Product Description
First appearing in the late 1980s, wavelets have developed rapidly, and their applications now reach from signal processing to numerical analysis, operator theory, and beyond. Among the generalizations of wavelets that have emerged, multiwavelets stand out because of their potential for short support and for their capability of being both symmetric and orthogonal. Some existing wavelet books have a short section covering multiwavelets, but to date, none offer a comprehensive treatment. Pulling together information scattered throughout the literature of mathematics and engineering, Wavelets and Multiwavelets offers a full exposition of wavelet and multiwavelet theory. Maintaining the delicate balance between mathematical rigor and readability, the author presents the theory of classical wavelets and general m-band multiwavelets in parallel. This provides a more coherent approach and yields alternative proofs and new insights even for standard wavelets. MATLAB routines that allow you to implement and experiment with multiwavelet algorithms are available from the CRC Press Web site. ... Read more

Customer Reviews (1)

For students.
While there has been a number of recent wavelet books on the market covering a variety of aspects of this important subject of applied math; of those books only a few are good for use in a beginning course; the kind of course aimed at advanced undergraduates, and at students in related fields of math such as numerical analysis; and students from other departments, especially students from engineering departments: EE, medical imaging, and Computer and Electrical Engineering; to mention just a few.
The present book seems especially pedagogical well designed for student needs; and the author clearly had students in mind. Rather than delving into a variety of technical issues, the book goes directly to the underlying geometric ideas that students can understand at an intuitive level; without too much background. The algorithmic steps in the subject well presented, and they are essential both for the theory, and for the applications to the analysis of number sets (data mining), of pictures, and of many other applications.
The book is certainly more limited in scope than for example Daubechies's book that appeared in the SIAM series in 1992, but it is also gentle on students, and is likely to serve as a lovely invitation to the subject.
When the students progress in the course, they will then build up a deeper understanding of the fundamental ideas, which in fact are quite simple when isolated from the traditional rather heavy notation and terminology. The fundamental ideas are nicely illustrated with tree diagrams which also serve as the underpinning for wavelet programs.
An additional advantage of this little book is that students will be able to get hands-on experience with graphics, and with MATLAB routines, as they work their way through the book.
Review by Palle Jorgensen, December 2004. ... Read more

Product Description
"Brimming with top articles from experts in signal processing and biomedical engineering, Time-Frequency and Wavelets in Biomedical Signal Processing introduces time-frequency, time-scale, wavelet transform methods, and their applications in biomedical signal processing. This edited volume incorporates the most recent developments in the field to illustrate thoroughly how the use of these time-frequency methods is currently improving the quality of medical diagnosis, including technologies for assessing pulmonary and respiratory conditions, EEGs, hearing aids, MRIs, mammograms, X rays, evoked potential signals analysis, neural networks applications, among other topics.

Time-Frequency and Wavelets in Biomedical Signal Processing will be of particular interest to signal processing engineers, biomedical engineers, and medical researchers. ... Read more

Customer Reviews (1)

The First Teacher for using Wavelet on Biomedical SP
Wanted Teacher. This book teaches us how to use wavelet on Biomedical Signal Processing, and the detailed usage of wavelet grammar and applications. It also explains how to apply the wavelet signal compressionand detection technique for the imaging system such as MRI and X-rayimages. We medical data processing team want to say thanks to the authorfor your providing the good source of material on medical computing.Bravo! ... Read more

Product Description
An indispensable guide to understanding wavelets
Elements of Wavelets for Engineers and Scientists is a guide to wavelets for "the rest of us"-practicing engineers and scientists, nonmathematicians who want to understand and apply such tools as fast Fourier and wavelet transforms. It is carefully designed to help professionals in nonmathematical fields comprehend this very mathematically sophisticated topic and be prepared for further study on a more mathematically rigorous level.
Detailed discussions, worked-out examples, drawings, and drill problems provide step-by-step guidance on fundamental concepts such as vector spaces, metric, norm, inner product, basis, dimension, biorthogonality, and matrices.
Chapters explore . . .
* Functions and transforms
* The sampling theorem
* Multirate processing
* The fast Fourier transform
* The wavelet transform
* QMF filters
* Practical wavelets and filters
. . . as well as many new wavelet applications-image compression, turbulence, and pattern recognition, for instance-that have resulted from recent synergies in fields such as quantum physics and seismic geology.
Elements of Wavelets for Engineers and Scientists is a must for every practicing engineer, scientist, computer programmer, and student needing a practical, top-to-bottom grasp of wavelets. ... Read more

Customer Reviews (4)

Small book, not much details
Small book with not much details.
I wish I should not have bought this book.

