A first course in Wavelets with Fourier analysis

;A first course in Wavelets with Fourier analysis КНИГИ ;ТЕХНИКА Название: A first course in Wavelets with Fourier analysis Автор: Boggess A., Narcowich F. J. Издательство: Prentice Hall Год: 1999 Страниц: 293 Формат: pdf Размер: 8.2 Mb Язык: английский Описание: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 analysisImproved sections devoted to continuous wavelets and two-dimensional waveletsThe analysis of Haar, Shannon, and linear spline waveletsThe general theory of multi-resolution analysisThe construction, smoothness, and computation of Daubechies' waveletsAdvanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transformApplications 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. Uploading.com 0