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Other titles in the Applied and Numerical Harmonic Analysis series:
An Introduction to Wavelet Analysisby David F. Walnut
Synopses & Reviews
"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!" --Bulletin of the AMS 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 elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one 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 prerequisites 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 about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure). * Complete background material on is offered on Fourier analysis topics. * 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. An Introduction to Wavelet Analysis 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.
This is a comprehensive and detailed presentation of the principles and methods of wavelet theory. The basic theory of wavelet bases and transforms are presented without assuming any 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.
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.
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
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