Cyrus Phd canidate
This is one of the best books on wavelets for engineers.As the authors mention most of the wavelet books currently on the market are targeted to mathematicians not engineers.Trust me my dissertation involves wavelets.If you are new to this topic my recommendation is to make sure you understand linear algebra and and some digital signal processing first.The books by Richard Lyons and R. W. Hamming are great.I also really like DSP by Michael Weeks.The classic would be Oppenheim & Schafer.

Probably the first to read is "A primer on wavelets by Walker"This book would be the second as it gets deeper into the definition and mathematical formalism than Walker yet is understandable to engineers.After that I would probably recommend Ripples in Mathematics on lifting and A wavelet tour by Mallat.

Great Book
Wavelets is a mathematically intensive subject. As such many books on the subject present the topic as an endless list of equations with very little insight.

This book on the other hand presents the material in a fashion that is digestable to the average engineer. This is a credit to their writting and teaching skill. They write as if their first goal is to let you understand (teach) not simply write.

I would say that the first books to read on this subject would be this one and the book by Walker. These books are sufficient to get a good understanding of Wavelets and to be able to use them. They also pave the way for more advanced books on the subject if desired.

As good as it gets
This is an excellent short introductory book for anyone who wants to understand and use wavelets via the filtering route. The presentation is entirely self-contained, and includes completely worked out wavelet examples and answers to all exercises. The authors develop wavelets as multirate quadrature mirror filters (explained within the text).Sample matlab source code is provided. Like Mix's text on Random Signal Processing, this one shines as being practical, easy-to-understand, filled with examples and prepares the reader for more advanced work. ... Read more

Product Description
This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. ... Read more

Product Description
Wavelets: Theory and Applications for Manufacturing presents a systematic description of the fundamentals of wavelet transform and its applications. Given the widespread utilization of rotating machines in modern manufacturing and the increasing need for condition-based, as opposed to fix-interval, intelligent maintenance to minimize machine down time and ensure reliable production, it is of critical importance to advance the science base of signal processing in manufacturing. This volume also deals with condition monitoring and health diagnosis of rotating machine components and systems, such as bearings, spindles, and gearboxes, while also:-Providing a comprehensive survey on wavelets specifically related to problems encountered in manufacturing-Discussing the integration of wavelet transforms with other soft computing techniques such as fuzzy logic, for machine defect and severity classification-Showing how to custom design wavelets for improved performance in signal analysisFocusing on wavelet transform as a tool specifically applied and designed for applications in manufacturing, Wavelets: Theory and Applications for Manufacturing presents material appropriate for both academic researchers and practicing engineers working in the field of manufacturing. ... Read more

Product Description
The last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction.

Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering.

As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression. ... Read more

Customer Reviews (2)

signals/math/engineering
Observations of signals, time series in telecommunication, or pictures in medical imaging reveal selfsimilarity, i.e., the signal/picture looks the same as the scale varies. Hence, the name "fractal" ! Pictures in the Intro make this scale-similarity visually apparent. But it is made precise in mathematical statistics, and the book further makes the connection to the engineering of signal/image processing. That's a main point of the book!

Selfsimilar processes are stochastic processes that are invariant in distribution under suitable scaling of time and/or space. Fractional Brownian motion or Brownian sheets are the best known of these. They were found by Kolmogorov long ago, but made popular by Mandelbrot and Ness in 1968. We now speak of 1/f processes.More recent use of wavelet bases in telecommunication and in stochastic integration has revived interest. Other even more recent applications include finance.

While the underlying idea behind all of this is quite simple, and can be traced back to Kolmogorov in the 1930ties, it is only recently, with the advent of wavelet methods, that the *computational* power has been better appreciated. The idea is analogous to that of random Fourier series: Instead of treating the Fourier coefficients as random variables, it is now wavelet coefficients that are analyzed statistically. Since wavelets have computational advantages, it is not surprising that the engineering applications abound. This little book is well written, and should be attractive both to members of the math community and to engineers.

Mathematicians will be pleased to note that wavelet analysis now brings *Hilbert space theoretic features* of the subject back to the fore. Amusingly, this was in fact a dominant feature which motivated both A. N. Kolmogorov and Norbert Wiener in the early days; e.g., curves in Hilbert space.

