Book Description

"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"

Customer Reviews (1)

From Fourier to wavelets to applications.
I take it as a healthy sign when there is a burst of new books in a sub-area of math. In wavelet analysis and its applications, we have seen a number of recent books arrive to university bookstores. Surprisingly there doesn't in fact seem to be much of an overlap of subject or scope, from one book to the next. The subject is infinite in many directions, for example the kind of student it is aimed at, the level, the specialized area within math itself, and the kind of application it is stressing. D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material, for example Fourier series, than is typically the case in a graduate text. It goes from Haar systems to multirelutions, and then the discrete wavelet transform, starting on page 215. The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes.-- Highly recommended! ... Read more

Book Description
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.

Key Features
* 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
New to the Second Edition
* Optical flow calculation and video compression algorithms
* Image models with bounded variation functions
* Bayes and Minimax theories for signal estimation
* 200 pages rewritten and most illustrations redrawn
* More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics ... Read more

Customer Reviews (10)

GreatBook
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 most universal treatment of the subject
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 areunable 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.

The worst textbook I have ever seen
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.

Algorithms and much more!
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!

A bold approach to wavelet transforms that simplifies
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. ... Read more

Book Description
The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance provides an overview of the theory and practical applications of wavelet transform methods. The author uses several hundred illustrations, some in color, to convey mathematical concepts and the results of applications.The first chapter presents a brief overview of the wavelet transform, including a short history. The remainder of the book is split into two parts: the first part discusses the mathematics of both discrete and continuous wavelet transforms while the second part deals with applications in a variety of subject areas, such as geophysics, medicine, fluid turbulence, engineering testing, speech and sound analysis, image analysis, and data compression. These application chapters make the reader aware of the similarities that exist in the use of wavelet transform analysis across disciplines. A comprehensive list of more than 700 references provides a valuable resource for further study.The book is designed specifically for the applied reader in science, engineering, medicine, finance, or any other of the growing number of application areas. Newcomers to the subject will find an accessible and clear account of the theory of continuous and discrete wavelet transforms, providing a large number of examples of their use across a wide range of disciplines. Readers already acquainted with wavelets can use the book to broaden their perspective. ... Read more

Customer Reviews (1)

An excellent and informative book
This book provides a comprehensive overview of wavelet transformmethodologies and applications. The emphasis is on practical applications which are illustrated with many detailed figures and examples from Science and Engineering. A particular interesting chapter on medical applications is provided. In the introductory chapters, Addison gives a clear account of the theory for both continuous and discrete wavelet transform and associated post-processing techniques. Unlike many of the other books in this area, Addison communicates the concepts with a level of detail, sufficient for the applied engineer and scientist, but without becoming bogged down in a fog of mathematical gymnastics (a feature of many of the books in this area). A welcome addition to the growing number of books on this important signal analysis technique. ... Read more

Product Description
Although DSP has long been considered an EE topic, recent developments have also generated significant interest from the computer science community. DSP applications in the consumer market, such as bioinformatics, the MP3 audio format, and MPEG-based cable/satellite television have fueled a desire to understand this technology outside of hardware circles.Designed for upper division engineering and computer science students as well as practicing engineers, Digital Signal Processing Using Matlab and Wavelets emphasizes the practical applications of signal processing. Over 100 Matlab projects and wavelet techniques provide the latest applications of DSP, including image processing, games, filters, transforms, networking, parallel processing, and sound. The book also provides the mathematical processes and techniques needed to ensure an understanding of DSP theory. Designed to be incremental in difficulty, the book will benefit readers who are unfamiliar with complex mathematical topics or those limited in programming experience. Beginning with an introduction to Matlab programming, it moves through filters, sinusoids, sampling, the Fourier transform, the Z transform and other key topics. An entire chapter is dedicated to the discussion of wavelets and their applications. A CD-ROM (platform independent) accompanies the book and contains source code, projects, and Microsoft® PowerPoint slides. ... Read more

Customer Reviews (1)

Great introduction to MatLab and DSP
This book is very readable and is chock-full of examples, sample code and explanations of DSP concepts.I think the best way to read it is to start with Chapters 1-2, which give an introduction to DSP and an overview of MatLab. Then, immediately follow this with Chapter 10, which covers applications.Subsequent chapters can be read as needed. ... Read more

Book Description
Describes the more recent, meteoric rise of wavelet analysis and its manypractical applications. Includes the new medical and genetic applicationssuch as mammography, heart disease, and fingerprints. DLC: Wavelets(Mathematics). ... Read more

Customer Reviews (13)

tells the story well
What is impressive is how the author has told a story about wavelets, at a level that correctly communicates the mathematical essence. Where specifically the impressive achievement is that that level is for a first year undergrad. The maths discussed involves Fourier series [of course!], definite integrals, and simple matrix manipulations.

En route, she explains the Fast Fourier Transform. She credits Gauss as the original inventor, but does not mention Cooley and Tukey who independently rediscovered it, when computers were available to actually make the method practical. There's a hilarious little aside, when she does some approximations and credits this to "minor" administrative overhead. Where the humour is that universities typically charge 40% overhead on government grants! Must remember that.

