An Introduction to Wavelet Analysis

David F. Walnut0817639624, 9780817639624

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.

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Table of contents :
Front Matter

Preliminaries

Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems

The Haar System

The Haar System
The Discrete Haar Transform

Orthonormal Wavelet Bases

Multiresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets

Other Wavelet Constructions

Biorthogonal Wavelets
Wavelet Packets

Applications

Image Compression
Integral Operators

Back Matter