Product Description
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University

The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing.The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.

Features:

* Balances presentation of the mathematics with applications to signal processing
* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox
* Companion website for instructors and selected solutions and code available for students

New in this edition

* Sparse signal representations in dictionaries
* Compressive sensing, super-resolution and source separation
* Geometric image processing with curvelets and bandlets
* Wavelets for computer graphics with lifting on surfaces
* Time-frequency audio processing and denoising
* Image compression with JPEG-2000
* New and updated exercises

A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.

Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.

Companion website: A Numerical Tour of Signal Processing

Product Description

HOW (AND WHY) THIS BOOK IS DIFFERENT

Wavelets are incredibly powerful, but if you can t understand them, you can t use them or worse, blissfully misuse them!

CONCEPTUAL WAVELETS is unique as a complete, in-depth treatment of the subject but from an intuitive, conceptual point of view. In this book we stress informed use of wavelets and leave the mathematically rigorous proofs to other texts. We do look at some key equations (at a high-school algebra level)--but only after the concepts are demonstrated so you can see the wavelets (and their associated equations) in action.

FEATURES

--More than 400 illustrations, figures, graphics, tables, visual comparisons, etc. are provided to simplify and clarify the concepts. All of these visual aids are explained in detail using familiar language and terminology.

--Specific properties and suggested applications of the various wavelets and wavelet transforms are clearly shown using step-by-step walk-throughs, demonstrations, case studies, examples, and short tutorials.

--Numerous Jargon Alerts and other Plain English explanations bring you up to speed with the current wavelet nomenclature.

--References to some of the best traditional (and non-traditional) texts, papers, and websites are given for further application-specific study. We also familiarize you with wavelet software and show you how to read the results of their various displays.

--Both the strengths and the weaknesses of the various wavelet transforms are revealed to help you avoid common traps and pitfalls (such as loss of alias cancellation).

--This book clearly explains how to add (literally) another dimension to your signal processing capability by using wavelets to simultaneously determine the frequency, the time, and even the general shape of events and/or anomalies in your data.

The last acknowledgment is to you, the reader, for having the courage to embark on a journey that you probably have heard was difficult but that has the promise of rich rewards as you add the power of wavelet processing to your professional repertoire.

John A. Shedd in 1928 wrote A ship in harbor is safe but that is not what ships are built for . As you leave the safe harbor of conventional Digital Signal Processing to sail upon the wavelets, may you find the treasures you seek. Welcome Aboard! ... Read more

Customer Reviews (7)

Wavelets in Detail
Full disclosure:I know Lee Fugal, and he asked me to review this book.I agreed and said I would be candid.
Conceptual Wavelets is at the extreme end of practicality regarding wavelets.It gives all the numbers, and steps through algorithms, in massive detail.I value this for verifying my understanding.I have just taught wavelets (basics only) in a senior-level electrical engineering course at the University of Utah, and the two primary references I used (after looking at about eight books) were Conceptual Wavelets and "Introduction to Wavelets and Wavelet Transforms, A Primer" by C. S. Burrus, et al.I would recommend these two books as the best one-two punch for understanding wavelets.Burrus, et al. gives a clear theoretical explanation, and Conceptual Wavelets has all the practical details.Think of Conceptual Wavelets as the applications manual for wavelets.
I have tried to think of shortcomings of the book but failed.Some people might eventually outgrow the book and want a more succinct summary of key points, but the book will be well worn by then.Others might feel that key points are dispersed throughout the book, but liberal use of sticky notes solves that problem.What everyone will find good about the book is that it holds nothing back in explaining wavelets in terms that are easy to understand.

Excellent Conceptual Book on Wavelets
I borrowed this book from a friend at work, but it's so good that I'm actually going to buy it even though I have already read it.I have a background in Electrical Engineering and took some classes a few years ago on signals and systems.However, I found the references on wavelets available on the internet and my local technical bookstore to be written by professors to help other professors understand the subject.I am great at programming because I can lookup everything I need to know on the internet.But when it comes to math, I often get a few pages into the book and then get stuck on terminology or symbols or operations that I do not understand and do not know where to look for the definitions.That's very frustrating and a waste of time.In general, I think the area of math is lagging centuries behind the computer industry (software and hardware design) when it comes to accessibility.In order to understand most advanced signal processing / DSP engineering textbooks, it seems like you already have to be a master on the subject.I don't know of a solution for that, but I wish there were more books like Conceptual Wavelets which take powerful mathematical and signal processing concepts (would love to read a conceptual book on particle filters) and make them more accessible.There are applications which do this -- R Project and RapidMiner.But there's really no analog in the math world.Ok, enough with my scattered thoughts.Buy the book!

Finally, a book on wavelets that makes sense!
I am a practicing signal processing engineer and have been working with wavelets since they were first invented.My applications have been in modulation (US Robotics), audio/image/video processing/compression/recognition, hybrid algorithms, predictive algorithms, flow prediction for a magnetically levitated artificial heart (spin-off from the University of Utah), x-ray florescence spectroscopy (XRF) detectors, and wavelet/neural network algorithms for gas chromatography.

