fossils lacking many homologous landmarks, such as several common bivalve groups as discussed by the authors.
Abstract: Elliptic Fourier shape analysis is a powerful, though under-utilized, biometric tool that is particularly suited for the description of fossils lacking many homologous landmarks, such as several common bivalve groups. The method is conceptually more parsimonious than more traditional biometric methods based on discrete linear and angular measurements. Most importantly, however, shape analysis captures a much higher proportion of the morphological information resident in any fossil than analyses based on discrete measurements. The number of harmonics required in an elliptic Fourier analysis can be estimated from a series of inverse Fourier reconstructions, or from the power spectrum. In most studies it is appropriate to normalize Fourier coefficients for size, although this information can be reincorporated at a later stage. The coefficients should probably not be standardized, unless there is evidence to suggest that high-frequency information was genetically as important as low-frequency information. Depending upon the aims of a particular study and the morphological disparity of the fossils in question, it might be appropriate to eliminate the first harmonic (‘best-fitting’) ellipse from an analysis. Meaningful comparison of the left and right valves of bivalves requires the digitized coordinates of one or other to be mirrored prior to computation of the Fourier coefficients. □Biometric analysis, Bivalvia, elliptic Fourier analysis, morphometrics.

302 citations


Journal ArticleDOI
TL;DR: It is shown that the eigenmodes for electromagnetic waves in an inhomogeneous dielectric medium can be obtained with an algorithm that scales linearly with the size of the system, using discretization of the Maxwell equations in both the spatial and the time domain.
Abstract: We show that the eigenmodes for electromagnetic waves in an inhomogeneous dielectric medium can be obtained with an algorithm that scales linearly with the size of the system. The method employs discretization of the Maxwell equations in both the spatial and the time domain and the integration of the Maxwell equations in the time domain. The spectral intensity can then be obtained by a Fourier transform. We applied the method to a few problems of current interest, including the photonic band structure of a periodic dielectric structure, the effective dielectric constants of some three-dimensional and two-dimensional systems, and the defect states of a periodic dielectric structure with structural defects.

Journal ArticleDOI
TL;DR: In this paper, the amplitude distributions of light on two spherical surfaces of given radii and separation are modeled as a process of continual fractional Fourier transform transformation, where the amplitude distribution evolves through fractional transforms of increasing order.
Abstract: There exists a fractional Fourier-transform relation between the amplitude distributions of light on two spherical surfaces of given radii and separation. The propagation of light can be viewed as a process of continual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through fractional transforms of increasing order. This result allows us to pose the fractional Fourier transform as a tool for analyzing and describing optical systems composed of an arbitrary sequence of thin lenses and sections of free space and to arrive at a general class of fractional Fourier-transforming systems with variable input and output scale factors.

Proceedings ArticleDOI
07 Nov 1995
TL;DR: An overview to the theory of wavelets and its application to communication problems is provided and two examples are discussed: using wavelets as a design tool to bridge time and frequency analysis in multiple access communication systems.
Abstract: Wavelets are being utilized in various communications applications either as an alternative to short-time Fourier transform for spectral analysis of non-stationary data or as a new tool to bridge between time domain and frequency domain analysis. The article provides an overview to the theory of wavelets and its application to communication problems. We discuss two examples. One involves using wavelets as a design tool to bridge time and frequency analysis in multiple access communication systems. The other involves using wavelets in transform domain excision in spread spectrum communication. For a detailed study of wavelets and their many uses in signal representation, bandwidth compression, clutter suppression, recognition, and multiresolution signal processing the readers are referred to a number of excellent review articles and references on this subject.

Journal ArticleDOI
TL;DR: In this paper, the authors derived figures of merit for image quality on the basis of the performance of mathematical observers on specific detection and estimation tasks, which were based on the Fisher information matrix relevant to estimation of the Fourier coefficients and closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford.
Abstract: Figures of merit for image quality are derived on the basis of the performance of mathematical observers on specific detection and estimation tasks. The tasks include detection of a known signal superimposed on a known background, detection of a known signal on a random background, estimation of Fourier coefficients of the object, and estimation of the integral of the object over a specified region of interest. The chosen observer for the detection tasks is the ideal linear discriminant, which we call the Hotelling observer. The figures of merit are based on the Fisher information matrix relevant to estimation of the Fourier coefficients and the closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford [Phys. Med. Biol. 39, 451 (1994)]. A finite submatrix of the infinite Fisher information matrix is used to set Cramer-Rao lower bounds on the variances of the estimates of the first N Fourier coefficients. The figures of merit for detection tasks are shown to be closely related to the concepts of noise-equivalent quanta (NEQ) and generalized NEQ, originally derived for linear, shift-invariant imaging systems and stationary noise. Application of these results to the design of imaging systems is discussed.

