Ripples in Mathematics [Paperback]

A. Jensen (Author), Anders la Cour-Harbo (Author)

Book Description

ISBN-10: 3540416625 | ISBN-13: 978-3540416623 | Publication Date: June 22, 2001 | Edition: 1

This introduction to the discrete wavelet transform and its applications is based on a novel approach to discrete wavelets called lifting. After an elementary introduction, connections of filter theory are presented, and wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals, problems with finite length signals are detailed, and MATLAB is used for examples and implementation of transforms.

Editorial Reviews

Review

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)

Product Details

• Paperback: 257 pages
• Publisher: Springer; 1 edition (June 22, 2001)
• Language: English
• ISBN-10: 3540416625
• ISBN-13: 978-3540416623
• Product Dimensions: 9.2 x 6.1 x 0.6 inches
• Shipping Weight: 14.1 ounces (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #645,116 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

45 of 47 people found the following review helpful:

4.0 out of 5 stars The best wavelet book I've found so far, October 30, 2001

By 

Ian Kaplan (Livermore, CA) - See all my reviews
(REAL NAME)   

This review is from: Ripples in Mathematics (Paperback)

There is a vast mathematics literature on wavelets.
Much of this literature deals with wavelets from
a theoretical point of view. Although books like
Strang and Nguyen's "Wavelets and Filter Banks" are
well written math books, their emphasis is on mathematics,
not application. For example, not until Chapter 8, half
way through the book, do Strang and Nguyen discuss the
mathematics for dealing with a finite, rather than an
infinite data set.

"Ripples in Mathematics" is the seventh book on wavelets that
I've worked with. So far it is the best. The concentration
is on applying wavelet techniques. The book approaches
wavelets through a relatively new technique developed
by Wim Sweldens and others called "the Lifting Scheme". The
lifting scheme provides a structure for wavelets that is
easier to understand. Lifting scheme wavelets also have the
elegant feature that the transform and the inverse transform
are mirrors of each other.

The authors of "Ripples in Mathematics" keep the mathematics
level at a relatively introductory level (e.g., relative
to some of the other wavelet books).

"Ripples in Mathematics" provides the first explaination of
wavelet packets that I have understood. Even better they
discuss the actual implementation of the wavelet packet
algorithm. They also provide a chapter that covers wavelets
applied to finite data sets in a clear non-theoretical fashion
(I found this much more approachable than Strang and Nguyen).

The perfect wavelet book for me has not yet been written,
so I have given this book only four stars. I think of
my perfect book on wavelets as "Wavelets for Dumb Engineers".
This book has been written for Fourier analysis and classical
signal processing (see Richard Lyons' outstanding book
"Understanding Digital Signal Processing").

There is a difference in point of view between mathematicans
and most software and hardware engineers. Our concern is
how the technique can be applied. "Ripples in Mathematics"
provides the necessary material to implement the algorithms,
but you will have to put in some work reading this book and
writing the software (or software models for a hardware
implementation). There are no application hints of the kind
that Lyons provides for applying the Fourier transform. Unlike
Lyons the authors are mathematicians, not practicing digital
signal processing engineers.

9 of 9 people found the following review helpful:

4.0 out of 5 stars Caveat, April 4, 2005

By 

E. Gregory - See all my reviews
(REAL NAME)   

This review is from: Ripples in Mathematics (Paperback)

This is a great book for understanding the specifics of implementation of wavelet transforms and lifting schemes. One warning, however, the book is rife with errors and the reader would be well-advised to check calculations.

6 of 6 people found the following review helpful:

5.0 out of 5 stars Very good book on how to do wavelet based signal processing, May 2, 2002

By 

Rajesh Venugopal (Syracuse,Ny) - See all my reviews
(REAL NAME)   

This review is from: Ripples in Mathematics (Paperback)

This is one of the books that shows you how to implement wavelets, it does so in a good way. Some of the sentences, although, could have been written better. It is not a book for 'dummies'. It does require you to think hard. Lifting is very well explained, as are the implementation issues that prop up when you try to work with finite data sets.

Example codes in Matlab, given at the end helped me to understand a lot. Wonderful book for implementation, provided that you work hard and think hard. This book does require you to be familiar with Z transform to understand how lifting is linked to Filter Banks. So be warned..