The science of wavelets was invented by mathematicians -- so, all of the early books were written by mathematicians and extremely difficult to navigate.The power of these new wavelet methods beyond Fourier Transforms was obvious, but quite difficult to understand and use.

I have a significant collection of books on wavelets from most of the mathematicians. When I received Lee Fugal's book, I was very pleased to see something that was written from a practical point of view.I found the book easy to read and understand, and even with a pretty heavy background in wavelets, I learned alot.Also as a MatLAB user, it was very nice to find useful code examples along with wavelet toolbox functions explained in detail.

Thank you Lee Fugal for taking all the time to write this book.Everything else on my bookshelf is gathering dust -- Lee's book, 'Conceptual Wavelets' is what I use every day in my work.

Best regards,

W. Kurt Dobson, CEO
Sigma Technology Holdings
Salt Lake City, UT

Just What I've Been Looking For
Wanting to learn something about wavelets, I've searched the Internet for "wavelet tutorial" material. What I found was pretty much all the same thing---material written by (I presume) university professors consisting of page after page of equations. Such material is difficult for beginners to comprehend. My company library did have one textbook on wavelets, but that book was, sadly, similar to the Internet material. Lots of equations, but little explanation of why wavelet transforms are important, how do we use them, and when should we use them to analyze signals.

Then I encountered Fugal's "Conceptual Wavelets in Digital Signal Processing". Wow, what a relief. Mr. Fugal begins by explaining the complicated topic of wavelet transforms in a gentle, clear, and ultimately meaningful way. He doesn't overwhelm (suffocate) the reader with equations. In the first chapter he gives several straightforward signal analysis examples that show how wavelet transforms can be used to analyze certain signal characteristics in ways that are not possible with traditional digital signal processing (DSP). After reading those examples, I sat back for a moment and thought, "Ah ha. So that's what wavelets are, and how they can be used. Now I'm beginning to understand why people are interested in wavelets." That 'made my day'.

Fugal uses this neat technique called "Jargon Alert". That's where, when he introduces new terminology, he clearly defines the meanings of special terminology (new words) for the reader. What a great idea. I wish more technical authors would do the same.

Now to be honest, I've only read the first chapter of Fugal's book, but I just wanted to advertise how happy I am to finally begin to grasp the meaning, and value, of wavelet transforms. I look forward to learning more as I continue reading.

Written for Accessibility
This book describes Wavelet theory in an accessible manner by employing graphics and MATLAB to clarify the basic principles of a difficult subject.Otherwise complex processes are broken down and explained in detail so that each step in the argument can be followed clearly.The style of the writing avoids mathematical formalisms and instead injects wry humor to entertain and enlighten the worst mathophobe among us. ... Read more

Product Description
In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include the latest developments, this second edition of A Primer on Wavelets and Their Scientific Applications guides readers through the main ideas of wavelet analysis in order to develop a thorough appreciation of wavelet applications.

Ingeniously relying on elementary algebra and just a smidgen of calculus, Professor Walker demonstrates how the underlying ideas behind wavelet analysis can be applied to solve significant problems in audio and image processing, as well in biology and medicine.

Nearly twice as long as the original, this new edition provides

·      104 worked examples and 222 exercises, constituting a veritable book of review material

·         Two sections on biorthogonal wavelets

·         A mini-course on image compression, including a tutorial on arithmetic compression

·         Extensive material on image denoising, featuring a rarely covered technique for removing isolated, randomly positioned clutter

·         Concise yet complete coverage of the fundamentals of time-frequency analysis, showcasing its application to audio denoising, and musical theory and synthesis

·         An introduction to the multiresolution principle, a new mathematical concept in musical theory

·         Expanded suggestions for research projects

·         An enhanced list of references

·         FAWAV: software designed by the author, which allows readers to duplicate described applications and experiment with other ideas.

To keep the book current, Professor Walker has created a supplementary website. This online repository includes ready-to-download software, and sound and image files, as well as access to many of the most important papers in the field. ... Read more

Customer Reviews (9)

wavelets basics good approach
Very good approach for wavelet analysis beginning with very well descripted, low complexity math and evolving to a more complex math and deep explanations in the medium to last part of the book. The first chapters get you tied to the arguments and evidences that will be explained more in detail in subsequent chapters.

Educationally, I consider this book a perfect introductory graduate level textbook with a good coverage of basic concepts that excites you to get more deep explanations.

My school must not have been very good
Mathematicians may find the "elementary algebra" in this book to be free of "mathematic rigor," but stupid people like me who went to public school will probably feel otherwise after struggling through the first page. I'm still looking for the wavelet equivalent of the excellent "Who is Fourier?"; this book is definitely not it, and it's definitely not worth $40.