Journal ArticleDOI
H. Schomberg1, J. Timmer
TL;DR: The authors explore a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f;, which provides a fast and accurate alternative to the filtered backprojection.
Abstract: The authors explore a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f/spl circ/. The method involves a window function w/spl circ/ and proceeds in three steps. First, the convolution g/spl circ/=w/spl circ/*f/spl circ/ is computed numerically on a Cartesian grid, using the available samples of f/spl circ/. Then, g=wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w/spl circ/*f/spl circ/ is much less error prone than merely interpolating f/spl circ/. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform. >

Journal ArticleDOI
TL;DR: In this article, a diffuse reflectance mid-infrared Fourier transform spectroscopy (DRIFTS) method is described for obtaining high quality Fourier Transform infrared (FTIR) spectra of cements.

Journal ArticleDOI
TL;DR: In this article, a numerical formulation for three-dimensional elastodynamic problems of fracture on planar cracks and faults is presented, where stress and displacement components are given a spectral representation as finite Fourier series in space coordinates parallel to the fracture plane.
Abstract: We present a numerical formulation for three-dimensional elastodynamic problems of fracture on planar cracks and faults. Stress and displacement components are given a spectral representation as finite Fourier series in space coordinates parallel to the fracture plane. The formulation is based on an exact representation, involving a convolution integral for each Fourier mode, of the elastodynamic relation existing between the time-dependent Fourier coefficients for the tractions acting on the fracture plane and for the resulting displacement discontinuities. A wide range of constitutive models can be used to relate the local value of the strength on the fracture plane with the displacement and velocity history. Efficiency of the code is achieved by using an explicit time integration scheme and by computing the conversion between the spatial and spectral distributions through a FFT algorithm. The method is particularly suited to implementation on massively parallel computers; a CM-5 was used in this work. The stability and precision of the formulation are discussed for tensile (mode 1) situations in a detailed modal analysis, and numerical results are compared with existing three-dimensional elastodynamic solutions. The adequacy of the method to investigate various three-dimensional dynamic fracture problems involving non-propagating and propagating tensile cracks is illustrated, including crack growth along a plane of heterogeneous fracture toughness.

Journal ArticleDOI
TL;DR: The specular and nonspecular intensity of x rays scattered from a rough surface with fluctuations in the electron density is calculated in the distorted-wave Born approximation and special geometries of density fluctuations are discussed.
Abstract: The specular and nonspecular intensity of x rays scattered from a rough surface with fluctuations in the electron density is calculated in the distorted-wave Born approximation. The contributions to the nonspecular intensity of roughness and density fluctuations can be separated. The structure factor is given by a convolution integral of the Fourier transform of the density correlation function. Special geometries of density fluctuations are discussed.

Journal ArticleDOI
TL;DR: In this article, Fourier analysis of phase shift algorithms is used to predict measurement errors as a function of the frequency, the phase, and the amplitude of the vibrations in phase shift interferometry.
Abstract: Unexpected mechanical vibrations can significantly degrade the otherwise high accuracy of phase-shifting interferometry. Fourier analysis of phase-shift algorithms is shown to provide the analytical means of predicting measurement errors as a function of the frequency, the phase, and the amplitude of vibrations. The results of this analysis are concisely represented by a phase-error transfer function, which may be multiplied by the noise spectrum to predict the response of an interferometer to various forms of vibration. Analytical forms for the phase error are derived for several well-known algorithms, and the results are supported by numerical simulations and experiments with an interference microscope.

