An Introduction to Wavelet Analysis

✍ Scribed by David F. Walnut (auth.)

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 453
• Series: Applied and Numerical Harmonic Analysis
• Edition: 1
• Category: Library

✦ Synopsis

An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. 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 motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The 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 guide for professionals. All readers will find

✦ Table of Contents

Front Matter....Pages i-xix
Front Matter....Pages 1-1
Functions and Convergence....Pages 3-25
Fourier Series....Pages 27-57
The Fourier Transform....Pages 59-86
Signals and Systems....Pages 87-111
Front Matter....Pages 113-113
The Haar System....Pages 115-140
The Discrete Haar Transform....Pages 141-159
Front Matter....Pages 161-161
Multiresolution Analysis....Pages 163-214
The Discrete Wavelet Transform....Pages 215-248
Smooth, Compactly Supported Wavelets....Pages 249-285
Front Matter....Pages 287-287
Biorthogonal Wavelets....Pages 289-333
Wavelet Packets....Pages 335-368
Front Matter....Pages 369-369
Image Compression....Pages 371-395
Integral Operators....Pages 397-421
Back Matter....Pages 423-451

✦ Subjects

Computational Science and Engineering; Signal, Image and Speech Processing; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Functional Analysis