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. ... Read more

Product Description
This book is the only source available thatpresents a unified view of the theory and applications of discrete andcontinuous- time signals.This is the only book to presentthe mathematical point of view, as well as the discrete-time signal processingperspective. It brings together information previously available only inresearch papers, in engineering and applied mathematics. Appropriate for researchers and practitioners in signal processing and appliedmathematics. ... Read more

Customer Reviews (6)

book is o.k. for mathematicians but NOT for the novice
The book seems to be written with an assumption that the reader has plenty of background in the relevant mathematics. I would NOT recommend this book for the novice; it's more for those already familiar with the general area but want to get more 'in depth'. It examples are sprinkled with math notations that may not be familiar to most. For the beginner, I would recommend other wavelet books that are written from an ENGINEERING viewpoint rather than a mathematician's viewpoint.
Overall, well-written (for its intended audience).

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. ... Read more

Product 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)

The review of Angel
This is an excellent self-contained book on wavelet theory and its applications. I am a physicist and I have found in this book not only a clear explanation of the fundamentals but a suitable exposition of the advanced topics. This is a very self-study text!!

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... ... Read more

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

Customer Reviews (16)

The real first edition is in French

I own the very first (French) edition of Mrs. Barbara's book.

It is nice reading, but not so fun as some would say.

It has some advanced calculus level math ( Fourier transform ) and treats mainly Haar wavelets.

As an introduction to the subject it is quite adequate, but if you need/want something more go elsewhere.

The World According to Wavelets:The Story of a Mathematical Technique in the Making, by Barbara Burke Hubbard
This book represents one of the wonderfull introducing courses for wavelets and wavelet transforms. Ideas that come from different parts of our material world are connected and visualized in mathematical models. These models show unexpected new relationships among phenomenons and deliverto us world in a new way.
Author deservs all compliments for his concise, charming and inspiring style of writing with clear and understandable explanations of complex and difficultmathemathics terminology.
It is recomended for those who are new in digital signal processing and for those experienced who lookfor new ideas and ideas burried in history of mathematics in all fieldsof human activities.
Gratulations to the author.
Dragan Matkovic, lecturer of the Polytechnic of Varazdin, Croatia

Best book on wavelets that I have ever read
Somewhat dated, but the best book on the subject. At least for the novice. Deep thought.

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.

... Read more

Product Description
This text has had an overwhelming response from readers. Lauded by some as a marriage between math and engineering, the text features useful and balanced explanations of wavelets for both engineers and mathematicians. The explanations of difficult topics are informal and very approachable, yet rigor is not sacrificed in the process.Also included in Wavelets and Filter Banks are many examples from the MATLAB Wavelet® Toolbox. ... Read more

Customer Reviews (10)

good book for a wavelet beginner
The book start from very basic concept, and then step by step lead you to wavelet, and end at applications.
You need only undergraduate level DSP knowledge to learn this.

Great Text/Reference
I have taken several courses on DSP.I found that this text takes topics that were presented, expanded them in great detail.It took some of the mystery out of my previous presentations.Anyone working with DSP should have this on their shelf!

avoid this book
After reading several other books on wavelets, I picked up this one.On first inspection, it appears to be reader friendly and practical.It is neither!The presentation is disjointed, unclear, and lacks depth.I think it would be very hard to learn about wavelets from this book.

Lost in Chapter 5
I bought this book with a great enthusiasm and hope to learn something about filter banks. Soon after I started to read it I figured that the book has a great deal of inconsistencies. To begin with the notation is awkward, and the dimensions of the vectors and matrices are often infinite! Clearly implying that the authors are not very practical after all... Chapter 4 on filter banks is more or less OK, with mentioning of many types and choices for filter designs but nothing deep and concrete (In Page 121 I couldn't find the reference "[VK]"). Chapter 5 is a disaster: Title of Section 5.2 should be "Orthogonal" instead of "Orthonormal", Page 148 says "presented below" but there are nothing "below", other mathematical proofs are sloppy and invalid. I recommend people interested in filter banks to read Vaidyanathan's book instead.

"overall a good text"!!! you gotta be kidding me
I just can't believe these reviews: "overall a good text" - doh! I was unfortunate enough to take a course about wavelets for which the professor used this book as the main text (btw the course was offered by Prof. Truong Nguyen, and yes he is one of the authors). After 3 months of painful !struggle! with this book I was sure about only one thing: I could not learn anything about wavelets. First of all, there is no logical flow, as a matter of fact there is no flow of any kind. The authors just leap forward and backward leaving lots of unanswered questions, which is in my humble opinion, a very annoying thing that should not happen while using a text book. Clear statements about what the hell is going on are very rare. Most of the time you are left with vague statements which tell only part of the story. Right now I am in the third year of my ph.d and I am yet to meet an electrical engineer who thinks this book is actually useful in some sense. Don't waste your money on it. Start with "Wavelet and Wavelet Transforms" Burrus, once you get the feel of it check the books that math departments use for teaching wavelets. ... Read more