Journal ArticleDOI
TL;DR: Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo.
Abstract: Describes how two-dimensional (2D) homomorphic deconvolution can be used to improve the lateral and radial resolution of medical ultrasound images recorded by a sector scanner. The recorded radio frequency ultrasound image in polar coordinates is considered as a 2D sequence of angle and depth convolved with a 2D space invariant point-spread function (PSF). Each polar coordinate sequence is transformed into the 2D complex cepstrum domain using the fast Fourier transform for Cartesian coordinates. The low-angle and low-depth portion of this sequence is taken as an estimate of the complex cepstrum representation of the PSF. It is transformed back to the Fourier frequency domain and is used to compute the deconvolved angle and depth sequence by 2D Wiener filtering. Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo. It was better than lateral or radial homomorphic deconvolution alone, and better than 2D Wiener filtering with a PSF recorded in vitro. >

Journal ArticleDOI
TL;DR: In this paper, a time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe the transient electromagnetic scattering from a perfectly conducting, arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront.
Abstract: A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a perfectly conducting, arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront. This TD-UTD impulse response is obtained by a Fourier inversion of the corresponding frequency domain UTD solution. An analytic signal representation of the transient fields is used because it provides a very simple procedure to avoid the difficulties that result when inverting frequency domain UTD fields associated with rays that traverse line or smooth caustics. The TD-UTD response to a more general transient wave excitation of the wedge may be found via convolution. A very useful representation for modeling a general pulsed astigmatic wave excitation is also developed which, in particular, allows its convolution with the TD-UTD impulse response to be done in closed form. Some numerical examples illustrating the utility of these developments are presented.

Journal ArticleDOI
TL;DR: An analysis of the 2-D Fourier transform of the modified sinogram reveals that all previously-proposed linear methods can be interpreted as special cases of a broad class of methods, and that each method in the class can be implemented, in principle, by any one of four distinct techniques.
Abstract: Exact methods of inverting the two-dimensional (2-D) exponential Radon transform have been proposed by Bellini et al. (1979) and by Inouye et al. (1989), both of whom worked in the spatial-frequency domain to estimate the 2-D Fourier transform of the unattenuated sinogram; by Hawkins et al. (1988), who worked with circularly harmonic Bessel transforms; and by Tretiak and Metz (1980), who followed filtering of appropriately-modified projections by exponentially-weighted backprojection. With perfect sampling, all four of these methods are exact in the absence of projection-data noise, but empirical studies have shown that they propagate noise differently, and no underlying theoretical relationship among the methods has been evident. Here, an analysis of the 2-D Fourier transform of the modified sinogram reveals that all previously-proposed linear methods can be interpreted as special cases of a broad class of methods, and that each method in the class can be implemented, in principle, by any one of four distinct techniques. Moreover, the analysis suggests a new member of the class that Is predicted to have noise properties better than those of previously-proposed members.

Journal ArticleDOI
TL;DR: The design principle of a single-mode arrayed-waveguide grating multiplexer with flat spectral response is proposed on the basis of a discrete Fourier transform to obtain a flat spectral region over 57.2 GHz for 100-GHz channel spacing.
Abstract: The design principle of a single-mode arrayed-waveguide grating multiplexer with flat spectral response is proposed on the basis of a discrete Fourier transform. By a beam propagation-method simulation, a flat spectral region (within 1-dB loss increase) is obtained over 57.2 GHz for 100-GHz channel spacing.

01 Jan 1995
TL;DR: This dissertation considers the identication of linear multivariable systems using finite dimensional time-invariant state-space models using vibrational analysis of mechanical structures and introduces a new model quality measure, Modal Coherence Indicator, and new multivariables frequency domain identification algorithms.
Abstract: This dissertation considers the identication of linear multivariable systems using finite dimensional time-invariant state-space models.Parametrization of multivariable state-space models is considered. A full parametrization, where all elements in the state-space matrices are parameters, is introduced. A model structure with full parametrization gives two important implications; low sensitivity realizations can be used and the structural issues of multivariable canonical parametrizations are circumvented. Analysis reveals that additional estimated parameters do not increase the variance of the transfer function estimate if the resulting model class is not enlarged.Estimation and validation issues for the case of impulse response data are discussed. Identication techniques based on realization theory are linked to the prediction error method. The combination of these techniques allows for the estimation of high quality models for systems with many oscillative modes. A new model quality measure, Modal Coherence Indicator, is introduced. This indicator gives an independent quality tag for each identified mode and provides information useful for model validation and order estimation.Two applications from the aircraft and space industry are considered. Both problems are concerned with vibrational analysis of mechanical structures. The first application is from an extensive experimental vibrational study of the airframe structure of the Saab 2000 commuter aircraft. The second stems from vibrational analysis of a launcher-satellite separation system. In both applications multi-output discrete time state-space models are estimated, which are then used to derive resonant frequencies and damping ratios.New multivariable frequency domain identification algorithms are also introduced. Assuming primary data consist of uniformly spaced frequency response measurements, an identification algorithm based on realization theory is derived. The algorithm is shown to be robust against bounded noise as well as being consistent. The resulting estimate is shown to be asymptotically normal, and an explicit variance expression is determined. If data originate from an infinite dimensional system, it is shown that the estimated transfer function converges to the transfer function of the truncated balanced realization.Frequency domain subspace based algorithms are also derived and analyzed when the data consist of samples of the Fourier transform of the input and output signals. These algorithms are the frequency domain counterparts of the time domain subspace based algorithms.The frequency domain identification methods developed are applied to measured frequency data from a mechanical truss structure which exhibits many lightly damped oscillative modes. With the new methods, high quality state-space models are estimated both in continuous and discrete time.

