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© 2011

A Friendly Guide to Wavelets

  • Considered one of the best textbooks on this topic for mathematicians and physicists interested in wavelet analysis

  • Covers all the fundamental concepts of wavelets in an elegant, straightforward way

  • Has a number of unique features, which makes the book particularly valuable for newcomers to the field

Textbook

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Basic Wavelet Analysis

    1. Front Matter
      Pages 1-1
    2. Gerald Kaiser
      Pages 3-43
    3. Gerald Kaiser
      Pages 44-59
    4. Gerald Kaiser
      Pages 60-77
    5. Gerald Kaiser
      Pages 123-138
    6. Gerald Kaiser
      Pages 139-175
    7. Gerald Kaiser
      Pages 176-199
  3. Physical Wavelets

    1. Front Matter
      Pages 201-201
    2. Gerald Kaiser
      Pages 203-244
    3. Gerald Kaiser
      Pages 245-270
    4. Gerald Kaiser
      Pages 271-290
  4. Back Matter
    Pages 297-300

About this book

Introduction

I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time.

—Proceedings of the IEEE

It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one.

—Computing Reviews

I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets.

—Physics Today

This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing.

—SIAM Review

The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field.

—Mathematical Reviews

The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis.

—Internationale Mathematische Nachrichten

For additional review samples and related material, please visit the author's website at www.wavelets.com.

Keywords

Daubechies' orthonormal wavelet bases continuous wavelet transforms generalized frames mutliresolution analysis physical wavelets time-frequency analysis, sampling time-scale analysis wavelet acoustics wavelet analysis wavelet electromagnetics windowed Fourier transforms

Authors and affiliations

  1. 1.Center for Signals & WavesAustinUSA

Bibliographic information

Reviews

From the reviews:

"I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time."

—Proceedings of the IEEE

"It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one."

—Computing Reviews

"I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets."

—Physics Today

"This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing."

—SIAM Review

"The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field."

—Mathematical Reviews

"The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis."

—Internationale Mathematische Nachrichten

"I loved 'A Friendly Guide to Wavelets'.  I advised it to my graduate students."

—Yves Meyer, Université Paris-Dauphine

“Taking into account the importance of the wavelet theory in … physics and engineering, there was a need for writing a textbook that is more suitable for students and researchers with a limited knowledge of the functional analytic background. The book by Gerald Kaiser aims at this goal. … the friendly guide to wavelets is still an interesting literature, taking a very special view to the tools of Fourier and wavelet analysis for applications in signal processing. … this book is very unique.” (Gerlind Plonka-Hoch, Zentralblatt MATH, Vol. 1230, 2012)

“This is a thorough introduction to most aspects of wavelets. It is an unaltered reprint of a 1994 book, but it is still reasonably up-to-date for the topics it covers. … The book is intended to be ‘friendly’ toward engineering and scientific readers by using the language of classical analysis … .” (Allen Stenger, The Mathematical Association of America, June, 2011)