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Ripples in Mathematics

The Discrete Wavelet Transform

Authors: Jensen, A., Cour-Harbo, Anders la

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  • ISBN 978-3-540-41662-3
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About this Textbook

Yet another book on wavelets. There are many books on wavelets available, written for readers with different backgrounds. But the topic is becoming ever more important in mainstream signal processing, since the new JPEG2000 standard is based on wavelet techniques. Wavelet techniques are also imporĀ­ tant in the MPEG-4 standard. So we thought that there might be room for yet another book on wavelets. This one is limited in scope, since it only covers the discrete wavelet transĀ­ form, which is central in modern digital signal processing. The presentation is based on the lifting technique discovered by W. Sweldens in 1994. Due to a result by I. Daubechies and W. Sweldens from 1996 this approach covers the same class of discrete wavelet transforms as the one based on two channel filter banks with perfect reconstruction. The goal of this book is to enable readers, with modest backgrounds in mathematics, signal analysis, and programming, to understand wavelet based techniques in signal analysis, and perhaps to enable them to apply such methods to real world problems. The book started as a set of lecture notes, written in Danish, for a group of teachers of signal analysis at Danish Engineering Colleges. The material has also been presented to groups of engineers working in industry, and used in mathematics courses at Aalborg University.

Reviews

From the reviews:

"This book is a very well-written introduction to discrete wavelet transforms, very convenient for students in electrical engineering, computer science, and applied mathematics. It is based on the lifting approach to discrete wavelet transforms ... . MATLAB is used as the computational environment for examples and implementations of discrete wavelet transforms." (Manfred Tasche, Zentralblatt MATH, Vol. 989 (14), 2002)

"This is an algorithm based, completely elementary introduction to the discrete wavelet transform (DWT) and wavelet packet transform, easy to read and easy to understand, well suited for an introductory course on wavelets for undergraduate students of applied sciences or mathematics. ... Implementations and examples using basic Matlab (TM) as well as the public domain ubi-wave wavelet toolbox help to further a deeper understanding of the algorithms." (C. Cenker, Internationale Mathematische Nachrichten, Vol. 56 (189), 2002)

"This book gives an introduction to the discrete wavelet transform and some of its applications. It is based on a novel approach to discrete wavelets called lifting. ... MATLAB is used as the computational environment for examples and implementation of transforms. The book is well suited for undergraduate mathematics and electrical engineering students and engineers in industry." (ETDE Energy Database, December, 2001)


Table of contents (14 chapters)

Buy this book

eBook $69.99
price for USA
  • ISBN 978-3-642-56702-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-540-78116-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • ISBN 978-3-540-41662-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ripples in Mathematics
Book Subtitle
The Discrete Wavelet Transform
Authors
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-56702-5
DOI
10.1007/978-3-642-56702-5
Softcover ISBN
978-3-540-78116-5
Softcover ISBN
978-3-540-41662-3
Edition Number
1
Number of Pages
IX, 246
Topics