Ripples in Mathematics (Paperback)

by A. Jensen (Author), Anders la Cour-Harbo (Author) "This book gives an introduction to the discrete wavelet transform, and to some of its generalizations..." (more)
Key Phrases: full wavelet packet decomposition, boundary filters, boundary correction method, Time Fig, Factorizing Coiflet, More Fourier Analysis (more...)

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 Description
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. The first part is a completely elementary introduction to the subject, and the prerequisites for this part are knowledge of basic calculus and linear algebra. The second part requires some knowledge of Fourier series and digital signal analysis. The connections between lifting and filter theory are presented and the wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals. The problems with finite length signals are treated in detail. 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.

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.com Sales Rank: #302,025 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

40 of 42 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)

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.

6 of 6 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 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 The non-mathematician-friendly introduction to wavelets, May 18, 2003

By	Steve Uhlig (Delft, The Netherlands) - See all my reviews (REAL NAME)

While most wavelets books are terribly difficult from a mathematical viewpoint, this book introduces the reader to wavelets from the practical viewpoint. It introduces the procedure to compute the wavelet coefficients without speaking about mathematical functions. If you don't care about functional spaces, then go to this one. I really think this book is the most friendly introduction to wavelets for people who don't care about maths.