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Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics)
Mark A. Pinsky
Manufacturer: Brooks Cole
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ASIN: 0534376606 |
Book Description
Written by a successful author and respected mathematician, this book emphasizes a concrete and computational approach to the subject of Fourier analysis and wavelet theory while maintaining a balance between theory and applications. In some cases, several different proofs are offered for a given proposition, allowing readers to compare different methods.
Customer Reviews:
For the Students!.......2002-07-23
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.
Book Description
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method.
*The first book to present a unified view of filtering techniques
*Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series
*Provides easy access to a wide spectrum of parametric and non-parametric filtering methods
Customer Reviews:
The Guide.......2001-12-24
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 with appropriate model selection criteria are provided.
Discussison of these relatively advanced topics is very simple and clear without sacrificing important details. Highly recommended.
Easy to understand!.......2001-10-27
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.
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Real Analysis with an Introduction to Wavelets and Applications
Don Hong ,
Jianzhong Wang , and
Robert Gardner
Manufacturer: Academic Press
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Cracking the GRE Math Test, 3rd Edition (Graduate Test Prep)
ASIN: 0123548616 |
Book Description
An in-depth look at real analysis and its applications, including an introduction to wavelet
analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral,
harmonic analysis and wavelet theory with many associated applications.
*The text is relatively elementary at the start, but the level of difficulty steadily increases
*The book contains many clear, detailed examples, case studies and exercises
*Many real world applications relating to measure theory and pure analysis
*Introduction to wavelet analysis
Book Description
This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals.
This is the only book to present the mathematical point of view, as well as the discrete-time signal processing perspective. It brings together information previously available only in research papers, in engineering and applied mathematics.
Appropriate for researchers and practitioners in signal processing and applied mathematics.
Customer Reviews:
Nice approach (for physicists).......2006-05-16
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.......2005-06-11
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.......2001-04-15
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 Wavelets transforms.......2001-02-03
The introduction to Wavelets and Wavelets transform aplications.
theoretically sound, non-trivial tutorial.......1998-07-22
This book is a crafted piece as opposed to one of those collections of journal articles that usually leave you wondering. It appears to have a sound theoretical foundation with some clearly presented definitions and theorems. I wouldn't hesitate to spend time with this one.
Book Description
"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"
—Bulletin of the AMS
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 with consistent assumptions about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure).
* Complete background material on 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 guide for professionals.
Customer Reviews:
From Fourier to wavelets to applications........2003-01-28
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!
Book Description
One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of discrete wavelet transforms. It examines joint probability distributions, ensemble averages, and correlation, Fourier analysis, spectral density and excitation response relations for linear systems, more. 1993 edition.
Customer Reviews:
Great for a beginner in this area........2007-01-24
I got it when this one is on sale at $2.99 plus shipping.
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.
I would recommend this book to any neophyte in this area.
Even not on-sale, only $20 can not be beaten.
Also note that everything in this edition is exactly the same as the hardcover one costing more than $100.
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Introduction to Random Vibrations, Spectral and Wavelet Analysis (3rd Edition)
D.E. Newland
Manufacturer: Prentice Hall
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ASIN: 0582215846 |
Book Description
This book is a substantially expanded edition of An Introduction to Random Vibrations and Spectral Analysis which now covers wavelet analysis. Basic theory is thoroughly described and illustrated, with a detailed explanation of how discrete wavelet transforms work. Computer algorithms are expalined and supported by examples and set of problems. An appendix lists 10 computer programs for calculating and displaying wavelet transforms.
Customer Reviews:
Good DWT section.......1999-09-02
I am only interested in the last section which is on DWT. This section is a good introduction to DWT analysis. The basic idea behind the wavelet analysis is expalined fairly good in this sectoin.
Book Description
The mathematical theory of wavelets is less than 15 years old, yet already wavelets have become a fundamental tool in many areas of applied mathematics and engineering. This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinite-dimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given. This text is ideal for a topics course for mathematics majors, because it exhibits and emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets.
Customer Reviews:
One of the best wavelet books.......2007-01-13
i use this book in order to write my bachelor thesis, it is great, very dynamic, and with a lot of examples and exercises.
