A First Course in Wavelets with Fourier Analysis

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.