Customer Reviews

Ripples in Mathematics: The Discrete Wavelet Transform

5 star:		(5)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

You always wondered, what is "Lifting" with respect to wavelets. Well you have this book..and I must say, this will definately solve all your doubts abt Lifting. I use this book, and recommend it to anyone, who wish to explore the wonderful world of wavelet based transforms. An in-depth analysis of multi-rate transforms, Laurent polynomial division and actual MATLAB-based exmaples enhance the beauty of this book. Amongst the vast majority of books out there, Check out this one !

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.

The users of wavelets include engineers who design filters. The wavelet lifting technique is a powerful tool, and extraordinarily practical. The authors present it very nicely, and the book is an attractive source where anyone can pick up the essentials.

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..

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.

If you're interested in the Discrete Wavelet Transform, have I got a book for you! "Ripples In Mathematics" is a complete discussion of the topic. It is chockablock with exercises and example MATLAB code. There are also URLs pointing to keen stuff available for free out in Internetland.

Technical books - particularly math books - usually mean some extra sleepy time for me. Not so with this book. The math is clear and to the point, with examples worked through very nicely. Great illustrations. There's a chapter devoted to different applications. It's just really well put together.

I'm new to wavelet filter design, but this book lays out all the background material I need to do a hardware implementation.