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Applied and Numerical Harmonic Analysis

An Introduction to Wavelet Analysis

Authors: Walnut, David F.

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Softcover $74.99
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  • ISBN 978-1-4612-6567-2
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About this Textbook

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

Reviews

"[This text] is carefully prepared, well-organized, and covers a large part of the central theory . . . [there are] chapters on biorthogonal wavelets and wavelet packets, topics which are rare in wavelet books. Both are important, and this feature is an extra argument in favour of [this] book . . . the material is accessible [even] to less advanced readers . . . the book is a nice addition to the series."   —Zentralblatt Math

"This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject."   —Mathematical Reviews

"This textbook is an introduction to the mathematical theory of wavelet analysis at the level of advanced calculus. Some applications are described, but the main purpose of the book is to develop—using only tools from a first course in advanced calculus—a solid foundation in wavelet theory. It succeeds admirably. . . . Part I of the book contains 112 pages of preliminary material, consisting of four chapters on ‘Functions and Convergence,’ ‘Fourier Series,’ ‘Fourier Transforms,’ and ‘Signals and Systems.’ . . . This preliminary material is so well written that it could serve as an excellent supplement to a first course in advanced calculus. . . . The heart of the book is Part III: ‘Orthonormal Wavelet bases.’ This material has become the canonical portion of wavelet theory. Walnut does a first-rate job explaining the ideas here. . . . Ample references are supplied to aid the reader. . . . There are exercises at the end of each section, 170 in all, and they seem to be consistent with the level of the text. . . . To cover the whole book would require a year. An excellent one-semester course could be based on a selection of chapters from Parts II, III, and V."   —SIAM Review

"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


Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4612-0001-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-0-8176-3962-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.99
price for USA in USD
  • ISBN 978-1-4612-6567-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Wavelet Analysis
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0001-7
DOI
10.1007/978-1-4612-0001-7
Hardcover ISBN
978-0-8176-3962-4
Softcover ISBN
978-1-4612-6567-2
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XX, 452
Additional Information
1st printing, 2001. Corrected 2nd printing, 2003.
Topics