The author is an authority in the field, and his book brings out beautifully the highpoints of the subject. I further expect that the book will go over well in the classroom; nice summaries at the end of each chapter!(Exercises would have helped though!) The book will help bridge mathematical analysis, probability, and engineering. Engineers may like that proofs are relegated to later in the book. Mathematicians will be pleased with having the proofs, and with the clarity of their presentation. Reviewed by Palle Jorgensen, July, 2005.

Graduate Student
This is a very good book that deals fractal self similar stocastic processes,linear scale invariant systems and wavelet theory. This book covers synthesizing,estimation methods and modeling of self similar processes and their broad field of applications like communication and signal processing. These areas are extensively covered and the book is organized in a text book manner.Overall I found this book very useful and this is one of the best books I have read. ... Read more

Product Description
Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets. ... Read more

Product Description
Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations. This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: 1) A weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and 2) Wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet ``saga'', Meyer gives new and as yet unpublished results throughout the book. It is recommended to scientists wishing to apply wavelet analysis to multifractal signal processing. ... Read more

Customer Reviews (1)

multifractal signals
Tools from applications have been used in wavelet analysis to great advantage, and powerful methods from wavelet algorithms have in turn found an impressive host of recent practical applications. This exchange of ideas is masterfully brought to light in Meyer's book. Meyer lets the reader look behind the curtain of the abstract math, or the technicalities of the algorithms; giving lucid explanation of the key concepts,-- where they come from, and how they are used. Central concepts in the book: Holder exponent, scaling exponent, Hausdorff dimension, microlocal spaces, homogeneous distributions, Littlewood-Paley expansion, cone of influence, Wilson basis, Heisenberg [time-frequency] boxes,... ... Read more

Product Description
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods.
This book offers a self-contained treatment of wavelets, which includes thistheoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are:

1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions.

2. Full treatment of the theoretical foundations that are crucial for the analysis
of wavelets and other related multiscale methods : function spaces, linear andnonlinear approximation, interpolation theory.

3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.

... Read more

Customer Reviews (2)

MISLEADING TITLE
When I saw the title of this book my expectation was to see examples of using Wavelets.The title uses the word 'Numerical'.It really should read 'Theoretical'.For those seeking applications of Wavelets, I do not recommend this book.

A new direction.
Themes from math, science and engineering that predate the more recent trends in wavelts are signal processing, atomic decomposions of Calderon, splines, and finite element techniques of numerical analysis. All of these earlier ideas have enriched math, given new life and power to applied wavelet technology. While signal processing, filter banks, and pyramid algorithms have formed the under-current of a number of recent books on the interface of wavelets and some the neighboring fields, including applications, the interaction with numerical analysis hasn't really been presented in a systematic fashion in book form; so that students, and the rest of us, can pick and learn the fundamentals from scratch;-- not before this lovely new book by Albert Cohen: You find the methods and tools needed in the discretization of problems from PDE and from analysis. I hope the publisher will promote the book. It deserves it. Give it a try! I believe you will not be disappointed. Albert Cohen shows how wavelet tools have enriched numerical analysis and vice versa. ... Read more

Product Description
This book contains 14 invited chapters addressing applications and interactions between wavelet theory and scientific, medical and geophysical problems. Topics covered include EGG signals, spectral analysis, wavelet transform from orthogonal spline wavelets, numerical modeling of Maxwell's equation, wavelet networks and nonlinear processes, etc. It is addressed to an interdisciplinary readership of professional applied mathematicians, electrical engineers, physicists and other scientists especially interested in applying the new ideas and techniques. ... Read more

Customer Reviews (1)

A great book!
I really enjoyed this book. It's fascinating! ... Read more

Product Description

Professor Noubari's recommendation: "Professor Starks book provides an effective entry into the field for engineering students who have little or no prior knowledge of this important subject. Avaibility of collection of computer codes and mfiles in combination with topics of the book, makes the book highly valuable to enhance student learning of the subject matter."

Product Description
This innovative and in-depth book integrates the well-developed theory and practical applications of one dimensional and multidimensional multirate signal processing. Using a rigorous mathematical framework, it carefully examines the fundamentals of this rapidly growing field. Areas covered include: basic building blocks of multirate signal processing; fundamentals of multidimensional multirate signal processing; multirate filter banks; lossless lattice structures; introduction to wavelet signal processing.
Multirate and Wavelet Signal Processing forms the basis for a graduate course in multirate signal processing. It includes an introduction to wavelet signal processing and emphasizes topics of ever-increasing importance for a wide range of applications. Concise and easy-to-read, this book is also a useful primer for professional engineers.

