Wavelets and Multiscale Signal Processing
By addebook • Jun 29th, 2008 • Category: Mathematics •
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Wavelets and Multiscale Signal Processing (Applied Mathematics and Mathematical Computation Series)
Publisher: Chapman & Hall/CRC
Number Of Pages: 238
Publication Date: 1995-12
Sales Rank: 3219584
ISBN / ASIN: 0412575906
EAN: 9780412575907
Binding: Hardcover
Manufacturer: Chapman & Hall/CRC
Studio: Chapman & Hall/CRC
Average Rating: 5
Since their appearance in mid-1980s, wavelets and, more generally, multiscale methods have become powerful tools in mathematical analysis and in applications to numerical analysis and signal processing. This book is based on “Ondelettes et Traitement Numerique du Signal” by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these relations can be exploited in the context of digital signal processing.
Throughout, the book concentrates on the fundamentals. It begins with a chapter on the concept of multiresolution analysis, which contains complete proofs of the basic results. The description of filter banks that are related to wavelet bases is elaborated in both the orthogonal case (Chapter 2), and in the biorthogonal case (Chapter 4). The regularity of wavelets, how this is related to the properties of the filters and the importance of regularity for the algorithms are the subjects of Chapter 3. Chapter 5 looks at multiscale decomposition as it applies to stochastic processing, in particular to signal and image processing.
Review:
The source!
This book is the original source for reading about the use of numerical methods from signal processing in wavelet constructions, with an eye to applications. Mathematically, it is especially elegant, and its author speaks the language of applied math, and numerical analysis. By now, it has in fact become a central area in numerical analysis. The book is actually an updated translation[by Robert D. Ryan] of the French version [RMA, v 25, by Albert Cohen in the Masson book series], and I can recommend both. I can also recommend the several other wonderful translations, from French to English, of wavelet books by R.D. Ryan, for example his translation of French language wavelet books by Yves Meyer et.al. In the years since Cohen’s book, we have seen a handful of books stressing the interface of
signal processing and wavelets which are very suitable for classroom use. I have taught from some of them, but always find pearles in Cohen’s original book when I take it down from my
shelf, or when I need to remind myself of the elegance of the presentation from the original source.
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