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 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 MATLABR 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
Table of Contents Preface and Overview. 0 Inner Product Spaces. 2 The Fourier Transform. 3 Discrete Fourier Analysis. 4 Haar Wavelet Analysis. 5 Multiresolution Analysis. 6 The Daubechies Wavelets. 7 Other Wavelet Topics.
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.