Product 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

Product Description
Contents

Preface Chapter 1: Getting started Chapter 2: The continuous wavelet transform 2.1 Introduction 2.2 The Wavelet 2.3 Requirements for the Wavelet 2.4 The Energy Spectrum of the Wavelet 2.5 The Wavelet Transform 2.6 Identification of Coherent Structures 2.7 Edge Detection 2.8 The Inverse Wavelet Transform 2.9 The Signal Energy: Wavelet Based Energy and Power Spectra 2.10 The Wavelet Transform in Terms of the Fourier Transform 2.11 Complex Wavelets: The Morlet Wavelet 2.12 The Wavelet Transform, Short Time Fourier Transform and Heisenberg Boxes 2.13 Adaptive Transforms: Matching Pursuits 2.14 Wavelets in Two or More Dimensions 2.15 The CWT: Computation, Boundary Effects and Viewing 2.16 Endnotes 2.16.1 Chapter Key Words and Phrases 2.16.2 Further Resources Chapter 3: The Discrete Wavelet Transform 3.1 Introduction 3.2 Frames and Orthogonal Wavelet Bases 3.2.1 Frames 3.2.2 Dyadic Grid Scaling and Orthonormal Wavelet Transforms 3.2.3 The Scaling Function and the Multiresolution Representation 3.2.4 The Scaling Equation, Scaling Coefficients and Associated Wavelet Equation 3.2.5 The Haar Wavelet 3.2.6 Coefficients from Coefficients: The Fast Wavelet Transform 3.3 Discrete Input Signals of Finite Length 3.3.1 Approximations and Details 3.3.2 The Multiresolution Algorithm - An Example 3.3.3 Wavelet Energy 3.3.4 Alternative Indexing of Dyadic Grid Coefficients 3.3.5 A Simple Worked Example: The Haar Wavelet Transform 3.4 Everything Discrete 3.4.1 Discrete Experimental Input Signals 3.4.2 Smoothing, Thresholding and Denoising 3.5 Daubechies Wavelets 3.5.1 Filtering 3.5.2 Symmlets and Coiflets 3.6 Translation Invariance 3.7 Biorthogonal Wavelets 3.8 Two-Dimensional Wavelet Transforms 3.9 Adaptive Transforms: Wavelet Packets 3.10 Endnotes 3.10.1 Chapter Key Words and Phrases 3.10.2 Further Resources CHAPTER 4: FLUIDS 4.1 Introduction 4.2 Statistical Measures 4.2.1 Moments, Energy and Power Spectra 4.2.2 Intermittency and Correlation 4.2.3 Wavelet Thresholding 4.2.4 Wavelet Selection using Entropy Measures 4.3 Engineering Flows 4.3.1 Jets, Wakes, Turbulence and Coherent Structures 4.3.2 Fluid-Structure Interaction 4.3.3 Two-Dimensional Flow Fields 4.4 Geophysical Flows 4.4.1 Atmospheric Processes 4.4.2 Ocean Processes 4.5 Other Applications in Fluids and Further Resources CHAPTER 5: ENGINEERING TESTING, MONITORING AND CHARACTERISATION 5.1 Introduction 5.2 Machining Processes: Control, Chatter, Wear and Breakage 5.3 Rotating Machinery 5.3.1 Gears 5.3.2 Shafts, Bearings and Blades 5.4 Dynamics 5.5 Chaos 5.6 Non-Destructive Testing 5.7 Surface Characterisation 5.8 Other Applications in Engineering and Further Resources 5.8.1 Impacting 5.8.2 Data Compression 5.8.3 Engines 5.8.4 Miscellaneous CHAPTER 6: MEDICINE 6.1 Introduction 6.2 The Electrocardiogram 6.2.1 ECG Timing, Distortions and Noise 6.2.2 Detection of Abnormalities 6.2.3 Heart Rate Variability 6.2.4 Cardiac Arrhythmias 6.2.5 ECG Data Compression 6.3 Neuroelectric Waveforms 6.3.1 Evoked Potentials and Event-Related Potentials 6.3.2 Epileptic Seizures and Epileptogenic Foci 6.3.3 Classification of the EEG using Artificial Neural Networks 6.4 Pathological Sounds, Ultrasounds and Vibrations 6.4.1 Blood Flow Sounds 6.4.2 Heart Sounds and Heart Rates 6.4.3 Lung Sounds 6.4.4 Acoustic Response 6.5 Blood Flow and Blood Pressure 6.6 Medical Imaging 6.6.1 Ultrasonic Images 6.6.2 Magnetic Resonance Imaging, Computed Tomography and other Radiographic Images 6.6.3 Optical Imaging 6.7 Other Applications in Medicine 6.7.1 Electromyographic Signals 6.7.2 Sleep Apnea 6.7.3 DNA 6.7.4 Miscellaneous 6.7.5 Further Resources CHAPTER 7: FRACTALS, FINANCE, GEOPHYSICS AND OTHER AREAS 7.1 Introduction 7.2 Fractals 7.2.1 Exactly Self-Similar Fractals 7.2.2 Stochastic Fractals 7.2.3 Multifractals 7.3 Finance 7.4 Geophysics 7.4.1 Properties of Subsurface Media 7.4.2 Surface Fea ... Read more

Customer Reviews (5)

Good introduction
The book is very useful if you know nothing or very little about wavelets. The maths is kept simple, if you remember the Fourier transform and convolution, then this book will be easy to follow. There are numerous examples and the graphical representations of the transforms really gives you the gist of the whole wavelet business. Practical applications of wavelets of numerous, rather different, fields are shown. The way wavelets are used is demonstrated in a very easy to follow, literally graphic manner.

