This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

Inhalt

Preface

Part I: Preliminaries

Functions and Convergence

Fourier Series

The Fourier Transform

Signals and Systems

Part II: The Haar System

The Haar System

The Discrete Haar Transform

Part III: Orthonormal Wavelet Bases

Mulitresolution Analysis

The Discrete Wavelet Transform

Smooth, Compactly Supported Wavelets

Part IV: Other Wavelet Constructions

Biorthogonal Wavelets

Wavelet Packets

Part V: Applications

Image Compression

Integral Operators

Appendix A: Review of Advanced Calculus and Linear Algebra

Appendix B: Excursions in Wavelet Theory

Appendix C: References Cited in the Text

Index