An Introduction to Wavelets

CHARLES K. CHUI (Eds.)0121745848, 9780121745844, 0121745651, 9780121745653, 9780585470900

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.

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Table of contents :
Content:
Wavelet Analysis and Its Applications
Page ii

Front Matter
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages ix-x
Charles K. Chui

1 – An Overview
Pages 1-22

2 – Fourier Analysis
Pages 23-48

3 – Wavelet Transforms and Time-Frequency Analysis
Pages 49-80

4 – Cardinal Spline Analysis
Pages 81-117

5 – Scaling Functions and Wavelets
Pages 119-176

6 – Cardinal Spline-Wavelets
Pages 177-214

7 – Orthogonal Wavelets and Wavelet Packets
Pages 215-243

Notes
Pages 245-249

References
Pages 251-255

Subject Index
Pages 257,259-264