منابع مشابه
Rational Transform Approximation via the Laguerre Spectrum
In t roduc t ion An important class of functions from the point of view of signal representation and approximation is the class with n th order rational Laplace transforms. These functions arise naturally in such fields as model identification and timedomain synthesis. The problem of finding the best n th order rational function to represent a given time function is, therefore, important; unfor...
متن کاملThe discrete Laguerre transform: derivation and applications
The discrete Laguerre transform (DLT) belongs to the family of unitary transforms known as Gauss-Jacobi transforms. Using classical methodology, the DLT is derived from the orthonormal set of Laguerre functions. By examining the basis vectors of the transform matrix, the types of signals that can be best represented by the DLT are determined. Simulation results are used to compare the DLT's e e...
متن کاملThe Laguerre Transform , Part I : Theory
THE LAGUERRE TRANSFORM, PART I : THEORY Ushio Sum ita University of Rochester Masaaki Kijima Tokyo Institute of Technology (Received June 8,1987; Revised March 3,1988) The Laguerre transform, introduced by Keilson and Nunn (1979), Keilson, Nunn and Sumita (1981) and further studied by Sumita (1981), provides an algorithmic framework for the computer evaluation of repeated combinations of contin...
متن کاملFourier-Laguerre transform, convolution and wavelets on the ball
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...
متن کاملThe Hilbert Transform Ofthe Generalized Laguerre and Hermiteweight Functions
Explicit formulae are given for the Hilbert transform Z R ? w(t)dt=(t ? x), where w is either the generalized Laguerre weight function w(t) = 0 if t 0, w(t) = t e ?t if 0 < t < 1, and > ?1, x > 0, or the Hermite weight function w(t) = e ?t 2 , ?1 < t < 1, and ?1 < x < 1. Furthermore, numerical methods of evaluation are discussed based on recursion, contour integration and saddle-point asymptoti...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1968
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1968-11909-3