Prolate Spheroidal Wave Functions of Order Zero - Mathematical Tools for Bandlimited Approximation

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.

List of contents

Introduction.- Mathematical and Numerical Preliminaries.- Overview.- Analysis of the Differential Operator.- Analysis of the Integral Operator.- Rational Approximations of PSWFs.-Miscellaneous Properties of PSWFs.- Asymptotic Analysis of PSWFs.- Quadrature Rules and Interpolation via PSWFs.- Numerical Algorithms .-

About the author

Andrei Osipov is a Professor at Yale University in the Department of Mathematics.Vladimir Rokhlin is a Professor at Yale University in the Department of Computer Science.  Hong Xiao is a Professor at University of California, Davis in the Department of Computer Science.

Summary

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.

Product details

• Authors: Andre Osipov, Andrei Osipov, Vladimi Rokhlin, Vladimir Rokhlin, Hong Xiao
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2016
• EAN: 9781489978653
• ISBN: 978-1-4899-7865-3
• No. of pages: 379
• Dimensions: 155 mm x 22 mm x 233 mm
• Weight: 593 g
• Illustrations: XI, 379 p. 30 illus.
• Series: Applied Mathematical Sciences; Applied Mathematical Sciences
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; B, Mathematics and Statistics, Signal, Image and Speech Processing, Mathematical and Computational Engineering, Signal Processing, Numerical analysis, Engineering mathematics, Applied mathematics, Mathematical and Computational Engineering Applications, Maths for engineers, Speech processing systems, Digital and Analog Signal Processing, Imaging systems & technology, Image processing