Customer Reviews: Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics)
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This book has become a classic,-- and a hit;-- for more than ten reasons. It is multilayered, and yet presents a unity of ideas: The material, and the writing is engaging for the beginner, and for the research mathematician alike. When I used it in my teaching, it was equally popular with the math students, and those from engineering. I don't know if I can say this about any other book I have taught from. The students could follow all the carefully presented proofs, and the engineer could generate algorithms from the applied chapters.
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on October 10, 2000
This is the document that started it all. It is by far a great mathematical and theoritical piece of work. HOWEVER, if you are just starting off and want to learn about wavelets and do not have an advanced math or engineering degree (and I do mean ADVANCED), do not pick up this book. At least not at the beginning. There are much better books written for explaining wavelets and to better present the material. Ten Lectures is essentially one big proof. Try Mallat/Kovacevic or Strang...once you've got a solid understanding, come back to Daubechies and marvel at her work.
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on June 22, 2014
As stated by the author in the first sentence of her redoubtable treatise (p.1), "The wavelet transform is a tool that cuts up data or functions or operators into different frequency components, and then studies each component with a resolution matched to its scale." She goes on to trace the evolution of this mathematical tool, that is seen to rely (in the case of Meyer wavelets, p.119) on "quasi-miraculous cancellations." Sigrid Daubechies' contribution was that of developing an algorithm for defining a wavelet function that did not suffer from the drawbacks of previously-defined analytical or digital functions. Analytical functions, while usually sufficiently smooth, are not truncated in temporal or configuration space--nor are the associated temporal or spacial frequencies commonly accessed by Fourier transforms (p.4). On the other hand, digital functions such as square waves or step functions (or the Haar wavelet, p.15) are often not sufficiently smooth. As the author observes on the first line of Chapter 6 (p.167) "Except for the Haar basis, all examples of orthonormal wavelet bases in the previous chapter consisted of infinitely supported functions." Daubechies, however, was able to unravel the Gordian knot by defining discrete/digital wavelets (pp.53-105) that are both sufficiently smooth and naturally truncated or "compact" (i.e. "compactly supported," pp.194-199).

The author lucidly derives and proves the incredible properties of what have come to be called Daubechies wavelets--thereby convincing the reader that these amazing mathematical entities actually exist! It is difficult, however, to digest every proof laid out by the author. I would therefore suggest that the reader begin with the most interesting proofs, which are found in the first section (5.1, pp.127-137) of Chapter 5: "Orthonormal bases of wavelets and multiresolution analysis." The reader should pay particular attention to p.132, which introduces the trigonometric polynomial m0(u), the properties of which are further detailed on pp.155, 168, and 216.

For those of us who are not heavily involved in signal and image processing, however, Daubechies' book is a difficult place to begin one's study of wavelets. A better starting place for the novice would be an introductory textbook such as that of Burrus et al.: Introduction to Wavelets and Wavelet Transforms: A Primer. In reading Burrus along with Daubechies, however, the reader needs to keep in mind that the two books use different notations for expressing wavelets and scaling functions (Daubechies p.130; Burrus p.15), such that scaling parameter as used in one book's notation is the reciprocal of that defined by the other.

A good overview of the field is also provided by Hubbard's The World According to Wavelets: The Story of a Mathematical Technique in the Making, Second Edition. It is also necessary that the reader have an understanding of Fourier transforms at the level of Bracewell's The Fourier transform and its applications (McGraw-Hill electrical and electronic engineering series).

I should also note that Daubechies' subject index spans only two pages--which is not nearly long enough! The shortcomings of the index and the detailed nature of this monograph limit its usefulness as a reference book. Therefore, the reader needs to buy his own copy of Daubechies and mark it up to his heart's content, including notes on the title page (and the pages immediately following it) that may supplement the subject index.
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on May 5, 2013
This is an excellent book, very lucid and rigorous. I took Daubechies' course on wavelet analysis while I was at Princeton some years ago, and her course essentially follows this book. So this book makes a lot of sense to me, after taking her class. But beware, this is a book on mathematical analysis. It is not a book to learn about wavelets from a practical standpoint. If you are engineer, most likely you do not have the required mathematical background to understand anything from this book. This is really for math people, or engineers/physicists who are mathematically inclined. The pre-requisite are real analysis, complex analysis and analysis in several variable, and maybe a slight amount of functional analysis, although the latter is not really needed because most of the theorems are derived in this book. So to re-iterate, this is an excellent book, but it is not for learning about wavelets. Read Stephane Mallat's textbook instead, which was written to teach the topic from a more practical standpoint.
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on May 23, 2002
This book is a treasure of details if you know what you are doing. As another reviewer noted, it is not for the beginner. But if you have had some experience with the subject this is a must have for your library shelf.
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on April 1, 2000
Clearly Dr. Daubechies (the inventor of wavelets herself) has written the best (and most comprehensive) introduction to wavelets available. This book is suitable for the beginning graduate student in mathematics or physics and will also provide a extremely useful reference guide for years to come!
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on May 14, 2015
Original papers ... a good starting point to learn about wavelets.
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on September 6, 2014
great book.
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on March 30, 2016
Thank you
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on July 15, 2000
This book is classic. For anyone who wants really to know wavelets, in particular comapctly supported wavelets, this book is a must-read. Also, this book is truly well-written, which makes it suitable for text of a beginning gradaute course. Thanks to Dr. Dabechies!
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