A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications) (Hardcover)

by Stephane Mallat (Author) "After a few minutes in a restaurant we cease to notice the annoying hubbub of surrounding conversations, but a sudden silence reminds us of the..." (more)
Key Phrases: thresholding risk, bounded variation signals, admissible binary tree, Fourier Parseval, The Hilbert-Schmidt (more...)

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 -- Review

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

See all Editorial Reviews

Product Details

• Hardcover: 637 pages
• Publisher: Academic Press; 2nd edition (September 15, 1999)
• Language: English
• ISBN-10: 012466606X
• ISBN-13: 978-0124666061
• Product Dimensions: 9 x 6.1 x 1.5 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars See all reviews (10 customer reviews)
• Amazon.com Sales Rank: #624,946 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

25 of 27 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 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

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 (Australia) - See all my reviews

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.