A Wavelet Tour of Signal Processing [Hardcover]

Stephane Mallat (Author)

Book Description

ISBN-10: 0124666051 | ISBN-13: 978-0124666054 | Publication Date: January 26, 1998

A Wavelet Tour of Signal Processing begins with a presentation of the wonders of the Fourier transform, and then describes its failures for transient signal processing. It presents local time–frequency methods and the related mathematical tools. The book uses an intuitive approach to important mathematical results, and emphasizes practical applications rather than proofs. It describes numerical discrete algorithms as well as some applications to information processing, fractal analysis, noise removal, and compact signal coding.
A Wavelet Tour of Signal Processing is intended for signal processing engineers who want to discover the potential applications of recent mathematical advances in time–frequency signal representations. Of interest to researchers in applied mathematics, the book highlights the applications of these new techniques and also provides an overview of signal processing problems.

Emphasizes practical applications rather than proofs
Presents local time–frequency methods and the related mathematical tools
Uses an intuitive approach to important mathematical results

Editorial Reviews

Review

"Mallat has not only written a treatise, but also an excellent graduate
text for students in computer science, electrical engineering, and
mathematics" John J. Benedetto, SIAM review --This text refers to an out of print or unavailable edition of this title.

From the Back Cover

This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École
Polytechnique in Paris.

*Provides a broad perspective on the principles and applications of transient signal processing with wavelets.
*Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms.
*Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection,
multifractal analysis, and time-varying frequency measurements.
*Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet.
*Content is accessible on several level of complexity, depending on the individual reader's needs.
*Reviews Fourier analysis and elementary signal processing.
*Introduces windowed Fourier transforms, continuous wavelet transforms, and Wigner-Ville transforms.
*Explains the construction of frames, wavelet orthogonal and biorthogonal bases, wavelet packet and local cosine bases.
*Covers basic approximation theory with applications to signal estimation and transform coding. --This text refers to an out of print or unavailable edition of this title.

See all Editorial Reviews

Product Details

• Hardcover: 577 pages
• Publisher: Academic Press (January 26, 1998)
• Language: English
• ISBN-10: 0124666051
• ISBN-13: 978-0124666054
• Product Dimensions: 9.1 x 6.1 x 1.8 inches
• Shipping Weight: 2.2 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #1,344,310 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

26 of 28 people found the following review helpful:

5.0 out of 5 stars A bold approach to wavelet transforms that simplifies, April 23, 2002

By 

Anthony Diepenbrock III "adiepenbrock" (San Jose, CA USA) - See all my reviews
(REAL NAME)   

This review is from: A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications) (Hardcover)

This is an outstanding tour through the field of wavelet decompositions of both continuous and discrete signals. It employs the formalism of Hilbert space, instead of linear algebra. This is important because the power of this formalism yields insights into the subject matter that are practically impossible in linear algebra. The formalized approach allows a wide variety of subjects to be placed on a common basis (no pun intended). For example, the transition of the treatment of the Fourier transform into Hilbert space, brings to bear the powerful guns of that space (such guns as inner product and completeness), and allows for a truly elegant proof of the Parseval and Plancherel formulas.
Parseval's theorem, simply stated, is that the inner products in Hilbert space are conserved by the Fourier transform. How simple. Linear algebra approaches cannot hope to make things this simple.

Proof of the General Sampling Theorem is equally elegant; it is shown that the projection of the function to be decomposed onto a basis function gives the discrete spectral coefficient.

Readers will also enjoy the treatment of windowed Fourier transforms and frames.

I should add a note about the style of the treatise. This treatise is not ordinary. It consistently uses very precise and carefully defined symbology. Contrary to popular belief, this makes the text easier to read, not more difficult. Once the reader understands the symbol set being used (they are all defined in the front of the text), even the proofs are tractable. Yes, I said proofs. That is another aspect of the text. There are proofs embedded in the text, without loss of continuity or clarity. Proofs are necessary to a good understanding of the subject matter. The formalism of theorems, lemmas and propositions makes the conclusions understandable, because the theorems, lemmas and propositions supporting the conclusions are identifiable.

I applaud the author for his approach and recommend that other text book writers use the same approach.

14 of 14 people found the following review helpful:

5.0 out of 5 stars Searching for an understanding of wavelet concepts ?, June 13, 2000

By A Customer

This review is from: A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications) (Hardcover)

As someone learning about wavelets on their own, I found this book much more approachable than many others. You don't need to chew through the proofs to understand the concepts - and if you do, they're ranked according to difficulty ! The chapters are relatively self-contained, and just when your mind begins to stray he throws in a really interesting example.

10 of 11 people found the following review helpful:

5.0 out of 5 stars GREAT and CLEAR, February 7, 2000

By 

A Customer - See all my reviews

This review is from: A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications) (Hardcover)

I bought this book because of the good name of the author at first. He used great and clear Mathematics and diagrams to explain the theory and applications of the wavelet. It is easy for graduate student to follow, I feel. And I kept this book as my faviour book in my bookself.