Key Features
* Integrates the well-developed theory and practical applications of one-dimensional and multidimensional multirate signal processing
* Emphasizes topics of ever-increasing importance for a wide range of applications
* Written in a concise, easy-to-read style
* Uses relevant examples
* General mathematical formulation permits extensions of concepts to diverse applications, such as speech, imaging, video, and synthetic aperture radar
* Emphasizes key topics of the field, allowing the reader to make the most efficient use of time in learning the fundamentals of multirate
* Designed to be completely covered in a single semester or quarter ... Read more

Customer Reviews (1)

A starting point to a new journey
Multirate and wavelet signal processing is an open field for research in major sientific graduate schools. This book is a great reference for those who are in this field and those who would is interested in. Although thereading of this book requires rigid mathematical background, but it reallyrewards if you would like to explore more about the beauty, elegance ofwavelet theory. And it is quite pratical,too. People have found numerousapplications for it, in everyday modern life, image processing, high speedmodem have benefited from wavelet a lot. So fasten your seat belt, andenjoy the ride. ... Read more

Product Description

This book offers a gentle introduction to Clifford geometric algebra, an advanced mathematical framework, for applications in perception action systems. Part I, is written in an accessible way allowing readers to easily grasp the mathematical system of Clifford algebra. Part II presents related topics. While Part 3 features practical applications for Computer Vision, Robotics, Image Processing and Neural Computing.

Topics and Features include: theory and application of the quaternion Fourier and wavelet transforms, thorough discussion on geometric computing under uncertainty, an entire chapter devoted to the useful conformal geometric algebra, presents examples and hints for the use of public domain computer programs for geometric algebra.

The modern framework for geometric computing highlighted will be of great use for communities working on image processing, computer vision, artificial intelligence, neural networks, neuroscience, robotics, control engineering, human and robot interfaces, haptics and humanoids.

Product Description
Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase. ... Read more

Product Description
The past decade has witnessed the rpid 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

Product Description
Since the study of wavelets is a relatively new area, much ofthe research coming from mathematicians, most of the literature usesterminology, concepts and proofs that may, at times, be difficult andintimidating for the engineer. Wavelet Basics has therefore been written as an introductorybook for scientists and engineers. The mathematical presentation hasbeen kept simple, the concepts being presented in elaborate detail ina terminology that engineers will find familiar. Difficult ideas areillustrated with examples which will also aid in the development of anintuitive insight. Chapter 1 reviews the basics of signal transformation and discussesthe concepts of duals and frames. Chapter 2 introduces the wavelettransform, contrasts it with the short-time Fourier transform andclarifies the names of the different types of wavelet transforms.Chapter 3 links multiresolution analysis, orthonormal wavelets and thedesign of digital filters. Chapter 4 gives a tour d'horizon oftopics of current interest: wavelet packets and discrete time wavelettransforms, and concludes with applications in signal processing. ... Read more

Customer Reviews (2)

Good Introduction to Wavelets for Physicists and Engineers
There are no great wavelet books. They all tend to be heavy on theory and skimpy on detailed examples.The authors seem to "show off"their mathematical muscle and leave the reader to work out the details.And,usually, the emphasis is on 1-D (i.e., time series) applications - andmultidimensional (e.g., image processing) problems are pretty much ignoredor treated incompletely (e.g.,non-separable approaches omitted orsummarized lightly).

Many of the books in the field appear to be"thrown together" without any consideration for thereader.

This book is somewhat expensive for its size but it is probablythe best introduction to the subject around. It has an informativediscussion on the differences between continuous and discrete wavelets thatis usually glossed over in other books. It sort ofpeters out at the endbut the first two chapters (only four chapters in all) are strong. And its attention to the details is what distinguishes it from other waveletbooks.

Good job Dr. Chan!

A Great Tutorial
I read this book and learned all the basics in less than three weeks. The author really knows how to write a book for newcomers. After reading this book, I felt more comfortable to read more advance book such as "AWavelet Tour of Signal Processing." I strongly recommend this book foranyone who is new to the field. ... Read more

Product Description
In all areas of modelling and numerical simulation scientists and engineers are faced with problems that require a collection of mathematical tools ranging from the classical - the Fourier transform, convolution, distributions - to the more recent wavelet-based techniques.

