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Fourier Coefficients (fourier + coefficient)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Subsampling in testing autocovariance for periodically correlated time series

JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2008
Ukasz Lenart
Abstract., The main purpose of this article was to describe the asymptotic properties of subsampling procedure applied to nonstationary, periodically correlated time series. We present the conditions under which the subsampling version for the estimator of Fourier coefficient of autocovariance function is consistent. Our result provides new tools in statistical inference methods for nonstationary, periodically correlated time series. For example, it enables to construct consistent subsampling test which successfully distinguishes the period of the series. [source]

Using form analysis techniques to improve photogrammetric mass-estimation methods

MARINE MAMMAL SCIENCE, Issue 1 2008
Kelly M. Proffitt
Abstract Numerical characterization of animal body forms using elliptical Fourier decomposition may be a useful analytic technique in a variety of marine mammal investigations. Using data collected from the Weddell seal (Leptonychotes weddellii), we describe the method of body form characterization using elliptical Fourier analysis and demonstrated usefulness of the technique in photogrammetric mass-estimation modeling. We compared photogrammetric mass-estimation models developed from (1) standard morphometric measurement covariates, (2) elliptical Fourier coefficient covariates, and (3) a combination of morphometric and Fourier coefficient covariates and found that mass-estimation models employing a combination of morphometric measurements and Fourier coefficients outperformed models containing only one covariate type. Inclusion of Fourier coefficients in photogrammetric mass-estimation models employing standard morphometric measurements reduced the width of the prediction interval by 24.4%. Increased precision of photogrammetric mass-estimation models employing Fourier coefficients as model covariates may expand the range of ecological questions that can be addressed with estimated mass measurements. [source]

Reconstructing small perturbations of scatterers from electric or acoustic far-field measurements

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2008
Mikyoung Lim
Abstract In this paper, we consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown scatterer boundary is a small perturbation of a circle, we develop a linearized relationship between the far-field data and the shape of the object. This relationship is used to find the Fourier coefficients of the perturbation of the shape. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Fast direct solver for Poisson equation in a 2D elliptical domain

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004
Ming-Chih Lai
Abstract In this article, we extend our previous work M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56,68, 2002 for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution as a truncated Fourier series, then solving the differential equations of Fourier coefficients by finite difference discretizations. Using a grid by shifting half mesh away from the pole and incorporating the derived numerical boundary value, the difficulty of coordinate singularity can be elevated easily. Unlike the case of 2D disk domain, the present difference equation for each Fourier mode is coupled with its conjugate mode through the numerical boundary value near the pole; thus, those two modes are solved simultaneously. Both second- and fourth-order accurate schemes for Dirichlet and Neumann problems are presented. In particular, the fourth-order accuracy can be achieved by a three-point compact stencil which is in contrast to a five-point long stencil for the disk case. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 72,81, 2004 [source]

Fast direct solvers for Poisson equation on 2D polar and spherical geometries

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2002
Ming-Chih Lai
Abstract A simple and efficient class of FFT-based fast direct solvers for Poisson equation on 2D polar and spherical geometries is presented. These solvers rely on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the second- and fourth-order finite difference discretizations. Using a grid by shifting half mesh away from the origin/poles, and incorporating with the symmetry constraint of Fourier coefficients, the coordinate singularities can be easily handled without pole condition. By manipulating the radial mesh width, three different boundary conditions for polar geometry including Dirichlet, Neumann, and Robin conditions can be treated equally well. The new method only needs O(MN log2N) arithmetic operations for M × N grid points. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 56,68, 2002 [source]

How well does the finite Fourier transform approximate the Fourier transform?,

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2005
Charles L. Epstein
We show that the answer to the question in the title is "very well indeed." In particular, we prove that, throughout the maximum possible range, the finite Fourier coefficients provide a good approximation to the Fourier coefficients of a piecewise continuous function. For a continuous periodic function, the size of the error is estimated in terms of the modulus of continuity of the function. The estimates improve commensurately as the functions become smoother. We also show that the partial sums of the finite Fourier transform provide essentially as good an approximation to the function and its derivatives as the partial sums of the ordinary Fourier series. Along the way we establish analogues of the Riemann-Lebesgue lemma and the localization principle. © 2004 Wiley Periodicals, Inc. [source]