Excellent Introduction to Wavelets
This is an excellent introduction to wavelets and also the Fourier Transform. The first part of the book is readily accessible to almost anyone who has a passing knowledge of high school math. The second half will mostly be useful to the more mathematically sophisticated. It is an ideal kick startfor any one who has the requisite knowledge and is motivated to learn more about the applications and theory behind wavelets.

It is not likely that this book will satisfy all your needs if you intend to master this subject but if you are just getting started, I would start here.

Good effort, but no
The author of this book states in the preface that her goal is to make wavelet theory accessible to the layman, without bombarding them with "paralyzing" "funny symbols or hieroglyphics" they haven't learned yet. I thought this was a wonderful idea, as I am a layman who never made it past high school geometry with an interest in learning all about the successor to the ubiquitous FFT used in engineering. Unfortunately, while she does manage to avoid using excessive amounts of "hieroglyphics" in the first part of the book, she makes up for it by throwing around a lot of mathematical terms which are never defined for the reader, so the net result in terms of comprehension is ultimately the same as if she had used the formulae, if not worse. Ms. Hubbard will dedicate three pages worth of text to an anecdotal retelling of some conversation that took place between two researchers in front of a Xerox machine, and then suddenly throw in one line at the end of all this nonsense about integrals and coefficients, as though the preceding story somehow prepared the reader for these terms well enough to divine their meaning from one terse little sentence devoid of any contextual clues. It may be presumptuous of me, but I don't think these words mean any more than the much maligned "hieroglyphics" would to the average layman this book is meant to be read by.

On top of that, the diagrams and illustrations are horrible, looking like something that came out of a dot-matrix printer in the late 70s, and ultimately illustrating nothing.

The world desperately needs a book that actually does what this one claims to. "Who is Fourier?" certainly managed to pull it off well enough for the Fourier Transform despite being translated from Japanese, so I'm certain it's possible even if Ms. Hubbard happened to fail miserably at her task.

Good for start
I was very happy reading this book. If you are familiar with the Fourier transform and don't know anything about wavelets, this is a book for you.

Actually, the book has got two parts. In the first part you can learn basic things about Fourier transform (about its usage but also about its limits), what we need wavelets for and what the wavelets are. It is explained in very simple language without any formulas. The second part contains basic formulas related to the topics in the first part. I find that the link between these two parts is very good. Also, the author gives physical explanation whenever it's possible.

If you are a specialist in the wavelets area, you probably know all these things but if you are new (like me!) you will find that this book is quite useful.

It can be done!
I am a math professor,-- and I often wondered if it wouldn't be possible to get some essential math ideas accross to almost anyone, --and with fewer equations. Ideas can be burried in symbolism;-- not always! But it does happen. Many of my colleagues tell me that if it were possible, then it would be done. The author of this lovely little book didn't take math courses (she says!). Professional mathematicians would most likely agree with me that she (the author) did in fact communicate the essential ideas behind wavelets (and did it well!);- and so she must have understood them!! Perhaps, anyone who really wants to, can penetrate a specialized math discipline;-- I would guess. Perhaps it is not even hard!? At least this book proves that it is not impossible to communicate
the beauty of math;--and its uses. Take a look at the book, and judge for yourself!
It is fun too! ... Read more

Book Description
An easily accessible introduction to wavelet analysis, this book explains the subject using algebra and some basic calculus and stresses applications, such as speech compression, removing noise from audio and images, image compression, and image enhancement. The author offers downloadable software that permits recording, playing, and modifying sound files using wavelet techniques, plus a facility for displaying, printing, and modifying standard IEEE gray field images. New sections include Biorthogonal Wavelets, The JPEG200 Image Compression Standard, Spectrograms, Analyzing Speech and Music with Spectrograms, Wavelet-Based Denoising of Images, and Thresholding Spectrograms for Denoising. ... Read more

Customer Reviews (7)

A Primer on Wavelets and Their Scientific Applications
This book is an excellent one to learn the fundamental concepts of the wavelet transform. I recommend to study this book before starting or while studying another more mathematical text.

A little pedantic at times, but generally quite good....
At times, particularly at the beginning, the author seems almost patronizing, but generally the tone and level of the book is just where it should be for what seeks to be a primer.However, it is unfortunate that one of the primary functions in the software is not more fully described in the text;it is only described as the method of preparing many of the examples.

Overall, an excellent start for somebody who knows little or nothing about wavelets.

Best introductory book on wavelets
This is the best introductory level book on wavelets I have read. It is written beautifully and is one of the few books that provides insight as to how and why wavelets are useful.

Everyone should start out their investigation of wavelets with this book first. Highly recommended.

The ideas and the software.
This lovely little book helps the novice to get an idea of the math which underlies wavelets;-- and at the same time to learn how one readily gets hold of software that is convinient,-- that will make it easy for anyone to start playing around with it. The author also explains in plain English the wavelet aspects, and some of the mathematical constructs, behind audio denoising, signal compression, image recognition, speech recognition and more.

