A First Course in Wavelets with Fourier Analysis
2nd Edition
Published on 20. September 2011
336 pages
978-1-118-21115-1 (ISBN)
Description
A comprehensive, self-contained treatment of Fourier analysisand wavelets--now in a new edition
Through expansive coverage and easy-to-follow explanations, AFirst Course in Wavelets with Fourier Analysis, SecondEdition provides a self-contained mathematical treatment of Fourieranalysis and wavelets, while uniquely presenting signal analysisapplications and problems. Essential and fundamental ideas arepresented in an effort to make the book accessible to a broadaudience, and, in addition, their applications to signal processingare kept at an elementary level.
The book begins with an introduction to vector spaces, innerproduct spaces, and other preliminary topics in analysis.Subsequent chapters feature:
* The development of a Fourier series, Fourier transform, anddiscrete Fourier analysis
* Improved sections devoted to continuous wavelets andtwo-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 signalprocessing
* 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 thebook, most involving the filtering and compression of signals fromaudio or video. Some of these applications are presented first inthe context of Fourier analysis and are later explored in thechapters on wavelets. New exercises introduce additionalapplications, and complete proofs accompany the discussion of eachpresented theory. Extensive appendices outline more advanced proofsand partial solutions to exercises as well as updated MATLABroutines that supplement the presented examples.
A First Course in Wavelets with Fourier Analysis, SecondEdition is an excellent book for courses in mathematics andengineering at the upper-undergraduate and graduate levels. It isalso a valuable resource for mathematicians, signal processingengineers, and scientists who wish to learn about wavelet theoryand Fourier analysis on an elementary level.
Reviews / Votes
"A first course in wavelets with Fourier analysis, second editionis an excellent book for courses in mathematics and engineering atthe upper-undergraduate and graduate levels. It is also a valuableresource for mathematicians, signal processing engineers, andscientists who wish to learn about wavelet theory and Fourieranalysis on an elementary level." (Mathematical Reviews,2011) "The discussions of applications avoid the deep jargon of signalprocessing ... accessible to a wider audience." (BookNews, December 2009)More details
Other editions
Additional editions
Albert Boggess | Francis J. Narcowich
A First Course in Wavelets with Fourier Analysis
Book
10/2009
2nd Edition
Wiley
€133.64
Shipment within 10-20 days
Persons
ALBERT BOGGESS, PhD, is Professor of Mathematics at TexasA&M University. Dr. Boggess has over twenty-five years ofacademic experience and has authored numerous publications in hisareas of research interest, which include overdetermined systems ofpartial differential equations, several complex variables, andharmonic analysis.
FRANCIS J. NARCOWICH, PhD, is Professor of Mathematicsand Director of the Center for Approximation Theory at TexasA&M University. Dr. Narcowich serves as an Associate Editor ofboth the SIAM Journal on Numerical Analysis andMathematics of Computation, and he has written more thaneighty papers on a variety of topics in pure and appliedmathematics. He currently focuses his research on applied harmonicanalysis and approximation theory.
Content
Preface and Overview.
0 Inner Product Spaces.
0.1 Motivation.
0.2 Definition of Inner Product.
0.3 The Spaces L² andl².
0.4 Schwarz and Triangle Inequalities.
0.5 Orthogonality.
0.6 Linear Operators and Their Adjoints.
0.7 Least Squares and Linear Predictive Coding.
Exercises.
1 Fourier Series.
1.1 Introduction.
1.2 Computation of Fourier Series.
1.3 Convergence Theorems for Fourier Series.
Exercises.
2 The Fourier Transform.
2.1 Informal Development of the Fourier Transform.
2.2 Properties of the Fourier Transform.
2.3 Linear Filters.
2.4 The Sampling Theorem.
2.5 The Uncertainty Principle.
Exercises.
3 Discrete Fourier Analysis.
3.1 The Discrete Fourier Transform.
3.2 Discrete Signals.
3.3 Discrete Signals & Matlab.
Exercises.
4 Haar Wavelet Analysis.
4.1 Why Wavelets?
4.2 Haar Wavelets.
4.3 Haar Decomposition and Reconstruction Algorithms.
4.4 Summary.
Exercises.
5 Multiresolution Analysis.
5.1 The Multiresolution Framework.
5.2 Implementing Decomposition and Reconstruction.
5.3 Fourier Transform Criteria.
Exercises.
6 The Daubechies Wavelets.
6.1 Daubechies' Construction.
6.2 Classification, Moments, and Smoothness.
6.3 Computational Issues.
6.4 The Scaling Function at Dyadic Points.
Exercises.
7 Other Wavelet Topics.
7.1 Computational Complexity.
7.2 Wavelets in Higher Dimensions.
7.3 Relating Decomposition and Reconstruction.
7.4 Wavelet Transform.
Appendix A: Technical Matters.
Appendix B: Solutions to Selected Exercises.
Appendix C: MATLAB® Routines.
Bibliography.
Index.