What you will not find in the book, however, is where to begin to solve *your* problem with wavelets. Which mother wavelet to use? Should you use discrete or continuous transform? Is there a fast method? What are the best ways of eliminating unwanted bits of the wavelet spectra? Just set things to 0? Use some smoothing? For all those questions you will have to go and find other books.

It is like a book on Fourier transform which tells you what it is, shows you how signals and their spectra are related, shows you the applications of FT in filtering, classification etc, with really good illustrative real-life examples so you now clearly understand what FT is and what it can do for you. But that's it. No mention of things like the FFT, the effects of finite precision, the Gibbs oscillation etc.

It is a very great book if you want to understand what wavelets and the wavelet transform are all about and what they can do (as was in my case). However, it is not the book for you if you know all that and want to actually use the transform for a practical problem. In that sense the title is misleading: it is not a handbook, it is a thorough and really easily understandable introduction to wavelets.

An excellent book on wavelet transform
This book is by far the best of all the books on wavelet transform I have seen. Not only it explains what wavelet transform is and how it can be used in practice, but also in a very clear and easy to understand manner. Books on wavelet transform tend to be highly mathematical, which can be intimidating for those who just want to use wavelet transform to solve some practical problem. However, this book is very easy to understand and provides lots of examples and end results, namely, formulations to get these results. I give two enthusiastic thumbs up for this excellent book.

Recommended for engineers
Well-written book with good explanations. It reads more like an engineering textbook than a mathematics book. I definitely recommend it to those that wish to gain a solid understanding of wavelet technology/principles.

Illustrated Wavelet Transform Hndbk review
Very good introduction to wavelet analysis. Not for someone looking for casual reading but for someone who wants to be able to dig in and start doing actual analysis it will get you going.

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

Customer Reviews (2)

Ideal background for computer vision and other related signal processing branches
If you are going to learn computer vision and you come from CS background you may not have a good enough mathematical knowledge in signal processing. This book is a easy to read material witch will give you the basic knowledge you should have to master computer vision and other related signal processing branches.
It uses intuitive proofs and explanations so if you are looking for a very abstract and deep book on signal processing you should not purchase this book.
Great for engineers and professionals, too basic for mathematicians.

Great for a beginner in this area.
I got it when this one is on sale at $2.99.
So I did not expect much from it; however, after I browsed for a while, it turned out to be one of the great books I own.
It introduces this topic in the straightforward fashion along with good examples and make everything less difficult than supposed to be.
Note that everything in this edition is exactly the same as the hardcover one costing more than $100.

Revised review
Random vibration composed of two things: Statistics and Vibrations.To understand well in the subject, it is necessary to have strong in Statistics.This book doesn't help much for this part so you'd better begin with some other basic statistical textbooks like Hsu's.

Unlike deterministic vibration, the random vibration problems are impossibly solved in time domain.Most of time, it is necessary to do the frequency analysis.This book will force you into this area a little early.I think it's better to practice the problems a little more.Then the book will bring you from Analog to Digital that requires the deep understanding of how to approximate the continuous functions to the discrete functions.It had taken me a few months to make some senses of random vibrations in the real applications.

I would say the topic is tough but don't be too discouraged.It is understandable. ... Read more

Product 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 (3)

More of an introduction to techniques in non-parametric regression
Despite the title, I don't find this book particularly useful as a book on wavelets. For one thing, a good fraction of the book is about filters or non-parametric regression in general; probably more than half. Some of the wavelet techniques are useful in finance; I wish more of these techniques were encoded in their R waveslim package. I strongly suspect there are more wavelet techniques used in finance than are listed here, but we're kind of restricted to the research they've done.
On the other hand, when I'm thinking about a problem in denoising or non parametric regression, paging through this book is often useful, or will at least point me towards a solution. The chapter on Kalman filtering is extremely well written, and the chapter on Neural Nets is pretty good too. I'd have rather the Kalman chapter had more on, say, unscented Kalman and particle filters, and I'd rather the NN chapter were on Kernel regression (which it does mention), but I'm reasonably happy with what was in there. Sure, it's kind of ad-hoc that a book on wavelets has chapters on Kalman filters and Neural Nets, but they're decent chapters worth having anyway. Everyone I know in a certain part of the finance business has this book, so it does serve a role. I would have liked more on wavelets, while keeping the idiosyncratic chapters, and perhaps more R packages.