Wavelets in 20 simple pages
This is simply the best book I have come across on introducing wavelets.

I am sure that within the first 20 pages, which are easy to understand and make for a very quick read, you will begin to see the beauty of this theory and will applaud the author's exposition.

While this book does not need much more than basic linear algebra, the author does not shy away from the mathematics where necessary - he simply motivates it by providing an intuitive understanding of the equations, so it's easy to follow.

In the very first chapter, he describes the wavelet method using examples that can be worked out by hand. (This is also mentioned in another review and contributed to me buying this book. I was doing research on anotherwavelet book on the site when I came across this book and it's reviews.)This helps to fix and brilliantly clarify the main ideas behind the theory. Armed with this knowledge, the reader can better appreciate the more sophisticated wavelet functions. But, the basics would be firmly planted by this book. This is rarely seen in other books dealing with this thoery.

This book is great for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts.

The discussion is motivated with real world examples such as removing noise from signals, image enhancements, etc. These are useful examples that you can relate to. There is enough in this book and the downloadable software that you may want to undertake meaningful projects yourself. That is the confidence that you get from this book.

An outstanding quality is that the book is thin. This is a strong motivating factor since it immediately sends the message that "this method can't be that hard to grasp if the book is so short." And, this subliminal message keeps your spirits up as you read this masterpiece.

Wavelets is a mathematically intensive technique, and it seems that most authors want to show how "macho" they are by shrouding the basics under a heavy cloak of complex equations.But, true "machoism" is displayed by how deftly an author can bring a difficult topic to the lay person. James Walker does this remarkably well. ... Read more

Book Description
The analysis of time series data is essential to many areas of science, engineering, finance and economics. This introduction to wavelet analysis "from the ground level and up," and to wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. Numerous examples illustrate the techniques on actual time series.The many embedded exercises--with complete solutions provided in the Appendix--allow readers to use the book for self-guided study. Additional exercises can be used in a classroom setting.A Web site offers access to the time series and wavelets used in the book, as well as information on accessing software in S-Plus and other languages. Students and researchers wishing to use wavelet methods to analyze time series will find this book essential. Author resource page: http://faculty.washington.edu/dbp/wmtsa.html ... Read more

Customer Reviews (7)

introduction to wavelets and its applications in time series
The purpose of this text is to introduce wavelet methodology targeted toward applications in time series analysis. Emphasis is placed on the discrete wavelet transform and other discrete wavelets. There are many analogies to the spectral analysis of time series that the authors make. The authors do not assume knowledge of Fourier analysis and cover the relevent theory in Chapter 2. Just as the frequency domain methods decompose the variance of a time series into frequency components so to do wavelets decompose the variance according to scales. The authors take great pains in demonstrating this with several wavelets including the DWT and MODWT. Fast transform methods exist for wavelets as well as for Fourier series and they are apparently even simpler and faster for wavelets.
The text tries to be self-contained and the authors start out at a very elementary level. They emphasize applications and practical aspects of wavelets.

Interesting hints in cumbersome expressions
The book has interesting features but presented to me several drawbacks. Though it tries to be self-contained in introducing the wavelet subject, the resultin theoretical structure is poor. and general properties of wavelets remain scattered for all over the book, leaving some gaps. Perhaps my opinion is biased by being used to classical introductions stressed on Multi Resolution Analysis. Moreover, the habit of carrying on calculation with explicit indexes, quoting intermediate results and unusual notations (e.g. denoting a function as x(.) instead of x(t) in order not to bind to a specificic variable) clutter the book with cumbersome expressions, even if in that form they can be straightforwardly rendered in computer routines. I just wonder how people without a previous knowledge about wavelet methods can have dealt with the textbook.

Well written.
Well written book. It would be nice to have some "MatLab" problems.Excellent motivational or explanatory examples.

I gave it three stars because most reviewers are far to liberal with their stars. To me 3 stars means worth buying, 4 means a must buy, and 5 means it'll be a classic for a long time.

I equate this book to Mallet's "A Wavelet Tour of Signal Processing". The subject matter is slightly different, but both are very readable.

Reference for time series analysts using wavelets
Few wavelet books offer such a deep insight into wavelet methods
for time series analysts. It goes very deep within the applied
side of wavelet analysis on real time series while not compromising
the mathematical side. A lot of books and papers insist too much
on the mathematical side of wavelets while this one provides just
the right balance between rigor and practical insight. If your
interest does not lie in maths but just in wavelets as a tool,
stick to this one.

As a bonus, it contains a lot of exercices along with answers
at the end of the book...a very good textbook indeed...

First rate all the way
As far as I am concerned,anything Don Percival writes about the topic of wavelets - or digital signal processing - is well worth reading. I was struggling to understand wavelets before I ran across a paper by Percival (and cohorts from the University of Washington) on interpreting remote sensing sea ice data using wavelets. After reading the very clear and compact description of wavelet analysis the light bulb clicked on for me. This book is a must read for anyone interested in wavelets from beginners to experienced practicioners. ... Read more

Book Description

This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals.

