: A first course in Wavelets with Fourier analysisАвтор
: Boggess A., Narcowich F. J.Издательство
: Prentice HallГод
: 8.2 MbЯзык
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
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.