For this reason, the object of this text, which focuses on Fourier analysis, signal analysis and filters, is two-fold. On the one hand it conveys to the mathematician a rigorous presentation illustrated with important practical applications of the theory, including a discussion of Fast Fourier Transform. On the other hand it imparts to the physicist and engineer a body of theory in which the `well-known' formulae find their justification.

There is a systematic development of fundamental concepts, such as the Lebesgue integration and theory of distribution, that allows one to establish precise relations among several domains: Fourier transform and convolution; filtering and sampling; time-frequency analysis (gabor transforms and wavelets).

Each of the 42 lectures provides an easily assimilated set of ideas and techniques, suitable for both classroom or self-study. Maneuvering through the book is facilitatedby grouping the lectures into 12 chapters and by adding numerous summary tables. This latter feature makes the book a handy reference for the subjects covered.

Senior undergraduate and graduate students in engineering, physics and mathematics will find this book helpful. It will also serve as a useful reference for scientists and engineers who deal with modelling and signal processing. ... Read more

Customer Reviews (1)

An excellent text for Fourier Analysis
I bought this book hoping to find a self-contained, semi-rigorous introduction to Fourier Analysis and its applications, and indeed I'm very pleased with the purchase. One aspect of the book's format that I enjoyed in a self-study setting is how it is partitioned into lessons (which are in turn divided into chapters). Indeed, it seemed that each lesson took me about 60-90 minutes to absorb, which is the average time most students (including myself) devote to one lesson.

Another aspect of the book I enjoyed was the fact that, on one hand the author took the time to introduce mathematically sophisticated ideas such as Lesbesgue measure and Hilbert spaces in order to make the proofs run more smoothly, but on the other there where more practical lessons on the fast Fourier transform, filters, and even wavelet analysis (last lesson). Such a blend of theory and practice in a relatively compact text seems quite rare.

Finally, I highly recommend this book for students of all levels; but especially to graduate students in mathematics, physics, and engineering. ... Read more

Product Description
An "applications first" approach to discrete wavelet transformations

Discrete Wavelet Transformations provides readers with a broad elementary introduction to discrete wavelet transformations and their applications. With extensive graphical displays, this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising.

The book begins with a cursory look at wavelet transformation development and illustrates its allure in digital signal and image applications. Next, a chapter on digital image basics, quantitative and qualitative measures, and Huffman coding equips readers with the tools necessary to develop a comprehensive understanding of the applications. Subsequent chapters discuss the Fourier series, convolution, and filtering, as well as the Haar wavelet transform to introduce image compression and image edge detection. The development of Daubechies filtersis presented in addition to coverage of wavelet shrinkage in the area of image and signal denoising. The book concludes with the construction of biorthogonal filters and also describes their incorporation in the JPEG2000 image compression standard.

The author's "applications first" approach promotes a hands-on treatment of wavelet transforma-tion construction, and over 400 exercises are presented in a multi-part format that guide readers through the solution to each problem. Over sixty computer labs and software development projects provide opportunities for readers to write modules and experiment with the ideas discussed throughout the text. The author's software package, DiscreteWavelets, is used to perform various imaging and audio tasks, compute wavelet transformations and inverses, and visualize the output of the computations. Supplementary material is also available via the book's related Web site, which includes an audio and video repository, final project modules, and softwarefor reproducing examples from the book. All software, including the DiscreteWavelets package, is available for use with Mathematica®, MATLAB®, and Maple.

Discrete Wavelet Transformations strongly reinforces the use of mathematics in digital data applications, sharpens programming skills, and provides a foundation for further study of more advanced topics, such as real analysis. This book is ideal for courses on discrete wavelet transforms and their applications at the undergraduate level and also serves as an excellent reference for mathematicians, engineers, and scientists who wish to learn about discrete wavelet transforms at an elementary level. ... Read more

Product Description
Nowadays, some knowledge of wavelets is almost mandatory formathematicians, physicists and electrical engineers. The emphasis inthis volume, based on an intensive course on Wavelets given at CWI,Amsterdam, is on the affine case. The first part presents a conciseintroduction of the underlying theory to the uninitiated reader. Thesecond part gives applications in various areas. Some of thecontributions here are a fresh exposition of earlier work by others,while other papers contain new results by the authors. The areas areso diverse as seismic processing, quadrature formulae, and waveletbases adapted to inhomogeneous cases. ... Read more