This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. This book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference for professionals.

The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series.


Contents
Preface
Part I Preliminaries
1 Functions and Convergence
2 Fourier Series
3 The Fourier Transform
4 Signals and Systems
Part II The Haar System
5 The Haar System
6 The Discrete Haar Transform
Part III Orthonormal Wavelet Bases
7 Multiresolution Analysis
8 The Discrete Wavelet Transform
9 Smooth, Compactly Supported Wavelets
Part IV Other Wavelet Constructions
10 Biorthogonal Wavelets
11 Wavelet Packets
Part V Applications
12 Image Compression
13 Integral Operators
Part VI Appendixes
Appendix A: Review of Advanced Calculus and Linear Algebra
Appendix B: Excursions in Wavelet Theory
Appendix C: References Cited in the Text
Index

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