Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics)

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.

An Introduction to Wavelets and Other Filtering Methods in Finance and Economics

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The Guide
Easy to understand!

An Introduction to Wavelets and Other Filtering Methods in Finance and Economics
Ramazan Gençay , Faruk Selçuk , and Brandon Whitcher
Manufacturer: Academic Press
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Binding: Hardcover

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An Introduction to High-Frequency Finance
Wavelet Methods for Time Series Analysis (Cambridge Series in Statistical and Probabilistic Mathematics)
Analysis of Financial Time Series, 2nd Edition (Wiley Series in Probability and Statistics)
Inside Volatility Arbitrage : The Secrets of Skewness
Volatility and Correlation: The Perfect Hedger and the Fox (Wiley Finance)

ASIN: 0122796705

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.

Real Analysis with an Introduction to Wavelets and Applications

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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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Binding: Hardcover

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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

Introduction to Wavelets and Wavelets Transforms

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Nice approach (for physicists)
Good Book
If you don't know anything about Wavelet Analysis Start Here
introduction to Wavelets and Wavelets transforms
theoretically sound, non-trivial tutorial

Introduction to Wavelets and Wavelets Transforms
C. Sidney Burrus , and Ramesh A. Gopinath
Manufacturer: Prentice Hall
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Binding: Paperback

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A Primer on Wavelets and Their Scientific Applications (Studies in Advanced Mathematics)
A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications)
An Introduction to Wavelet Analysis
The Illustrated Wavelet Transform Handbook
Ripples in Mathematics

ASIN: 0134896009

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.

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From Fourier to wavelets to applications.

An Introduction to Wavelet Analysis
David F. Walnut
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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Computational Turbulent Incompressible Flow: Applied Mathematics: Body and Soul 4 (Applied Mathematics: Body and Soul)
Computational Intelligence

ASIN: 0817639624

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!

An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)

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One of the best wavelet books
Notation...
basis construction using wavelets is very well developed
Obscure presentation
Obscure presentation

An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)
Michael W. Frazier
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Fourier Analysis: An Introduction (Princeton Lectures in Analysis, Volume 1)

ASIN: 0387986391

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.

Obscure presentation.......2001-06-12

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.

An Introduction to Wavelets, Volume 1 (Wavelet Analysis and Its Applications)

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Infinite in all directions.
Great introduction for Wavelet

An Introduction to Wavelets, Volume 1 (Wavelet Analysis and Its Applications)
C. K. Chui
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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Wavelets: A Tutorial in Theory and Applications (Wavelet Analysis and Its Applications, Vol 2)
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A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications)

ASIN: 0121745848

Book Description

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.

Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

Customer Reviews:

Infinite in all directions........2002-07-09

I have used the book, teaching a beginning course in wavelets, and it went over well with the students: they like that the proofs are clearly spelled out, and that the presentation is systematic. I supplemented it with S Mallat and Y Meyer's books. That was to give the course a more algorithmic slant. However, I feel that there are many valid approaches, and that the subject is infinite in all directions.

Great introduction for Wavelet.......2000-05-12

For those who would like to learn the beauty of Wavelet theory, which is a great finding in Mathematics, this book would shed some light on it. Wavelet is elegant, a simple formula leads to so much interests, the application of Wavelet is everywhere, particularly in modern communications and signal processing, and there is still more waiting for people to explore. Enjoy the new journey.

A Mathematical Introduction to Wavelets (London Mathematical Society Student Texts)

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The mathematics of wavelets

A Mathematical Introduction to Wavelets (London Mathematical Society Student Texts)
P. Wojtaszczyk
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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An Introduction to Frames and Riesz Bases
Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics)

ASIN: 0521578949

Book Description

This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analyzing functions and function spaces, both in one and in several variables. Starting with a detailed and self-contained discussion of the general construction of one dimensional wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. The author discusses wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces and provides wavelet characterizations of those spaces. Also included are periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets.

Customer Reviews:

The mathematics of wavelets.......2000-04-11

The literature on wavelets has been growing at an increasing pace, as testified by 129 titles listed in Amazon.com, the great majority which were first published in the last five years. Many of these books are either (i)popular accounts for the general reader, (ii) user's guides for the practitioner or (iii) advanced mathematical treatises for experts. Thus we find very few textbooks where the serious student can obtain an honest introduction to the subject from a recognized authority. This is even more surprising, given that the origins of the subject can be traced back to the mathematics literature in the early part of the 20th century under the names of Alfred Haar, Phillip Franklin and Sir Edmund Whittaker---and later to further work by Alberto Calderon in the 1960's. With the flurry of activity in the 1980's in the French school, the subject came alive and is now a permanent part of the literature in mathematical analysis, growing by leaps and bounds.

The book of Wojtaszczyk is a welcome addition to the literature on wavelets. Without the benefit of glossy pictures or computer output, the author has been extremely successful in presenting a clear and correct approach to the subject for readers who have a minimal acquaintance with mathematical analysis at the level of integration theory and elementary Fourier analysis. Going beyond other introductory works, the book contains a systematic sets of exercises at the end of each chapter, as a sort of "reality check" for the student, to test his/her understanding of the theory.

The first four chapters of the book deal with wavelets in one dimensions, continued in chapter 9. Following the examples of the classical Haar system and the Stromberg spline wavelet, done in great detail, we are introduced to MRA systems as a systematic method for generating wavelet bases of the space of square-integrable functions on the line. An MRA (multi-reolution analysis) is defined by a "scaling function", which satisfies an orthonormality condition, a scaling condition and a smoothness condition in the Fourier domain. Any such function generates an MRA, which in turn generates a wavelet basis. In particular one can generate in this framework the smooth wavelets of Meyer by this method, followed by the compactly supported wavelets of Daubechies. Wavelet theory is first formulated for square integrable functions, but can be extended to other Banach spaces, where it often provides an "unconditional basis", which is not true of the classical Fourier series.

Chapters 5-8 deal with some of the multi-dimensional theory, where several wavelets are necesary to generate the MRA, suitably defined. Chapter 6 contains a self-contained treatment of some important topics in analysis: the Hardy-Littlewood maximal inequality, the Banach spaces H^1 and BMO, the John-Nirenberg inequalty. These are used to develop the property of unconditional basis for wavelets in the spaces L^p and H^1.

The author suceceds admirably in carrying out his stated goal beyond any reasonable expectation: in the preface we read "This is a purely mathematical book, although I constantly try to make the calculations as explicit as possible and I concentrate on theoretical questions that should have relevance in appplications, but regrettably discuss no real applications". With the flurry of literature on the uses of wavelets, these applications are best left to other works.

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