Introduction to Wavelets and Wavelets Transforms

This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. This is the only book to present the mathematical point of view, as well as the discrete-time signal processing perspective. It brings together information previously available only in research papers, in engineering and applied mathematics. Appropriate for researchers and practitioners in signal processing and applied mathematics. Introduction To Wavelets -- A Multiresolution Formulation Of Wavelet Systems -- Filter Bands And The Discrete Wavelet Transform -- Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, And Unconditional Bases -- The Scaling Function And Scaling Coefficients, Wavelet And Wavelet Coefficients -- Regularity, Moments, And Wavelet System Design -- Generalizations Of The Basic Multiresolution Wavelet System -- Filter Banks And Transmultiplexers -- Calculation Of The Discrete Wavelet Transform -- Wavelet-based Signal Processing And Applications -- Summary Overview. C. Sidney Burrus, Ramesh A. Gopinath, And Haitao Guo ; With Additional Material And Programs By Jan E. Odegard And Ivan W. Selesnick. Includes Bibliographical References (p. 224-245) And Index. Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods. This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.