Unidimensional and bidimensional prolate spheroidal wave functions and applications
type: Item
instance of: scholarly article
title: Unidimensional and bidimensional prolate spheroidal wave functions and applications
zbMATH Open document ID: 1229.42033
author: Abderrazek Karoui
published in: Journal of the Franklin Institute
publication date: 2011-11-22T00:00:00Z
review text: The author gives a brief description of the theory and the properties of the 1-D and 2-D prolate spheroidal wave functions (PSWFs). Then, he studies some efficient methods for the computation of the different PSWFs and their associated eigenvalues. More precisely, he develops a quadrature method for the approximation of the 1-D PSWFs. Then, he extends this method to the construction of 2-D PSWFs that are concentrated on the unit disk. Also, he gives a brief review of the quality of approximation of almost band-limited functions by 1-D PSWFs. Moreover, he uses some numerical tests to compare between PSWFs and wavelets as signal processing tools. In particular, he gives some numerical tests that highlight the efficiency of PSWFs in processing band-limited signals.
reviewed by: Francisco Pérez Acosta
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 5975818
MaRDI profile type: Publication
full work available at URL: j.jfranklin.2010.09.001
OpenAlex ID: W2000495455
cites work: Q2701929
cites work: On generalized Gaussian quadratures for exponentials and their applications
cites work: Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms
cites work: Q3999241
cites work: Ten Lectures on Wavelets
cites work: Uncertainty Principles and Signal Recovery
cites work: Q3244534
cites work: New efficient methods of computing the prolate spheroidal wave functions and their corresponding eigenvalues
cites work: Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions
cites work: Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II
cites work: Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty-III: The Dimension of the Space of Essentially Time- and Band-Limited Signals
cites work: Fourier and Hankel bandlimited signal recovery
cites work: Prolate spheroidal wave functions, an introduction to the Slepian series and its properties
cites work: Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit
cites work: Prolate spheroidal wave functions on a disc -- integration and approximation of two-dimensional bandlimited functions
cites work: Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
cites work: Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
cites work: Some Asymptotic Expansions for Prolate Spheroidal Wave Functions
cites work: A new friendly method of computing prolate spheroidal wave functions and wavelets
cites work: Prolate spheroidal wavefunctions, quadrature and interpolation
cites work: High-frequency asymptotic expansions for certain prolate spheroidal wave functions
DOI: 10.1016/J.JFRANKLIN.2010.09.001
description: scientific article; zbMATH DE number 5975818