It also has an excellent walk through from linear algebra to wavelets, giving a more understanding point of view of this signal analysis tool.
Notation..........2004-04-15
I used this book for my first course in wavelets. Professor Frazier did a nice job bringing the material down to the undergrad by not starting off in hilbert space. He motivates it through linear algebra (for which the first chapter is an excellent review of the basics!). My only complaint is that the notation gets a bit overwhelming starting in chapter 3 (though I dont' know if I could come up with a better way to do it; just my experience). If you're looking into the subject, check out this book. It'll get you going in the right direction.
basis construction using wavelets is very well developed.......2003-12-24
Although the notation can be a little tight, the explanation of the
construction of a basis using wavelets is very well developed. He starts
with finite dimensional spaces and then moves onto wavelets on the real
line. He has a good series of graphs of signals and their corresponding
wavelets transforms and points out meaningful features of the wavelet
transform graph.
Obscure presentation.......2001-06-12
While I don't consider myself a math expert, I have certainly had to navigate my way through undergrad level math texts on more than a few occasions. In preparation for this book, I re-read Strang's "Linear Algebra and Its Applications" (an excellent text) and felt confident that I should be able to assimilate the material from this book. From the outset, the order of presentation of material in this book seemed promising: start with a review of Linear algebra and complex numbers, continue with Discrete Fourier Transforms, and then develop discrete wavelet transforms followed by continuous wavelet transforms.
Unfortunately, in spite of a promising game plan, this book serves to obscure the subject rather than providing a accessible introduction. The writing style is very terse and takes the reader through Lemma after Lemma without much in the way of explaining the motivation of these theorems or providing connecting narratives. The the reader is required to assimilate numerous disconnected mathematical ideas before a attempt is made to pull together the main ideas. And when the main points are developed, the treatment is uneven and generally too sparse. The only illustrations in this book come from MatLab or some other wavelet software package and there is a lack of conceptually oriented diagrams found in other types of text books.
Overall this book seems to be a compilation of material drawn from various sources and "sewn" together with mathematical proofs. Rather than focus on the main problems that wavelets are supposed to address (namely temporal and spatial localization) and develop the mathematics from that perspective, the emphasis on Lemmas and proofs drowns the reader in too much detail too fast. While this book may be a good supplement with other material, I found that this book too tedious to read and is a poor introduction to the subject without the benefit of a good instructor.
Obscure presentation.......2001-06-12
While I don't consider myself a math expert, I have certainly had to navigate my way through undergrad level math texts on more than a few occasions. In preparation for this book, I re-read Strang's "Linear Algebra and Its Applications" (an excellent text) and felt confident that I should be able to assimilate the material from this book. From the outset, the order of presentation of material in this book seemed promising: start with a review of Linear algebra and complex numbers, continue with Discrete Fourier Transforms, and then develop discrete wavelet transforms followed by continuous wavelet transforms.
Unfortunately, in spite of a promising game plan, this book serves to obscure the subject rather than providing a accessible introduction. The writing style is very terse and takes the reader through Lemma after Lemma without much in the way of explaining the motivation of these theorems or providing connecting narratives. The the reader is required to assimilate numerous disconnected mathematical ideas before a attempt is made to pull together the main ideas. And when the main points are developed, the treatment is uneven and generally too sparse. The only illustrations in this book come from MatLab or some other wavelet software package and there is a lack of conceptually oriented diagrams found in other types of text books.
Overall this book seems to be a compilation of material drawn from various sources and "sewn" together with mathematical proofs. Rather than focus on the main problems that wavelets are supposed to address (namely temporal and spatial localization) and develop the mathematics from that perspective, the emphasis on Lemmas and proofs drowns the reader in too much detail too fast. While this book may be a good supplement with other material, I found that this book too tedious to read and is a poor introduction to the subject without the benefit of a good instructor.
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Wavelets and Signal Processing: An Application-Based Introduction
Hans-Georg Stark
Manufacturer: Springer
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Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (Springer Finance)
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Applied Partial Differential Equations:: A Visual Approach
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Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)
ASIN: 3540234330 |
Book Description
The wavelets transform is a mathematical technique in the field of image compression and digital signal analysis.
