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Wavelets: a mathematical tool for signal analysis. (English) Zbl 0903.94007
SIAM Monographs on Mathematical Modeling and Computation 1. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics (ISBN 0-89871-384-6; 978-0-89871-972-7/ebook). xviii, 210 p. (1997).
This very fine book, derived from a set of lectures given in 1993, covers the expected material of localization, multiresolution analysis, orthonormality, and biorthogonality for wavelets. The last two chapters (nearly half the book) are devoted to algorithms and to applications to detection of singularities and image analysis, to data compression, and to the numerical solution of integral equations. The author emphasizes the analogies with the theory of splines and the utility of wavelets in signal analysis (as opposed to their purely mathematical interest). He gives many examples and includes nice pictures of computations. This book should be useful for anyone interested in wavelets from the point of view of applications to communications and signaling theory.
Reviewer: J.S.Joel (Kelly)

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T99 Numerical methods in Fourier analysis
42-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
65R20 Numerical methods for integral equations
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