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

Product Description
This long-awaited update of Meyer's Wavelets: Algorithms& Applications includes completely new chapters on four topics:wavelets and the study of turbulence, wavelets and fractals (whichincludes an analysis of Riemann's nondifferentiable function), datacompression, and wavelets in astronomy. The chapter on datacompression was the original motivation for this revised edition, andit contains up-to-date information on the interplay between waveletsand nonlinear approximation. The other chapters have been rewrittenwith comments, references, historical notes, and new material. Fourappendices have been added: a primer on filters, key results (withproofs) about the wavelet transform, a complete discussion of acounterexample to the Marr-Mallat conjecture on zero-crossings, and abrief introduction to Hölder and Besov spaces. In addition, all of thefigures have been redrawn, and the references have been expanded to acomprehensive list of over 260 entries. The book includes severalnew results that have not appeared elsewhere.

Wavelet analysis-an exciting theory at the intersection of thefrontiers of mathematics, science, and technology-is a unifyingconcept that interprets a large body of scientific research. Inaddition to its intrinsic mathematical interest, its applications haveserious economic implications in the areas of signal and imagecompression. For these expanding fields, this book provides a clearset of concepts, methods, and algorithms adapted to a variety ofapplications ranging from the transmission of images on the Internetto theoretical studies in physics. The use of wavelet-based algorithmsadopted by the FBI for fingerprint compression and by the JointPhotographic Experts Group for the new JPEG-2000 compression standardconfirms the success of this theory.

The authors present with equal skill and clarity the mathematicalbackground and major wavelet applications, including the study ofturbulence, fractal objects, and the structure of the universe. Neverbefore have the historic origins, the algorithms, and the applicationsof wavelets been discussed in such scope, providing a unifyingpresentation accessible to scientists and engineers across alldisciplines and levels of training.

Written specifically for scientists and engineers with diversebackgrounds, the material is presented in a manner that will appeal toboth experts and nonexperts alike. This book is a valuable tool foranyone (from graduate student to expert) faced with signal or imageprocessing problems. It also answers the question, "What arewavelets?"

The first seven chapters trace the historical origins of wavelettheory and describe the different time-scale and time-frequencyalgorithms used today under the term "wavelets." Specific examplesinclude the application of wavelet techniques to FBI fingerprintcompression problems and the use of wavelets in the new JPEG standardfor still image compression. Applying wavelet analysis methods tosignal and image processing, fractals, turbulence, and astronomy iscovered in the balance. ... 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

Product Description

Wavelet methods have recently undergone a rapid period of development with important implications for a number of disciplines including statistics. This book has three main objectives: (i) providing an introduction to wavelets and their uses in statistics; (ii) acting as a quick and broad reference to many developments in the area; (iii) interspersing R code that enables the reader to learn the methods, to carry out their own analyses, and further develop their own ideas. The book code is designed to work with the freeware R package WaveThresh4, but the book can be read independently of R.

The book introduces the wavelet transform by starting with the simple Haar wavelet transform, and then builds to consider more general wavelets, complex-valued wavelets, non-decimated transforms, multidimensional wavelets, multiple wavelets, wavelet packets, boundary handling, and initialization. Later chapters consider a variety of wavelet-based nonparametric regression methods for different noise models and designs including density estimation, hazard rate estimation, and inverse problems; the use of wavelets for stationary and non-stationary time series analysis; and how wavelets might be used for variance estimation and intensity estimation for non-Gaussian sequences.

The book is aimed both at Masters/Ph.D. students in a numerate discipline (such as statistics, mathematics, economics, engineering, computer science, and physics) and postdoctoral researchers/users interested in statistical wavelet methods.

Customer Reviews (2)

Wavelets in R
This is an interesting book, but is very condensed and suffers (for the non-expert) from a lack of intuitive reasoning on why we are doing what and when. Then there is the R-package itself. The limitations of dyadic sets of data are apparent when one comes, for example, to time-series analysis. Yet, the R-software in "wavethresh"for non-decimated wavelets seems to restrict the user to dyadic data and to full decomposition rather than partial decomposition, and cannot handle "reflection" rather than "periodic" boundaries. (According to Percival and Walden (2000) these relaxations or adjustments are some of the main advantages of non-decimated wavelets). One of the potentially most interesting parts of the book is the section on time-series dealing with locally-stationary processes for which the author is an authority. Yet, the section leaves one a bit bewildered with not much sense as to what has been achieved at the end. Clearly, the book is designed for graduate and post-graduate students with much more than my limited mathematical and statistical skills, butthe fact that the software is available on non-proprietary R is to be commended. Nevertheless, it is to be hoped that the book and the software may become more user friendly over time (like for example PC-Give (although proprietary) which made advances in econometric analysis much more readily available to all). I should stress that in writing this review I am handicapped by my limited mathematical abilities and by my restricted understanding of the use of wavelets, but I think that time-series applications of wavelets can be an important tool in an economist's tool-box.