The author aims at providing the reader with a working understanding of wavelets. In numerous examples, he discusses the potentials and limits of the tool in industrial applications.
The book is completed by the author`s own Matlab codes.
It is very well suited for electrical engineering students and engineers in industry.
Average customer rating:
- Better wavelet books out there
- An excellent book on signal processing
- An excellent book on signal processing
- A Friendly Guide to Time-Frequency Analysis
- An excellent guide to time frequency and wavelet analysis
|
Introduction to Time Frequency and Wavelet Transforms
Shie Qian
Manufacturer: Prentice Hall PTR
ProductGroup: Book
Binding: Paperback
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ASIN: 0130303607 |
Customer Reviews:
Better wavelet books out there.......2004-11-30
This book is divided into two sections: Time Frequency and Wavelets. Sadly, Shie Qian does not provide comprehensiveness in either subject, nor does he add to the knowledge base. I was expecting a more "cookbook" introductory approach to wavelets, but alas, for naught. To add insult to injury, there is not a hardcover version available to date. For shame.
My recommendations:
1. If you want to learn Time-Frequency analysis (windowed Fourier Transforms, Wigner-Ville ala Cohen's Class) -- download the Rice Time-Frequency Toolbox(for Matlab) and associated documentation. It's free, and the tutorials are outstanding. Not to mention, Qian seems to make liberal usage of it the book in question.
2a. For the electrical engineer, find a book that approaches wavelets by either branching off of Fourier Theory(provides a grounding in orthogonal, separable bases) or via subband coding(which correlates with the computation of wavelet transforms). Mallat's Wavelet Tour of Signal Processing is pretty good.
2b. For the math wiz(or those engineers with masochistic tendencies), find something with an angle on Riesz frames and bases. Avoid subband coding like the plague if you're not into block diagrams. A good start is Daubechies 10 Lectures on Wavelets, or anything through Birkhauser publishing.
An excellent book on signal processing.......2002-05-29
This book studies the two signal properties we are most interested in, time and frequency. Unlike other books, which usually concentrate on one topic of advanced signal processing, this book covers both time-frequency and wavelet analysis. The author organizes these topics in a clear structure with vivid English. The reviews at the beginning of every chapter are very
helpful for readers. Before I have this book, I read some mathematics books on wavelet analysis that were difficult to understand. The author explains the theories not only mathematically but also physically. Thus, this book gives me great help during my research on vibration and noise control,
modal analysis and acoustical signal processing. I strongly recommend this book to those who study signal processing.
An excellent book on signal processing.......2002-05-28
This book studies the two signal properties we are most interested in, time and frequency. Unlike other books, which usually concentrate on one topic of advanced signal processing, this book covers both time-frequency and wavelet analysis. The author organizes these topics in a clear structure with vivid English. The reviews at the beginning of every chapter are very
helpful for readers. Before I have this book, I read some mathematics books on wavelet analysis that were difficult to understand. The author explains the theories not only mathematically but also physically. Thus, this book gives me great help during my research on vibration and noise control,
modal analysis and acoustical signal processing. I strongly recommend this book to those who study signal processing.
A Friendly Guide to Time-Frequency Analysis.......2002-05-23
The aim of time-frequency analysis is to describe how the frequency or spectral content of a signal evolves. For engineers, scientists, and mathematicians, this self-contained book brings together the methods that have been developed to study time-varying spectra, and presents in simple language the physical and mathematical ideas, their origin and motivation, and the challenges of the field. The book is written clearly and well by a leading researcher
in the area of time-frequency analysis.
I would strongly recommend this book to anyone
with an interest in the field of signal processing.
An excellent guide to time frequency and wavelet analysis.......2002-01-15
This book is very successful in setting out the uses of time frequency analysis and wavelet transforms, employing interesting examples of their applications throughout. Starting from a nice discussion of Fourier transforms, it develops an intuitively appealing presentation of time variant filters, the wavelet transform and the Wigner-Ville distribution. The mathematics is clearly presented without unduly simplifying the proofs or concepts involved. I would strongly recommend this book to anyone with an interest in the field of signal processing.
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- Introduction to the Design and Analysis of Algorithms (2nd Edition)
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- Mathematical Methods For Physicists
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