Adapted Wavelet Analysis: From Theory to Software

by Mladen Victor Wickerhauser

This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients

498 pages, Paperback

First published July 1, 1994

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Page 26. Theorem 1.17 (Fourier Convolution)
If u and v are Schwartz functions then fourier(u*v)=fourier(u)fourier(v)

Corollary 1.18: If u is integrable and v belongs to L^p (1<=p<=infinity)
then u*v is in L^p

Proposition 1.19: If u is absolutely integrable on R then the convolution
v->u*v as a map from L^2 to L^2 has operator norm sup{|Fourier(u)(xi): xi in R}