Introduction to wavelet analysis

David F. Walnut

450 pages, parution le 04/12/2001

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Résumé

A new text/reference offering a comprehensive and detailed presentation of wavelet theory, principles and methods. It presents basic theory of wavelet bases and transforms without assuming knowledge of advanced mathematics. The book motivates the central ideas of wavelets by discussing Hoar series in depth and then presenting a more generalized viewpoint. The material is presented with many examples, exercises and thorough references. An essential text/reference for applied mathematicians, engineers and scientists.

The goal of this book is to present the basics of wavelet theory in a complete, rigorous, and cogent fashion, but at a level that is truly appropriate for upper level undergraduates, first year graduate students, or anyone who has had a course in advanced calculus. The book presents the basic theory of wavelt 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 doing a detailed exposition of Haar series, and then shows how a more abstract approach allows us to generalize and improve upon Haar series. Once thes ideas have been established and explored, variations and extensions of the Haar construction are presented. Applications of the theory are to be stressed throughout the book as a means of motivating the usefullness of the theory, but a more complete treatment of applications will be saved for the last three chapters of the book. The book will also include exercises at the end of each chapter.

Table of Contents

1. Preface
2. Functions and Convergence
3. Fourier Series
4. The Fourier Transform
5. Signals and Systems
6. The Haar System
7. The Discrete Haar Transform
8. Mulitresolution Analysis
9. The Discrete Wavelet transform
10. Smooth
Compactly Supported Wavelets
11. Biorthogonal Wavelets
12. Wavelet Packets
13. Image Compression
14. Integral Operations; Appendices

L'auteur - David F. Walnut

David Walnut is Professor of Mathematics at George Mason University. His research interests are also in harmonic analysis, especially sampling theory, Radon transforms, and tomography. He is the author of Introduction to Wavelet Analysis.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	David F. Walnut
Parution	04/12/2001
Nb. de pages	450
Format	16 x 24
Couverture	Relié
Poids	455g
Intérieur	Noir et Blanc
EAN13	9780817639624
ISBN13	978-0-8176-3962-4