Introduction to wavelets and wavelet transforms : a primer

This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. KEY TOPICS: 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. MARKET: 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.