Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool.
The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.
Author(s): Andrei Osipov, Vladimir Rokhlin, Hong Xiao (auth.)
Series: Applied Mathematical Sciences 187
Edition: 1
Publisher: Springer US
Year: 2013
Language: English
Pages: 379
Tags: Numerical Analysis; Signal, Image and Speech Processing; Appl.Mathematics/Computational Methods of Engineering
Front Matter....Pages i-xi
Introduction....Pages 1-3
Mathematical and Numerical Preliminaries....Pages 5-32
Overview....Pages 33-71
Analysis of a Differential Operator....Pages 73-133
Analysis of the Integral Operator....Pages 135-169
Rational Approximations of PSWFs....Pages 171-223
Miscellaneous Properties of PSWFs....Pages 225-242
Asymptotic Analysis of PSWFs....Pages 243-274
Quadrature Rules and Interpolation via PSWFs....Pages 275-351
Numerical Algorithms....Pages 353-370
Back Matter....Pages 371-379