Customer Reviews (1)

One of the most fascinating books which I have ever seen.
Modern electronic devices such as cameras and computers use (among others) the
jpeg-format to store photographs. Millions of people employ such wavelet-based
technology every day. In sharp contrast to that, only a few thousand people on
the planet have a detailed understanding of the mathematics concerning the
C*-algebras O_n even though (as the book under review shows) there is a
strong relationship between the two.

This book entertains and educates the reader with a high-precision tour
connecting very current technological advances such as high-tech filters and
compression methods, classical mathematics such as wavelets and probability
theory and advanced, new mathematical methods such as non-commutative Hilbert
space operator algebra applications. This book distinguishes itself by placing
modern mathematics close to modern technology and by showing (again) that pure
mathematics is not necessarily only for mathematics' sake. The author Palle
E.T. Jorgensen is a world-class mathematician with a distinguished publication
record. This is a book that *every* student of mathematics should read in
order to be guided and motivated what courses to take, what other more basic
books to read, and what research to pursue. This is a book that computer
scientists, physicists and engineers should read. In my opinion, it could
spawn new innovation, maybe no patents, but benefits for all of mankind. ... Read more

Book Description

This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. This is the only book to present the mathematical point of view, as well as the discrete-time signal processing perspective. It brings together information previously available only in research papers, in engineering and applied mathematics. Appropriate for researchers and practitioners in signal processing and applied mathematics.

Customer Reviews (5)

Nice approach (for physicists)
If you studied Mathematical Physics or if you like the mathematical approach that physicists used to write their papers and lectures, it 's a pleasant book to understand wavelets.

Good Book
Before reading this book, read the wavelet chapter from

Digital Image Processing (2nd Edition)
by Rafael C. Gonzalez, Richard E. Woods

If you don't know anything about Wavelet Analysis Start Here
I have examined most of the popluar books printed on the subject of Wavelet Analysis and this is the best book for those who want to understand what a wavelet is, where is comes from, and how is it is useful for performing Time Scale signal analysis. I strongly suggest starting with this book.

introduction to Wavelets and Waveletstransforms
The introduction to Wavelets and Wavelets transform aplications.

theoretically sound, non-trivial tutorial
This book is a crafted piece as opposed to one of those collections of journal articles that usually leave you wondering.It appears to have a sound theoretical foundation with some clearly presented definitions and theorems.I wouldn't hesitate to spend time with this one. ... Read more

Book Description
The mathematical theory of wavelets is less than 15 years old, yet already wavelets have become a fundamental tool in many areas of applied mathematics and engineering. This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinite-dimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given. This text is ideal for a topics course for mathematics majors, because it exhibits and emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets. ... Read more

Customer Reviews (6)

One of the best wavelet books
i use this book in order to write my bachelor thesis, it is great, very dynamic, and with a lot of examples and exercises.

It also has an excellent walk through from linear algebra to wavelets, giving a more understanding point of view of this signal analysis tool.

Notation...
I used this book for my first course in wavelets.Professor Frazier did a nice job bringing the material down to the undergrad by not starting off in hilbert space.He motivates it through linear algebra (for which the first chapter is an excellent review of the basics!).My only complaint is that the notation gets a bit overwhelming starting in chapter 3 (though I dont' know if I could come up with a better way to do it; just my experience).If you're looking into the subject, check out this book.It'll get you going in the right direction.

basis construction using wavelets is very well developed
Although the notation can be a little tight, the explanation of the
construction of a basis using wavelets is very well developed. He starts
with finite dimensional spaces and then moves onto wavelets on the real
line. He has a good series of graphs of signals and their corresponding
wavelets transforms and points out meaningful features of the wavelet
transform graph.

Obscure presentation
While I don't consider myself a math expert, I have certainly had to navigate my way through undergrad level math texts on more than a few occasions. In preparation for this book, I re-read Strang's "Linear Algebra and Its Applications" (an excellent text) and felt confident that I should be able to assimilate the material from this book. From the outset, the order of presentation of material in this book seemed promising: start with a review of Linear algebra and complex numbers, continue with Discrete Fourier Transforms, and then develop discrete wavelet transforms followed by continuous wavelet transforms.

Unfortunately, in spite of a promising game plan, this book serves to obscure the subject rather than providing a accessible introduction. The writing style is very terse and takes the reader through Lemma after Lemma without much in the way of explaining the motivation of these theorems or providing connecting narratives. The the reader is required to assimilate numerous disconnected mathematical ideas before a attempt is made to pull together the main ideas. And when the main points are developed, the treatment is uneven and generally too sparse. The only illustrations in this book come from MatLab or some other wavelet software package and there is a lack of conceptually oriented diagrams found in other types of text books.

