Customer Reviews

A Friendly Guide to Wavelets

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

 

 

I bought this book when I was particularly interested in continuous wavelet transforms. I found myself flying through the exposition. I felt confident about the knowledge I was acquiring and I was quickly able to apply it. Although I come at this book as a mathematician, I think that it is ideal for engineers and physical scientists who usually have far better grounding in signal processing and related issues in Fourier analysis than do mathematicians. I have recommended this book to students, friends and colleagues with high praise.

A classic text *but* look at the graph on the cover very carefully because it is the only one you'll get until you reach the last chapters of the book. In terms of the presentation of the basic theorems and equations, the text is excellent ... BUT ... there is precious little to guide a student to an intuitive and practical understanding of the theory. In practice, one looks at the graphical representations of wavelets quite often -- just like the ones used for Fourier analysis (can you imagine your first Fourier analysis class with no graphs of convolution, impulses, etc? Wavelets *are* Fourier analysis taken a step further in order to handle time varying systems. Graphs are essential to the uninitiated.) In fact, it is helpful to think of wavelets (i.e., wavelet packet decompositions) as a Fourier spectrum with an additional time axis added so you can see how the spectrum changes over time. The "wavelet" method simply optimizes the resolution used at different frequencies. True, it is a little more complicated than that, but it is easy to lose sight of the simple elegance of the topic when so many equations are flung at you without intuitive context. The topic could be presented MUCH better, so don't worry that it takes a long time to get through this material. Read other basic wavelet texts first and then *definitely* come back to this one. You will appreciate its otherwise *excellent* presentation much more and the principles will be easier to put into actual practice rather than mere academic conjecture.

This book provides a solid mathematical foundation for wavelets, however the title (no doubt responsible for selling a lot of books) is extremely misleading. This book is "friendly" only if you have recently passed your Ph.D. qualifying exam in mathematical analysis. Nevertheless, advanced readers looking for a good overview of wavelets will find that material here.

Some reviewers have commented that this is not such a "friendly"
guide if you are not friends with upper division or graduate
level mathematics. There is some truth to this. Unlike the
pragmatic approach taken in "Ripples in Mathematics" this is
a mathematical coverage of wavelets.

For me the value in this book is that it provides a clear
introduction to the notation and theory behind wavelets. This
book provides the tools you need to understand the wavelet
literature better. If you are a software engineer searching
for a quick guide to wavelet algorithms, this book may disappoint.

After trying a couple of other books this was the one that took some pages (or time) to guide me through the preeliminaries necessary that are not necessarily trivial. After that it develops the theory in very accessible terms. Solutions of the exercises and some focus on discrete algorithms would enhance its value even further.

I really did find this lovely book reader friendly! The author has succeeded in communicating the exciting subject of wavelets, and their many applications, to students and more advanced readers alike. He realized that different communities, math, computer science, engineering, and physics,--
that they have variations in their emphasis, their terminology,
and their thinking. When authors speak to the various user groups, and do it well,-- like in this case, the result is a cucess. This friendly book is!

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There are several reasons why it's fundamentally important:
1. a. It has an 'uncanny' parallel with modern quantum mechanics that is explained below.
b. Modern quantum mechanics is based on axioms but are tenuous at best.
c. The book is so formally developed as to actually give credence to the parallel field.
d. If modern QM was presented this way, the field would actually be somewhat palatable.
2. It provides the formal basis for wavelet analysis and theory.
3. Wavelets are the 'thing' of the future.

For those unfamiliar with modern quantum mechanics, it would be best to study first a primer or popular book on the subject - really digest the concepts/axioms QM is based on.. Then, go more formal: study an actual textbook on the subject.. This gives a real feel for the issues at hand.. Pay particular attention to 'caveats' such as renormalization..

To prepare for this book (to be able to absorb it meaningfully), you should take courses or read textbooks covering:
1. linear algebra
2. Fourier series and integral transforms
3. signals and systems
A course in linear systems theory would not 'hurt' as prerequisite.. Of course, the courses/textbooks mentioned above have their own prerequisites.. Finally, an analysis course Rudin-style and a course on complex variables certainly 'could not hurt either'.. One final note about preparation: you cannot underestimate the importance of a good physics/engineering teacher/course!

Physics has its basis in reality (we hope;); math has its basis in formal structures. To combine the two effectively means we must choose what is appropriate from math to model apparent structures in physics/reality. Wavelets may be the thing physicists have been waiting for to 'tie it all together'.. Only time will tell.. Only time will tell..

This book gives detailed explanations and derivations of wavelet transform. However, one tends to get lost on a vast number of formulations that are not really helpful for practical uses. If you just want to learn how to use wavelet transform to solve practical problems, this is not the book you should read.

I think this book is writen to be used by mathematicians and not by engineers , it has many equations and a few drawings,the mathematics are not complicated but it lacks a phisycal approach.I buy by mail and I get dissapointed when I received it.

It is not a friendly guide to Wavelets. However, chapters 1 one to six are excelent. Chapter 7, Multiresolution Analysis, the heart of the matter is hard to understand. So, you get the flavor of Wavelets but not learn to use it.