Wavelets and Subband Coding

Over the past few years, wavelets and their discrete-time cousins, filter banks, or, subband coding have been used in a variety of signal processing applications. From work in harmonic analysis and mathematical physics, and applications such as speech, image compression and computer vision, different disciplines have built up methods and tools now cast in the common framework of wavelets. Offering a unified view of this exciting field, Wavelets and Subband Coding develops the theory in both continuous and discrete time, and presents important applications. Chapter 1 gives an overview of the topics covered and introduces the concept of multiresolution that is central in both theory and applications. Chapter 2 is a review of fundamentals that makes the book self-contained, and it includes discussions of vector spaces, Fourier theory, signal processing and time-frequency analysis. Chapter 3 develops discrete-time linear expansions based on filter banks or subband coding. The two-channel case is studied in detail. The multichannel case as well as transmultiplexers are developed and design examples are given. Chapter 4 develops wavelets, both with direct approaches and based on filter banks, and describes wavelet series and their computation, as well as the construction of modified local Fourier transforms. Chapter 5 discusses continuous wavelet and local Fourier transforms that are used in signal analysis, as well as discretized versions leading to frames. Chapter 6 addresses efficient algorithms for filter banks and wavelet computations. Chapter 7 concludes coverage by describing signal compression where filter banks and wavelets play important roles, including speech, audio, image and video compression. Source coding using transforms, quantization, and entropy coding are studied in detail, and the usefulness of multiresolution coding in current applications is discussed. In addition, each chapter includes numerous illustrative examples and several appendices cover additional material. The book includes about a hundred homework problems, and contains 130 illustrations and photographs.Vetterli, Martin is the author of 'Wavelets and Subband Coding', published 0008 under ISBN 9780130970800 and ISBN 0130970808.