Journal ArticleDOI
TL;DR: In this paper, a new approach to measuring fabric appearance objectively using image processing techniques by Fourier trans-fusion trans-foils has been proposed, based on the Fourier transform.
Abstract: Protruding yarns influence a fabric's properties and its end use. This paper discusses a new approach to measuring fabric appearance objectively using image processing techniques by Fourier transfo...


Journal ArticleDOI
TL;DR: A continuum of “fractional” domains making arbitrary angles with the time and frequency domains is considered, derived by the fractional Fourier transform, to derive transformation, commutation, and uncertainty relations among coordinate multiplication, differentiation, translation, and phase shift operators between domains making arbitrarily angles with each other.

Book
31 Jul 1995
TL;DR: In this paper, the convergence rate of Fourier series and best approximations in the spaces Lp and Lp are presented. But they do not consider the problem of approximating functions and their derivatives by Fourier sums.
Abstract: Preface. Introduction. 1. Classes of periodic functions. 2. Integral representations of deviations of linear means of Fourier series. 3. Approximations by Fourier sums in the spaces c and L1. 4. Simultaneous approximation of functions and their derivatives by Fourier sums. 5. Convergence rate of Fourier series and best approximations in the spaces Lp. 6. Best approximations in the spaces C and L. Bibliographical notes. References. Index.

Proceedings ArticleDOI
09 May 1995
TL;DR: The optimal fractional Fourier domain filter is derived that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel.
Abstract: The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum mean square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.

Book
01 Jan 1995
TL;DR: In this article, a survey of electromagnetic computational methods is presented, including the conjugate gradient fast Fourier transform (CG-FFT) method, and the generalized biconjugate gradient method.
Abstract: Part 1 Introduction to the conjugate gradient fast Fourier transform (CG-FFT) method: brief survey of electromagnetic computational methods CG methods Toeplitz symmetries and the CG-FFT method. Part 2 Fourier transforms: discrete Fourier transform (DFT) continuous Fourier transform (CFT). Part 3 Static problems: formulating a one-dimensional continuous convolutional problem for individual structures discretization of the continuous EPP discretization of periodic problems spectral domain discretization of problems involving individual structures. Part 4 Conjugate gradient algorithms: integral equation formulation of electromagnetic problems the method of moments solution of the integral equation iterative solutions of the integral equation conjugate gradient methods the generalized biconjugate gradient method examples of convergence rates. Part 5 Arbitrary flat conducting plates: formulation of the problem discretization process discretization of the integral equation results for induced current applications to radiation and scattering problems. Part 6 Three-dimensional bodies: discretization process discretization of the integral equation, resolution of the operator, and final results results for induced equivalent currents application to radiation and scattering problems. Part 7 Problems formulated in terms of systems of integral equations: formulation of the continuous SIE discretization of the SIE. Part 8 Metallic surfaces that conform to bodies of revolution: integral equation surfaces that conform to cylinders surfaces that conform to arbitrary BORs. Part 9 Flat periodic structures: direct and reciprocal lattices Floquet's Theorem MPIE formulation for periodic structures discretization process completing the discretization in the spectral domain operational form of the MPIE reflection and transmission coefficients. Part 10 Flat periodic structures in multilayer media: integral equation in the spectral domain discretization process some numerical results and applications. Part 11 Finite-sized conducting patches in multilayer media: formulation of the problem formulation of the equivalent continuous operator equation computation of the windowed Green's function some results for induced currents application to scattering problems application to S-parameter analysis of open microstrip structures. Part 12 Volumetric analysis of 3D bodies that are periodic in one direction: formulation of the continuous operator equation for a VODIPEB formulation of the discrete operator equation computation of convolutional integrals using FFT results.