A Wavelet Tour of Signal Processing (Wavelet Analysis & Its Applications)

Rating:
Summary: Searching for an understanding of wavelet concepts ?
Review: 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.

Rating:
Summary: The worst textbook I have ever seen
Review: I just finished Chapter 3 of this book, but I have had enough of it. Conceptions about Fourier Transform are not clear at all. And the most unbearable thing is that, there are many printing errors which may lead to misunderstanding.

Rating:
Summary: I could rate this book with all the stars in the Universe.
Review: The book is difficult to follow. Though Mallat has attempted to be mathematically rigorous, the proofs unfortunately involve steps that have never been satisfactorily explained. So, to get a solid foundation, I believe it is important to go through the proofs of the theorems, not just the statements & that's hard in this book. The portion on Fourier Analysis especially was important to get a good foundation on why wavelets are important but it was way too short & the proofs had problems as mentioned above. If you are looking for an easy guide (as some non-serious programmers do tend to do), it however involves sifting through too much material till you can piece together what you need so the book is not for the dilettante either.

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Summary: Algorithms and much more!
Review: The subject of wavelets has many facets, --infinite in all directions;-- some of the more exciting sides of the subject
are algorithmic, and the underlying mathematical principles are both simple and powerful. Stephane Mallat's great, and readable, book, in both of its editions, brings
this out wonderfully!

Rating:
Summary: A bold approach to wavelet transforms that simplifies
Review: 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.