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A contral goal of signal processing is to describe real life signals, be it for computation, compression, or understanding. This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, development of wavelets, continuous wavelet and local Fourier transforms, efficient algorithms for computations, and signal compression.
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 compressionwhere 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.
|1||Wavelets, Filter Banks and Multiresolution Signal Processing||1|
|2||Fundamentals of Signal Decompositions||14|
|3||Discrete-Time Bases and Filter Banks||92|
|4||Series Expansions Using Wavelets and Modulated Bases||201|
|5||Continuous Wavelet and Short-Time Fourier Transforms and Frames||299|
|6||Algorithms and Complexity||333|
|7||Signal Compression and Subband Coding||369|
Posted February 12, 2003
There are few books that sucessfully cover the interface of diverse fields, and yet this lovely book represents a subject that thrives on the interconnections. It is a great textbook, and it works well for selfstudy. The two subjects wavelets and subband filtering [from signal processing] are quite different, and have distinct and independent lives, they have different aims, and different histories. And yet, it is the happy marriage of the two that enriches the the union to an extraordinary degree. Multiresolutions are the bread and butter of wavelet algorithms, and they thrive on methods from signal processing, the quadrature-mirror filter construction, for example. One reason some books in the subject miss the target is that most authors know one of the subjects well, but not the others. Diverse subjects have quite different languages, and different terminology. The present authors are indeed on target, and they know it all. They come from engineering, but they know all the math;--the connections are made. And they strike a balance: Engineers can find what they want for the practical problems, and the mathematicians will not be disappointed. Programmers can pick up what is needed in their world. The book has been tested in courses, including mine. If you pick it for a course, the authors have material on their web pages that serves as a wonderful supplement. Lovely!Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.