Overall this book seems to be a compilation of material drawn from various sources and "sewn" together with mathematical proofs. Rather than focus on the main problems that wavelets are supposed to address (namely temporal and spatial localization) and develop the mathematics from that perspective, the emphasis on Lemmas and proofs drowns the reader in too much detail too fast. While this book may be a good supplement with other material, I found that this book too tedious to read and is a poor introduction to the subject without the benefit of a good instructor.

Obscure presentation
While I don't consider myself a math expert, I have certainly had to navigate my way through undergrad level math texts on more than a few occasions. In preparation for this book, I re-read Strang's "Linear Algebra and Its Applications" (an excellent text) and felt confident that I should be able to assimilate the material from this book. From the outset, the order of presentation of material in this book seemed promising: start with a review of Linear algebra and complex numbers, continue with Discrete Fourier Transforms, and then develop discrete wavelet transforms followed by continuous wavelet transforms.

Unfortunately, in spite of a promising game plan, this book serves to obscure the subject rather than providing a accessible introduction. The writing style is very terse and takes the reader through Lemma after Lemma without much in the way of explaining the motivation of these theorems or providing connecting narratives. The the reader is required to assimilate numerous disconnected mathematical ideas before a attempt is made to pull together the main ideas. And when the main points are developed, the treatment is uneven and generally too sparse. The only illustrations in this book come from MatLab or some other wavelet software package and there is a lack of conceptually oriented diagrams found in other types of text books.

Overall this book seems to be a compilation of material drawn from various sources and "sewn" together with mathematical proofs. Rather than focus on the main problems that wavelets are supposed to address (namely temporal and spatial localization) and develop the mathematics from that perspective, the emphasis on Lemmas and proofs drowns the reader in too much detail too fast. While this book may be a good supplement with other material, I found that this book too tedious to read and is a poor introduction to the subject without the benefit of a good instructor. ... Read more

Book Description
This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. They are a fairly simple mathematical tool now being applied to the compression of data, such as fingerprints, weather satellite photographs, and medical x-rays - that were previously thought to be impossible to condense without losing crucial details. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval. ... Read more

Customer Reviews (7)

Well... It was written by Ingrid!!
What can I say, Wavelets explained by Ingrid Daubechies! You can't go wrong.

Over rated
There are so many well written books on Wavelts out nowadays. Don't waste your money on this one. It's famous because it was first (or one of the first). On the positive side, it does present a strong mathematical foundation. I recommend you buy a readable book (just do a search on Amazon.com and you'll find half a dozen great books on Wavelets), then when you approach the "expert" level, use this one a s a reference (if at all).

Great for everyone!
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.

Not for the faint of heart!
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.

Theoretical Wonder....but you won't learn wavelets from it!
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. ... Read more

Book Description

This book, written at the level of a first course in calculus and linear algebra, offers a lucid and concise explanation of mathematical wavelets. Evolving from ten years of classroom use, its accessible presentation is designed for undergraduates in a variety of disciplines (computer science, engineering, mathematics, mathematical sciences) as well as for practising professionals in these areas.

This unique text starts the first chapter with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra.

The second part of this book provides the foundations of least squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets.

Customer Reviews (6)

too much standard Fourier non-wavelet material
Wavelets have been making a splash in some circles. Here is a chance to acquire a rigorous education in them. Basically, wavelets are a topic in advanced Fourier analysis, as the book makes clear. In fact, of the book's 3 parts, one is a recap of basic Fourier analysis. It is somewhat of a pity that the author included it. The coverage is a synopsis of standard texts on Fourier analysis. Omitting it would have left more space for wavelets.

Along these lines, the last part, on computation and design of wavelets, has one of its three chapters being a standard discussion about Fourier transforms.

Of the book's 9 chapters, only 5 are on wavelets. Too few.

Finally, Wavelets are explained !!
Thank Yves.

I enrolled in an online graduate course for wavelets and could not understand the book and the professor liked to give very few problems with very little help to ensure that he would not have to grade many problems and to ensure that we would not understand the material well. I searched the web and checked out about 10 wavelet book in the library and still I could not get a clue on wavelets in how they actually worked and the mathematics behind them.

But, ... with Yves' book, ... it does still take some mental effort, but his book is readable and the homework assignments are doable without an instructor leading you or mis-leading you as the case may be.

Wavelets applications fascinate me and without Yves book, I still wouldn't have a clue.

Excellent.
The book is excellent in the sense that it has the right mixture of both theoretic and practical aspects. The portions on Fourier transforms also are apt for a newcomer to understand the theory. Of course, the first impression formed by seeing the title is that the matter inside would be plain english without any mathematics. However, the mathematics in the book has been kept elementary and in places where that wasn't possible, a thorough introduction has been provided.

The applications are explicitly mentioned and algorithms are written down clearly, instead of simply providing the theory and leaving the implementation for the student to figure out for himself. For the less mathematically oriented, the exercises at the end of each chapter will provide a good intuition to what will be encountered in the consequent sections. Once this book is read, other books that concentrate on specific aspects of wavelets will appear to be more understandable.

