A Primer on Wavelets and Their Scientific Applications (Studies in Advanced Mathematics) [Paperback]

James S. Walker (Author)

Book Description

ISBN-10: 0849382769 | ISBN-13: 978-0849382765 | Publication Date: March 26, 1999 | Edition: 1

The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques.

Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.

Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.

Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.

Product Details

• Paperback: 168 pages
• Publisher: CRC Press; 1 edition (March 26, 1999)
• Language: English
• ISBN-10: 0849382769
• ISBN-13: 978-0849382765
• Product Dimensions: 9.1 x 6.1 x 0.4 inches
• Shipping Weight: 8.8 ounces
• Average Customer Review: 4.1 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #1,853,795 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

33 of 34 people found the following review helpful:

5.0 out of 5 stars Wavelets in 20 simple pages, October 11, 2001

By 

Nihal Mehta (Plano, TX United States) - See all my reviews
(REAL NAME)   

This review is from: A Primer on Wavelets and Their Scientific Applications (Studies in Advanced Mathematics) (Paperback)

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.

27 of 27 people found the following review helpful:

5.0 out of 5 stars Excellent Introduction for us Beginners, September 2, 2001

By 

James B. Sisson (Idaho Falls, ID United States) - See all my reviews

This review is from: A Primer on Wavelets and Their Scientific Applications (Studies in Advanced Mathematics) (Paperback)

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.

11 of 12 people found the following review helpful:

5.0 out of 5 stars The ideas and the software., July 27, 2002

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: A Primer on Wavelets and Their Scientific Applications (Studies in Advanced Mathematics) (Paperback)

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.