Wavelets: A Primer [Hardcover]

Christian Blatter (Author)

Book Description

Publication Date: January 15, 1999

The Wavelet Transform has stimulated research that is unparalleled since the invention of the Fast Fourier Transform and has opened new avenues of applications in signal processing, image compression, radiology, cardiology, and many other areas. This book grew out of a short course for mathematics students at the ETH in Zurich; it provides a solid mathematical foundation for the broad range of applications enjoyed by the wavelet transform. Numerous illustrations and fully worked out examples enhance the book.

Editorial Reviews

Review

Wavelets: A Primer is a fine recommendation for any college-level collection strong in engineering, and grew out of a short course for math students on the subject of wavelets. Illustrations, examples, and discussions offer a fine introduction to the field. A pick for math students who have knowledge of analysis with little practical applications.
—Midwest Book Review, October 2011

Language Notes

Text: English (translation)
Original Language: German

Product Details

• Hardcover: 212 pages
• Publisher: A K Peters/CRC Press (January 15, 1999)
• Language: English
• ISBN-10: 1568810954
• ISBN-13: 978-1568810959
• Product Dimensions: 9.1 x 6 x 0.7 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #2,809,066 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

4.0 out of 5 stars Wavelets: from valley to crest, December 13, 2000

By 

Marcel G. de Bruin (Delft, The Netherlands) - See all my reviews

This review is from: Wavelets: A Primer (Hardcover)

Choosing a book on Wavelets to use as material for an introductory course is far from simple: there are many books on the subject and often the mathematical starting level of the audience is not uniform. But the book by Blatter is in my opinion very good if one wants to start from scratch (well, not quite of course: some knowledge of Lebesgue integration and infinite dimensional Banach and Hilbert spaces of functions is needed) in a mathematical or technical environment.

Starting with 2 chapters on Fourier analysis, going from windowed Fourier transform to a first introduction of continuous wavelet transform (CWT), and giving connections to several well known facts from signal analysis (the Heisenberg uncertainty priciple and the Shannon sampling theorem), the theoretical framework of the CWT is given in chapter 3. Interesting are the results on the decay of the wavelet transform in terms of the smoothness of the signal and the number of vanishing moments for the wavelet.

This is followed by a chapter on the important subject of 'frames' and one on multiresolution analysis (the foundation for the hierarchy of orthonormal bases for L^2(R)). The scaling function (time domain) is actuallly constructed from its properties in the Fourier domain (i.e. the frequency domain).

The final chapter treats the basic idea behind and constructions of orthonormal wavelets with compact support (including the Daubechies wavelets), also touching upon binary interpolation and so called spline wavelets.

For applications to a host of disciplines it is possible to consult one of the many applied books: in my opinion it is necessary to have a firm grasp of the underlying theoretical framework before really understanding what one is doing. I have nothing against applications, but once one has to go back to the roots: back to the valley to be able to reach the crest of the wavelet without accidents.

5 of 6 people found the following review helpful:

4.0 out of 5 stars Good on theory-bad on application, July 10, 2000

By 

K. Qureshi (Cincinnati, OH United States) - See all my reviews
(REAL NAME)   

This review is from: Wavelets: A Primer (Hardcover)

This book is a good tool for those who want to explore the mathematical rigors of wavelet theory. The "primer" assumes that the user is a fairly well versed mathematician, but the derivations are complete. There is little to nothing said about the practical applications of wavelets. For applications, look to other books.

1 of 2 people found the following review helpful:

4.0 out of 5 stars A real primer, October 4, 2000

By 

Marcel G. de Bruin (Delft, The Netherlands) - See all my reviews

This review is from: Wavelets: A Primer (Hardcover)

This booklet, the translation of the original German version "Wavelets - Eine Einfuehrung" (published by Vieweg-Verlag), is indeed a real primer.

It removes old layers of thinking about the structure of signals and replaces them by an elegant formalism rooted in the theory of Hilbert spaces and orthonormal bases.

A graduate background on Hilbert spaces (L_2 etc.), the Fourier transform and some integration theory (Lebesgue integration) is recommended.

There are very few (easily corrected) typos and the book can be used as a basis for a one quarter course of 4 hours each week during 7 weeks (or a semester of 2 hours), with a backing of handout problems on several aspects of the theory.