Customer Reviews

A Wavelet Tour of Signal Processing

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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.

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.

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.

I say universal because this book would appeal to engineers, computer scientists, and mathematicians alike. Mallat was particularly successful to present the topic in a sufficiently rigorous way but without losing sight of the practical and more intuitive side. The presentation comprises the mathematical and the signal processing viewpoints simultaneously. The wavelet field is very vast by now with several subfields. In this respect, Mallat made a great selection of topics in this book. There is a chapter on estimation which offers great review material and pretty much the state-of-the art on signal estimation over a wavelet basis. The chapter on approximation is particularly useful for those who are not well versed in approximation theory and thus are unable to understand other treatments. If you're interested in learning wavelet theory to solve practical problems such as image compression, signal estimation, etc, this is the book to have.

A great tool for Harmonic Analysis. The book is really well written, a most read for any one who is interested in the area of wavelets, S.P. or harmonic analysis.

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.

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!

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.

1980:Marr:"Theory of edge detection" Subject text:"A major difficulty with natural images is that changes can and do occur over a wide range of scales. NO single filter can be optimal SIMULTANEUSLY at all scales, so it follows that one should seek a way of dealing separately with the changes occuring at different scales"...

Well here is the man who used unconsiously wavelets I thought when I first read this article. Canny just computerized these thoughts embedding some additional signal theory. They both concluded on the same filter: Gaussian filter. Well the gaussian is a wavelet I thought...(Year 2000)

1990:Mallat:He extended these filters producing a family of wavelets. And of course the gaussian is now a wavelet base shattering my dreams of a new discovery. I thought of another thing, found in this book, and another thing also found in this book. So in this book I see what I wanted for wavelts to repesent. Well I am using images as signals but I am convinced that the same happens with other kind of signals.

This book is a must in Signal Processing. Obtain it!

This book shows distict figures about wavelet through easy and comportable tour.