The complex cannot be made easy, but it can be made clear
When I first saw this book, which is heavy on equations, I thought "wow, if this is wavelets made easy, I'd hate to see the hard version". And indeed this book is not light reading. But it is clear and there are plenty of examples. This book is far and away the best book on wavelets that I've found.
Wavelets are a complex topic. It would be unfair to think that you can pick up a book like this an read it like a popular science book. Reading a book like this takes concentration and effort. Implementing wavelet software is even more work, since some of the "in-place" algorithms are difficult. "Wavelets Made Easy" is a great foundation for anyone who wants to apply Haar wavelets for data analysis and filtering.
...

Nievergelt's coverage of Daubechies wavelets is not as
good as his coverage of Haar.He clearly explains the matrix
(linear algebra) view of Daubechies wavelets.The
coverage of edge effect issues is also good.However, as the
chapter proceeds, it fell apart, at least for me.There
appear to be errors in some of the algorithms.For example,
Nievergelt uses an average of the input time series over the
Daubechies wavelet.As far as I can see, this average cannot
be inverted to yield the original time series.Nievergelt's
Daubechies algorithm also does not seem to match algorithms
like the one published in Numerical Recipies.

So in summary, I'd say that this is a book that started out
well in the first few chapters but became less useful as
I worked through it.

wavelet made easy
This is an excellent book. Wavelet IS a quite advanced concept in Math. The author did a good job to minimize the math backgrond needed to understand wavelet. DON'T BLAM author because you have way too little mathtraining. ... Read more

Book Description
This book fills the gap between volumes on wavelets that are either too advanced (in terms of mathematical background required) or that contain too little mathematical theory underlying wavelets.It presents most of the theory underlying Fourier analysis and wavelets in a clear and comprehensive fashion-- without requiring advanced background in real analysis. Provides a careful balance between theory and practical algorithms, and features a clear presentation of applications to digital signal processing--e.g., data compression, digital filtering and singularity detection. Includes illustrations and MATLAB code used in many of the algorithms.Inner Product Spaces. Fourier Series. The Fourier Transform. Discrete Fourier Analysis. Wavelet Analysis. Multiresolution Analysis. The Daubechies Wavelets.For anyone interested in Wavelets and Fourier Analysis. ... Read more

Customer Reviews (3)

Learn Wavelet
If you want to learn Wavelet theory in a easy way like reading a story book then this is the book. It deals with the most complicated thing in the easiest way.

Informative Book for Wavelet Analysis!!!!
...this book is one of most informative and legible books on wavelt theories and applications.

The author paves the theoretical development about wavelets and multi-resolution analysis EXCELLENTLY. With this book, you can construct wavelets for your own applications in engineering and science disciplines.

This book is very good for first year engineering-majored graduate students and all engineering scholars.

A good Starter on Wavelets
At the time of writing of this review (October 2001), a standard academic search procedure
produces about twenty references per week of scientific papers using wavelet analysis in a very wide spectrum of sciences. More than 160 english language books have been published on wavelets since the first books appeared around 1990. Yet even now it is rare to find a book on this subject which is aiming at undergraduate students and yet is mathematically responsible, without being heavy going. Boggess and Narcovich have tried to do just that, and to my mind have admirably succeeded.
Assuming a standard background knowledge in calculus and linear algebra that many science and engineering students acquire in their first two years at university, they present the basics of Fourier analysis and wavelets in eight brief chapters. To prepare the way, they start in chapter 0 with an introduction to inner product spaces, without using advanced analysis, and building on the experience with ordinary vector spaces.
Also a sniff of linear operator theory is offered.
Chapter 1 introduces Fourier series in real and complex form. These originated in the eighteenth century study of vibrations and in the theory of heat, made famous by Fourier's classic book of 1808: Analytical Theory of Heat. The mathematical claims Fourier made, but which he could not all prove himself, gave the impetus to an enormous development of both mathematical theory and applications in all fields of natural science, which is still going on today. The applications briefly mentioned here are denoising and compression of signals, and finding the solution of partial differential equations. Various aspects of the convergence of Fourier series are dealt with. All concepts are illustrated with a good set of clear figures, and the chapter finishes with exercises that are going from very elementary to a little more ambitious, sometimes involving the use of simple computer algebra tasks. This format is maintained thorugh the entire text, except for the last chapter.
Chapter 2 proceeds with the Fourier Transform, including the important theory of linear time invariant filters. The existence of the impulse response function and its convolution character are shown. As an example the noise reducing Butterworth filter is presented. Sampling and the Nyquist frequency are touched upon, and a derivation of the uncertainty relations, originally coming from quantum mechanics, is given.
To analyse discrete data, one needs the discrete Fourier Transform, which is the subject of chapter 3, including of course the Fast Fourier Transform. Also the z-transform is introduced. Examples given are elementary cases of parameter identification in vibration, numerical solution of ordinarydifferentialequations, as well as in the exercises: noise reduction and data compression.

