C. Sidney Burrus, Rice University
Ramesh A. Gopinath, IBM
Haitao Guo, Chromatic Research

Copyright 1998, 282 pp.
Paper
ISBN 0-13-489600-9

Summary:

This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.

Features:

• Uses a mathematical as well as a signal processing viewpoint to give an accurate picture of what can be done and what cannot.
• Develops an insight and intuition that is more general and versatile than that based only on Fourier methods.
• Uses a language that is a mixture of that from the mathematical and the signal processing literature.
• Develops both the signal expansion and the filter bank approaches.
• Contains an impressive array of new and exciting generalizations of the basic wavelet system (many which have only been in journals, conference proceedings, and on websites) including M-band wavelets, biorthogonal systems, wavelet packets, and multiwavelets.
• Gives an example application of wavelets to an approximate FFT algorithm that has order-N arithmetic complexity.
• Contains an extensive guide to other wavelet literature.

Contents:

1. Introduction.

2. A Multiresolution Formulation.

3. Filter Banks and the Discrete Wavelet Transform.

4. Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases.

5. The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients.

6. Regularity, Moments and Wavelet System Design.

7. Generalizations of the Basic Multiresolution Wavelet System.

8. Filter Banks and Transmultiplexers.

9. Calculation of the Discrete Wavelet Transform.

10. Wavelet Based Signal Processing and Applications.

Summary Overview.

References.

Bibliography.

Appendix A. Derivations for Chapter on Scaling Function.

Appendix B. Derivations for Section on Properties.

Appendix C. Matlab Programs.

Index.

Software:

You can download Matlab programs in the appendix of book now. They have been tested using Matlab 5.0 on both Win95 PC and Sun workstation. Please choose

• The PC version as a Zip file.
• The UNIX version as a compressed tar file.

Java Demo Wavelet applets

Publisher Prentice Hall

Order Order from Amazon

Corrections:

page 91.  equation (6.46):  The lower limit on the sum should be zero.
          equation (6.47):  Insert a minus sign before the left side.
          equation (6.48):  Should be positive and (6.49) negative.
          equation (6.51):  Insert a minus sign before the left side.