Excellent Introduction
This book is an excellent introduction to wavelet techniques in statistics. It takes a very heavily applied approach and sometimes reads like a set of different tutorials on accomplishing certain tasks in R with the author's own wavethresh package. In truth, one can almost think of it as a very detailed manual. This may sound like a criticism but it is in fact one of the book's greatest strengths. There are already plenty of treatments out there on the theory of wavelets and their applications in a variety of fields ranging from the very mathematical to the heavily applied.

However, apart from this book, I have been unable to find any other book that actually deals with the nitty-gritty of implementation using a particular software package. The mathematical details of wavelet analysis are certainly interesting and should be looked into, but it's also nice to have a hugely accessible and detailed cookbook on how to implement techniques quickly and painlessly. Recommended to anyone who is looking to apply wavelets in their field. ... Read more

Product 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!"--- Bulletin of the AMS

"[This text] is carefully prepared, well-organized, and covers a large part of the central theory...[there are] chapters on biorthogonal wavelets and wavelet packets, topics which are rare in wavelet books.Both are important, and this feature is an extra argument in favour of [this] book...the material is accessible [even] to less advanced readers...the book is a nice addition to the series." --Zentralblatt Math

"This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject." --Mathematical Reviews

"This textbook is an introduction to the mathematical theory of wavelet analysis at the level of advanced calculus.Some applications are described, but the main purpose of the book is to develop---using only tools from a first course in advanced calculus---a solid foundation in wavelet theory. It succeeds admirably.... Part I of the book contains 112 pages of preliminary material, consisting of four chapters on 'Functions and Convergence,' 'Fourier Series,' 'Fourier Transforms,' and 'Signals and Systems....' This preliminary material is so well written that it could serve as an excellent supplement to a first course in advanced calculus.... The heart of the book is Part III: 'Orthonormal Wavelet bases.'This material has become the canonical portion of wavelet theory.Walnut does a first-rate job explaining the ideas here.... Ample references are supplied to aid the reader.... There are exercises at the end of each section, 170 in all, and they seem to be consistent with the level of the text....To cover the whole book would require a year.An excellent one-semester course could be based on a selection of chapters from Parts II, III, and V." --SIAM Review

"An Introduction to Wavelet Analysis" provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases.

The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical prerequisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts.

Features:

* Rigorous proofs have consistent assumptions about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure).

* Complete background material is offered on Fourier analysis topics.

* Wavelets are presented first on the continuous domain and later restricted to the discrete domain for improved motivation and understanding of discrete wavelet transforms and applications.

* Special appendix, "Excursions in Wavelet Theory," provides a guide to current literature on the topic

* Over 170 exercises guide the reader through the text.

"An Introduction to Wavelet Analysis" is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference for professionals. ... Read more

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

Product Description
This concisely written book gives an elementary introduction to a classical area of mathematics---approximation theory---in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.

Key features and topics:

* Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass' and Taylor's theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI's use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series

"Approximation Theory: From Taylor Polynomials" to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas. ... Read more

Customer Reviews (1)

Outstanding book and a fast read
The book is very well written.Very clear and makes for a fast read.Only drawback is all notation is not completely defined; however, this problem has only been observed in very few instances.Overall, very well done! ... Read more

Product Description

Prevalent in animation movies and interactive games, subdivision methods allow users to design and implement simple but efficient schemes for rendering curves and surfaces. Adding to the current subdivision toolbox, Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces introduces geometry editing and manipulation schemes (GEMS) and covers both subdivision and wavelet analysis for generating and editing parametric curves and surfaces of desirable geometric shapes. The authors develop a complete constructive theory and effective algorithms to derive synthesis wavelets with minimum support and any desirable order of vanishing moments, along with decomposition filters.

Through numerous examples, the book shows how to represent curves and construct convergent subdivision schemes. It comprehensively details subdivision schemes for parametric curve rendering, offering complete algorithms for implementation and theoretical development as well as detailed examples of the most commonly used schemes for rendering both open and closed curves. It also develops an existence and regularity theory for the interpolatory scaling function and extends cardinal B-splines to box splines for surface subdivision.

Keeping mathematical derivations at an elementary level without sacrificing mathematical rigor, this book shows how to apply bottom-up wavelet algorithms to curve and surface editing. It offers an accessible approach to subdivision methods that integrates the techniques and algorithms of bottom-up wavelets.

Product Description
This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs-Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(\mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz-Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry-Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material. Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-37660-4. ... Read more

Customer Reviews (3)

Excellent textbook and reference, which is readable!
I needed to learn Fourier Analysis and Wavelets, and this book is excellent as a textbook and as a reference.It is also quite readable.We need more mathematics books like this one.