These first 153 pages serve as a good undergraduate introduction to Fourier analysis.
The second half of the book is devoted to wavelets. Chapter 4 deals exclusively with Haar wavelets which are the oldest wavelets because they date from 1910! These wavelets constitute an orthonormal basis of functions, which makes for fast calucation, a very important aspect for many applications. The core ideas of the central concept of a "multiresolution analysis" of a signal, can be demonstrated with these simple wavelets. All of this is already understandable without the machinery of the preceding Fourier analysis, so you could jump into the book here and start reading about wavelets right away, picking up the Fourier analysis from the first part bit by bit as the need arises. As applications denoising and compression are mentioned again, as is the detection of a discontinuity in a signal.
The general case of a multiresolution analysis is the subject ofchapter 5. Again a large part of the discussion can be swallowed without the need of the Fourier transform point of view. The explanation of the structure of a multiresolution analysis leading to an orhtonormal basis of wavelets is straightforward and clear. It is only when we want to go into more detail about the precise characteristics of the underlying wavelet and scaling function that the Fourier point of view is introduced. This then leads up to the presentation of the famous Daubechies wavelets in chapter 6. These wavelets revolutionised the field after their publication in 1988.
Chapter 7 which closes the book, gives several short remarks about various other topics among which are two-dimensional wavelets, and the continuous wavelet transform.
This chapter is more sketchy than the others, and left me much less satisfied. Also the motivation why these subjects are chosen was lacking almost completely, and there are no exercises. I was particularly disappointed not to find any discussion of the relative merits of the continuous versus the discrete wavelet transform, and there is no mention of any application of the continuous case. Yet the latter is also used frequently in many important scientific applications, and it started the modern wavelet endeavour in the early eighties in France.
That being said I still think this is a very useful book for anybody wanting to start withwavelets at an undergraduate level. A few helpful Matlab Codes are collected in an appendix as well as the more difficult parts of some proofs.The exercises make this good course material, but as a text for self study it will also be quite satisfactory for many newcomers that find most of the existing books too demanding. ... Read more

Book Description
This book takes an "applications first" approach, allowing students to learn about them immediately. Readers gain an appreciation and mastery of the discrete wavelet transform and learn of its value in problems such as data compression, signal de-noising, and image edge detection. Subjects covered include digital images, quantitative/qualitative measures, and encoding; introduction to the Fourier Series; and detailed development of pseudocode. ... Read more

Book Description
This long-awaited update of Meyer's Wavelets: Algorithms and Applications includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy. The chapter on data compression was the original motivation for this revised edition, and it contains up-to-date information on the interplay between wavelets and nonlinear approximation. The other chapters have been rewritten with comments, references, historical notes, and new material. Four appendices have been added: a primer on filters, key results (with proofs) about the wavelet transform, a complete discussion of a counterexample to the Marr-Mallat conjecture on zero-crossings, and a brief introduction to Hölder and Besov spaces. In addition, all of the figures have been redrawn, and the references have been expanded to a comprehensive list of over 260 entries. The book includes several new results that have not appeared elsewhere. ... Read more

Customer Reviews (2)

Lots of new additions.
Of the many recent books on wavelets, this one by Jaffard, Meyer et al stands out. This is a new edition of earlier ones, starting with a French one, then a first translation, and now this expanded version. There is lots of new material, covering new developments, both with regards to theory and applications. The authors communicate the main points in a clear and attractive way, and it stresses lucid presentation of ideas over formulas. And with an infectious enthusiasm! The presentation is especially refreshing, in that the authors do not hide behind excessive technicalities and mathematical jargon. It is the central idea that shines through. And yet the mathematically sophisticated reader is paid his dues,-- in some cases via the appendices. At that point, the technical mathematical points have been well motivated. The emphasis of the book is the mathematics behind the many algorithms that emerged from the wavelet trends since the 1980ties. And lots of new stuff added (for example JPEG-2000), right up to the present. The book is rich in applications, many of which are not found elsewhere. The inclusion of motivation and historical remarks is welcome, and makes the book enjoyable reading.

Good covering of wavelets applications
Although this book emphasis is on algorithms and applications, the general presentation of wavelets for signal processing is great. The introduction to the subject is really excellent and great care has been given to explaining the use of wavelets for applications in signal processing. On the other side i found the last chapters dealing with applications a little too light for being useful...

Anyway, a great book for "wavelets and applications in signal processing"...(also go to "Time-Frequency Time-scale analysis" by Patrick Flandrin which is wonderful). ... Read more

Book Description
The past decade has witnessed the rapid development of a new mathematical tool, called wavlet analysis, for analyzing complex signals. It has begin to play a serious role in applications ranging from communications to geophysics, and from simulations to image processing. Like Fourier analysis (of which it is a generalization), or musical notation, wavelet analysis provides a method for representing a set of complex phenomena in a simpler, more compact, and thus more efficient manner. This text introduces the ideas and methods of wavelet analysis, relates them to previously known methods in mathematics and engineering, and shows how to apply wavelet analysis to digital signal processing. It begins by describing the multiscale (sometimes called "fractal") nature of information in many aspects of thereal world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functins on a space. The discussion then turns from the continuous to the discrete and shows how a properly selected set of wavelets can be used to represent -- and even differentiate -- a wide range of signls efficiently and effectively. The last part of the book presents a wide variety of applications of wavelets to probllems in data compression and telecommunications. ... Read more

Customer Reviews (6)

Difficult reading, filled with distracting errors
I am a graduate student in Math and was attracted to the book because it treats topics -- wavelets of rank other than 2, tilings, and others -- that are missing from many of the standard texts.Wavelets are approached through the introduction of matrices with certain algebraic properties rather than through orthonormal bases in L2 or scaling functions.

