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Computational signal processing with wavelets. (English) Zbl 0928.94002
Applied and Numerical Harmonic Analysis. Boston: Birkhäuser (ISBN 0-8176-3909-8; 3-7643-3909-8). xxiv, 324 p. (1998).
This book provides a bridge between theory and practice of wavelet-based signal processing and is written for both students and professionals.
A solid mathematical foundation is given in the beginning chapters: (2) Mathematical preliminaries. (3) Signal representation and frames. (4) Continuous wavelets and Gabor transforms. (5) Discrete wavelet transforms.
The sixth chapter departs from the mainstream of wavelet theory and deals with the rich area of overcomplete wavelet systems. The author introduces an overcomplete wavelet transform, its inverse and their filter bank implementations.
Several applications of wavelet-based signal processing including noise suppression, signal compression, signal identification and digital communication are presented in Chapter 7.
Chapter 8 gives numerical illustrations and examples of wavelet methods using MATLAB 5. The accomanying MATLAB-based software is available on the world wide web.
Every chapter of the book contains a collection of exercises.

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
94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
65T60 Numerical methods for wavelets
44A15 Special integral transforms (Legendre, Hilbert, etc.)
41A30 Approximation by other special function classes
68N99 Theory of software