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An Introduction to Wavelet Analysis (Applied and Numerical Harmonic Analysis)

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en Limba Engleză Carte Paperback – 11 Dec 2013
"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.
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Carte Paperback (1) 17158 lei  Economic 5-7 săpt. +17236 lei  8-12 zile
  Birkhäuser Boston – 11 Dec 2013 17158 lei  Economic 5-7 săpt. +17236 lei  8-12 zile
Carte Hardback (1) 19925 lei  Economic 5-7 săpt. +19294 lei  8-12 zile
  Birkhäuser Boston – 27 Jan 2004 19925 lei  Economic 5-7 săpt. +19294 lei  8-12 zile

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Specificații

ISBN-13: 9781461265672
ISBN-10: 1461265673
Pagini: 472
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.72 kg
Ediția: 2004
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Applied and Numerical Harmonic Analysis

Locul publicării: Boston, MA, United States

Public țintă

Research

Cuprins

Preface
Part I: Preliminaries
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
Part II: The Haar System
The Haar System
The Discrete Haar Transform
Part III: Orthonormal Wavelet Bases
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Part IV: Other Wavelet Constructions
Biorthogonal Wavelets
Wavelet Packets
Part V: Applications
Image Compression
Integral Operators
Appendix A: Review of Advanced Calculus and Linear Algebra
Appendix B: Excursions in Wavelet Theory
Appendix C: References Cited in the Text
Index

Recenzii

"[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