Fourier Analysis and Wavelets for Everyone
As a probabilist and statistician, with a Ph.D., having worked at universities, as a consultant, and in industry for approximately forty years, I had previously employed Fourier Analysis only as a tool, not having studied the subject as a discipline unto itself. Dr. Pinsky's book has allowed me to learn the subject more deeply, and from a different, exciting viewpoint. In addition, I needed a resource that would permit me to learn about wavelets. How wonderful to find a book that includes both topics! Moreover, this book is a pleasure to read, with pencil and paper, to work through the ideas. It is extraordinarily well-written, which is not surprising, given the clarity and excellence of Dr. Mark A. Pinsky's other works. Pinsky's grammar is excellent, which is extremely refreshing. Many modern authors cause me to believe that I should have a red pen to correct grammatical errors while reading their works. This book is much more than just a textbook; it is beautiful mathematically and beautifully written.

For the Students!
Courses in harmonic analysis have a central place in the course offerings of every math department, be it pure or applied;-- and the subject is as important as ever! Yet it has not always been easy for an instructor to find a book that is right for the students. Some books might be too skimpy on proofs, or not deep enough.-- Or the applications may somehow be artificial, or contrived. Afterall, we teach the material to engineers!-- It is a relief to find, in Pinsky's lovely new book, a balanced approach to the subject. The motivation and the history receive a beautiful presentation, as do the technical points and proofs. And the historical comments- sprinkled throughout the book- bring the subject to life. At the same time, the book is forward looking, and it has been tested in courses. Great exercises! The structure of the exposition is friendly, and gently leads the reader toward the exciting new wavelet material in the last hundred or so pages of the book. The student thereby gets a sense of how the central questions in wavelet theory have their root in the more classical ideas of harmonic analysis. ... Read more

Product Description
"Wavelets Made Easy", 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 practicing 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. Particular attention is paid to Daubechies' wavelets.

Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the classroom as well as a valuable resource for self study.

Key features of this work:

Written at an undergraduate level, prerequisites being only a first course in calculus and linear algebraEarly chapters focus on Haar wavelets; only high school math requiredGradual progression to one-, two-, and three-dimensional wavelets (chapters 4,5,6) -- good background in Fourier analysis; provides the foundations of least squares approximation, the discrete Fourier transform, and Fourier seriesDemonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets; particular attention is paid to Daubechies' waveletsNumerous exercises, a bibliography, and comprehensive indexAn excellent text for the classroom as well as a valuable resource for self study ... Read more

Customer Reviews (9)

Now there's a misnomer!
There's not much easy in this book; it's neither intuitive nor graphical. Instead, you're guided through a rough introduction and then given authoritative proofs of all the relevant material. The book is quick, though, and doesn't waste time on non-applicable topics (save for a rehashing of Fourier theory that seems out of context). If you're interested in getting a fast but authoritative introduction to the math required for wavelets, this is a good pick. Just don't rely on the title to mean anything.

Realmente Wavelets Hecho Fácil
Para los que recién comienzan a investigar el tema en forma autodidacta es excelente y fácil de comprender.

You need a graduate degree in Mathmatics to read this
Wavelets made easy, the title is sarcastic.It only uses high school algebra or basic trig functions? WRONG! It starts out as advanced text to 2nd year grad students or those working on a PhD, almost every page has unproven formulae, its up to YOU and your team of 10 or so grad students and billions of dollars in lab tools and resources to double check the work they provide.

Professors of Math or those with 20 years of wavelet research may be able to mull thru the book in a few months perhaps.The style of writing is typical of authors who dont want to explain the concept but only pretend to appear smarter than they really are.

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.


... Read more

Product Description
Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. 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.

This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.

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. Because of their interdisciplinary origins, wavelets appeal to scientists and engineers of many different backgrounds. ... 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

Product Description
Wavelets analysis--a new and rapidly growing field of research--has been applied to a wide range of endeavors, from signal data analysis (geoprospection, speech recognition, and singularity detection) to data compression (image and voice-signals) to pure mathematics. Written in an accessible, user-friendly style, Wavelets: An Analysis Tool offers a self-contained, example-packed introduction to the subject. Taking into account the continuous transform as well as its discretized version (the ortho-normal basis) the book begins by introducing the continuous wavelets transform in one dimension.It goes on to provide detailed discussions of wavelet analysis of regular functions, tempered distributions, square integrable functions, and the continuous wavelet transform.Throughout, the language of group theory is used to unify various approaches.Profusely illustrated and containing information not available elsewhere, this book is ideal for advanced students and researchers in mathematics, physics, and signal processing engineering. ... Read more

Customer Reviews (1)

All the proofs:wavelets....Fourier methods.
This is a great book from which students, instructors, math researchers, signal processing workers,and communications engineering, can pick
up the rigorous tools from Fourier analysis and sub-band filtering theory;-- and see in full mathematical detail how they are used in the study of wavelets in their traditional settings (from the 1980ties)of scaling of multiresolutions, spectral estimates, orthogonality,
Cohen's condition, tilings, and a priory regularity...The proofs are complete, crisp and elegant. The book can now be supplementedwith newer ones that emphasize algorithms more. And others with a more applied bent!
But Holschneider's book will likely remain a classic. ... Read more