Customer Reviews

A Primer on Wavelets and Their Scientific Applications, Second Edition (Studies in Advanced Mathematics)

5 star:		(7)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(2)

 

 

This is simply the best book I have come across on introducing wavelets.

I am sure that within the first 20 pages, which are easy to understand and make for a very quick read, you will begin to see the beauty of this theory and will applaud the author's exposition.

While this book does not need much more than basic linear algebra, the author does not shy away from the mathematics where necessary - he simply motivates it by providing an intuitive understanding of the equations, so it's easy to follow.

In the very first chapter, he describes the wavelet method using examples that can be worked out by hand. (This is also mentioned in another review and contributed to me buying this book. I was doing research on another wavelet book on the site when I came across this book and it's reviews.) This helps to fix and brilliantly clarify the main ideas behind the theory. Armed with this knowledge, the reader can better appreciate the more sophisticated wavelet functions. But, the basics would be firmly planted by this book. This is rarely seen in other books dealing with this thoery.

This book is great for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts.

The discussion is motivated with real world examples such as removing noise from signals, image enhancements, etc. These are useful examples that you can relate to. There is enough in this book and the downloadable software that you may want to undertake meaningful projects yourself. That is the confidence that you get from this book.

An outstanding quality is that the book is thin. This is a strong motivating factor since it immediately sends the message that "this method can't be that hard to grasp if the book is so short." And, this subliminal message keeps your spirits up as you read this masterpiece.

Wavelets is a mathematically intensive technique, and it seems that most authors want to show how "macho" they are by shrouding the basics under a heavy cloak of complex equations. But, true "machoism" is displayed by how deftly an author can bring a difficult topic to the lay person. James Walker does this remarkably well.

Ch. 1: Haar Wavelets: The chapter lays out the basic concepts underpinning wavelet analysis using examples that require only hand calculations. Shows how a signal is broken down into is low frequency (i.e. trend) and the high frequency components (i.e. fluctuations). The concept of the transform inverse is presented and demonstrated through examples. The chapter goes on to introduce multiresolution analysis and requires some algebra but for my meager math background a piece of cake. Signal compression is discussed and emphasized. Removing noise from audio signals is examined. Chapter ends with a demonstration of why we need some wavelet beyond the Haar.
Ch. 2: Daubechies Wavelets: While there are numerous Daubechies wavelets Walker picks the simplest and develops important concepts. Some comfort with linear algebra and matrix notation makes this chapter easy to understand. The examples in the Haar chapter are carried forward to show how the Daubechies take care of discontinuities created by the Haar wavelet. Other Daubechies wavelts are then discussed and the Coiflets are introduced along with the need for these additional wavelets. More examples and the removal of pop noise and background static is examined. Image processing is introduced along with more examples. Great stuff even if I am not particularly interested in these topics. Chapter ends with notes and references where several URL's are presented on the various aspects of wavelets.
Ch. 3: Frequency analysis: Some familiarity with Fourier transforms will make the reader comfortable here but I do not think the familiarity essential to get the gist of where Walker is leading the reader. The idea of detecting a given sub image within a larger image is where we are lead. Chapter concludes on a roll your own wavelet section and again a notes and reference section.
Ch. 4: Beyond wavelets: Wavelet packet transforms are introduced and a few of their applications to signal compression presented. The concept of a continuous wavelet transform is brought in.
Appendix A. Software for wavelet analysis. Walker presents the URL for his software and data files.
For an introductory book I gave it the 5 stars. I really found it useful in getting me into the subject and a feeling for the level of effort I need to put forward to use wavelets for my application.

This lovely little book helps the novice to get an idea of the math which underlies wavelets;-- and at the same time to learn how one readily gets hold of software that is convinient,-- that will make it easy for anyone to start playing around with it. The author also explains in plain English the wavelet aspects, and some of the mathematical constructs, behind audio denoising, signal compression, image recognition, speech recognition and more.

This book is an excellent one to learn the fundamental concepts of the wavelet transform. I recommend to study this book before starting or while studying another more mathematical text.

Book is well written. But the kindle edition is the very old first edition. This was my first kindle purchase, and I am very disappointed. Now I have to go buy the paper version, since it looks like that is the only way to get the updated second edition. So amazon has effectively tricked me into wasting some money. Granted, I should have looked closer, but amazon should not put a link to the kindle first edition of the book directly on the second edition's paper page.

As for the book itself, it is very well written, and is a great introduction to the topic. I would have given it 5 stars if Amazon had not misled me and cost me some money. If you are just looking for an introduction to the topic, the first edition still isn't bad. But in my case there were new topics in the second edition I was specifically wanting to learn.

At times, particularly at the beginning, the author seems almost patronizing, but generally the tone and level of the book is just where it should be for what seeks to be a primer. However, it is unfortunate that one of the primary functions in the software is not more fully described in the text; it is only described as the method of preparing many of the examples.

Overall, an excellent start for somebody who knows little or nothing about wavelets.

This is the best introductory level book on wavelets I have read. It is written beautifully and is one of the few books that provides insight as to how and why wavelets are useful.

Everyone should start out their investigation of wavelets with this book first. Highly recommended.

This book is really good and is a great reference for understanding what Wavelet Transforms are and their valuable uses. Be prepared for quite a bit of college level math, and knowledge of frequency analysis and transform that would also be helpful. If you find this book difficult to grasp the following online tutorial is also wonderfully helpful[...]
Once you are able to go through it, this book is more accessible.

Very useful introduction. Many examples from audio and image processing. The software (available free from web site) makes it easy to demo some more advanced techniques. Must have for signals types.

Very good approach for wavelet analysis beginning with very well descripted, low complexity math and evolving to a more complex math and deep explanations in the medium to last part of the book. The first chapters get you tied to the arguments and evidences that will be explained more in detail in subsequent chapters.

Educationally, I consider this book a perfect introductory graduate level textbook with a good coverage of basic concepts that excites you to get more deep explanations.