A Wavelet Tour of Signal Processing

by Stéphane Mallat

A Wavelet Tour of Signal Processing begins with a presentation of the wonders of the Fourier transform, and then describes its failures for transient signal processing. It presents local time–frequency methods and the related mathematical tools. The book uses an intuitive approach to important mathematical results, and emphasizes practical applications rather than proofs. It describes numerical discrete algorithms as well as some applications to information processing, fractal analysis, noise removal, and compact signal coding.
A Wavelet Tour of Signal Processing is intended for signal processing engineers who want to discover the potential applications of recent mathematical advances in time–frequency signal representations. Of interest to researchers in applied mathematics, the book highlights the applications of these new techniques and also provides an overview of signal processing problems.

Emphasizes practical applications rather than proofs
Presents local time–frequency methods and the related mathematical tools
Uses an intuitive approach to important mathematical results

Genres: Mathematics, Science, Engineering

577 pages, Hardcover

First published January 1, 1998

Reviews

[David Cournapeau]

(I initiall ready the book in French when I was a master student).

For people interested in getting a strong basis in the foundation of (sparse) signal processing, this is an excellent introduction. This is maybe my favorite "applied math book", that review a lot of the advances in signal processing of late 90ies.

It unfortunately went a bit too early to really cover compressed sensing, though it does cover some related sparse-coding topics.

[Joe Cole]

It can be a fine book for a college class on wavelets. For readers familiar with MATLAB, all the examples in the book can be reproduced with MATLAB "workouts."

[Alex Gittens]

It's a great reference, if you take it with a ton of salt: there are way too many typos and subtle mathematical issues to take any result from this book without verification, and once you try to reproduce the plots, you'll realize that there is often not enough information given for you to know exactly how to do so. On the flip side, it covers a range of topics that you wouldn't usually see all in one place.

[Carlos O'Donell]

I have read large portions of this book, but not every page. The book is an excellent example of how a textbook should be written with clear sections on theory, proofs, examples, and questions to solve. If you are bored of FFT and want to discover *why* sin/cos are useful orthogonal functions, then read this book.

[DJ]

wavelets!

[DJ]

apparently human visual cortex does something similar to a wavelet transform

[Galal]

Very good book for the basics and suitable for the beginners .