A First Course in Wavelets with Fourier Analysis

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John Wiley & Sons, Sep 20, 2011 - Mathematics - 336 pages
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A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition

Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level.

The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature:

  • The development of a Fourier series, Fourier transform, and discrete Fourier analysis

  • Improved sections devoted to continuous wavelets and two-dimensional wavelets

  • The analysis of Haar, Shannon, and linear spline wavelets

  • The general theory of multi-resolution analysis

  • Updated MATLAB code and expanded applications to signal processing

  • The construction, smoothness, and computation of Daubechies' wavelets

  • Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform

Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples.

A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.


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I am doing my PhD course in IIT Hyderabad. My research work includes video processing using wavelets. First I want to know about the basics of wavelets. Our guide suggested to follow
this book. I am also doing Teaching Assistant where I have allocated the subject of Wavelet Fundamentals. So please send a complimentary copy of this book to below address, which will be useful in my research work and teaching assistance.
Thank you sir.
ROLL NO: EE13P1006
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Yeddumailaram 502205
Andhra Pradesh, INDIA

User Review - Flag as inappropriate

This book does a very good job of covering the basics of signal processing, and it gives the most comprehensive covering on the Haar wavelet function that I have been found. That being said, I found it a little light on explication on certain points. The exercises are well-balanced and useful, however, and for an introduction to the field for someone with little to no previous experience, I found it readable and extremely useful for getting up to speed on the subject quickly. 


Preface and Overview
Inner Product Spaces
Fourier Series
Haar Wavelet Analysis
Discrete Fourier Analysis
The Daubechies Wavelets
Other WaveletTopics
Technical Matters
SolutionstoSelected Exercises

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About the author (2011)

ALBERT BOGGESS, PhD, is Professor of Mathematics at Texas A&M University. Dr. Boggess has over twenty-five years of academic experience and has authored numerous publications in his areas of research interest, which include overdetermined systems of partial differential equations, several complex variables, and harmonic analysis.

FRANCIS J. NARCOWICH, PhD, is Professor of Mathematics and Director of the Center for Approximation Theory at Texas A&M University. Dr. Narcowich serves as an Associate Editor of both the SIAM Journal on Numerical Analysis and Mathematics of Computation, and he has written more than eighty papers on a variety of topics in pure and applied mathematics. He currently focuses his research on applied harmonic analysis and approximation theory.

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