Interesting, say I.This will give me a different perspective on many of the basic results and let me read some papers I've been struggling with.

The book, however, did not fully live up to my expectations.Many difficult concepts are introduced in a cursory way, and the proofs skip a lot of details.This is not uncommon in graduate level texts, as it is expected that the reader can fill in the gaps.When I filled in the gaps, however, I discovered more than a few errors.Often, these were just distractions such as missing or incorrect constants.But at least one proof contained more serious errors.

Graduate level math is hard enough without having to figure out what the authors *meant* to say.I would advise a student of my level of sophistication to look elsewhere.

One of the best!
The Wells-Resnikoff book on wavelets is in my opinion
one of the best:-- both with regard to the math--the proofs and all that!--, and the applications. The ideas in the book are timeless, and, I expect, it will be a great book for decades to come. It is very strong on both scores. And it is beautifully written: It is all there,- the history, the
motivation, the philosophical points, the applications, the guided tours with friendly author-explainations of what it is all about. For me, this book was a page-turner. I read it on
a long plane flight,- on my way to a wavelet conference in Guangzhou, China. -- And I didn't have jet-lag when I arrived
more than a day later. It may be a bit demanding on some students, but it will be well worth their effort!

Not good.
If the authors were less enthusiastic about mathematics for its own sake, they probably would have written a better book.This one is said to be suitable for undergraduates, but I don't think so.I have a master's degree in electrical engineering, and several of the mathematical concepts they mention were just vaguely familiar names to me.That would be OK if I were persuaded that those concepts were essential to an understanding of wavelets, but I'm not.The book seems somewhat ill organized as well; new terminology should be defined before it's used, not fifty pages later.

Strong mathematical foundations
This is a wonderful book for the pure mathematicians out there. Unlike many other texts, this book spans the entire range of explanation from high-level outline throughthe algebraic foundations to real-world applications. If you're just interested in applying wavelets with a minimum of fuss, you may want another book. But if you want to really understand the theory behind them, this is the one for you.

beyond signal processing
In most books on wavelets, signal and image processing are the only topics of application considered, because they are written by people from that field. However, the applicability of wavelets is much wider. For instance, the solution of partial differential equations, which has allowed the entrance of wavelets to the finite element world. This and other links to classical math problems, such as fractal geometry, are carefully addressed in this book besides the conventional signal processing issues. I recommend it for people of various fields. ... Read more

Book Description
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method.

*The first book to present a unified view of filtering techniques

*Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series

*Provides easy access to a wide spectrum of parametric and non-parametric filtering methods ... Read more

Customer Reviews (2)

The Guide
Various types of non-stationarities are common in time series data from financial markets. This requires a guide for selecting among numerous tools to deal with the non-stationarity. A unified treatment of filters like this book is a great help since it provides a fast and rigorous introduction.

Chapter 2 is on the general linear filtering theory with cleverly designed applications for illustrative purposes. "Optimum Linear Estimation" is the focus of Chapter 3 in which the Wiener Filter and the Kalman Filters among others are studied. Chapter 4 is on Discrete Wavelet Transforms and provides applications like filtering intraday seasonality in FX market and an examination of the relation between money growth and inflation. Long memory processes with seasonal components are analyzed using wavelets in Chapter 5. Denoising of economics and financial time series is the topic of Chapter 6. The decomposition of variance across different frequency bands as well as the cross-covariance between two time-series at different scales is covered in Chapter 7. Finally, Chapter 8 is on artificial neural networks in which both an introduction to the concept and some design issues withappropriate model selection criteria are provided.

Discussison ofthese relatively advanced topics is very simple and clear without sacrificing important details. Highly recommended.

Easy to understand!
The book is a wonderful reference in that it brings together various filtering methods. It is an excellent introduction to the topic, clearly written and easy to understand. The text does not assume a high-level math background. Further, unlike the various books which simply provide the theory but include very few or no applications at all, this book by Gencay, Selcuk, and Whitcher has many applications that help you get the right picture. ... Read more

Book Description
...a practical guide eeto image compression...using numerous computerexamples...includes Windows software... access to C/C++ source code willbe available to readers. ... Read more

Customer Reviews (1)

This is book is on target
This book is on target for those who would like to learn the application of wavelet theory in image processing, which is an exciting field waiting for more people to explore. The applications of wavelet theory is numerous,but this is a hard-to-find book that concentrates on image processing, itworths a trial. ...