Wavelets And Subband Coding

A central goal of signal processing is to describe real-time 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, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. *provides broad coverage of theory and applications and a different perspective based on signal processing. *gives framework for applications in speech, audio, image and video compression as used in multimedia. *includes sufficient background material so that people without signal processing knowledge will find it useful.

The scientists and engineers of today are relentless in their continuing study and analysis of the world about us from the microcosm to the macrocosm. A central purpose of this study is to gain sufficient scientific information and insight to enable the development of both representative and useful models of the superabundance of physical processes that surround us. The engineers need these models and the associated insight in order to build the information processing systems and control systems that comprise these new and emerging technologies. Much of the early modeling work that has been done on these systems has been based on the linear time-invariant system theory and its extensive use of Fourier transform theory for both continuous and discrete systems and signals. However many of the signals arising in nature and real systems are neither stationary nor linear but tend to be concentrated in both time and frequency. Hence a new methodology is needed to take these factors properly into account.

This book provides an in-depth, integrated, and up-to-date exposition of the topic of signal decomposition techniques. Application areas of these techniques include speech and image processing, machine vision, information engineering, High-Definition Television, and telecommunications. The book will serve as the major reference for those entering the field, instructors teaching some or all of the topics in an advanced graduate course and researchers needing to consult an authoritative source. n The first book to give a unified and coherent exposition of multiresolutional signal decomposition techniques n Classroom tested textbook clearly describes the commonalities among three key methods-transform coding, and wavelet transforms n Gives comparative performance evaluations of many proposed techniques

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 speech, image compression and computer visions, 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 the 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.

This book presents connections between the different aspects of wavelet and subband theory.

An in-depth treatment of algorithms and standards for perceptual coding of high-fidelity audio, this self-contained reference surveys and addresses all aspects of the field. Coverage includes signal processing and perceptual (psychoacoustic) fundamentals, details on relevant research and signal models, details on standardization and applications, and details on performance measures and perceptual measurement systems. It includes a comprehensive bibliography with over 600 references, computer exercises, and MATLAB-based projects for use in EE multimedia, computer science, and DSP courses. An ftp site containing supplementary material such as wave files, MATLAB programs and workspaces for the students to solve some of the numerical problems and computer exercises in the book can be found at ftp://ftp.wiley.com/public/sci_tech_med/audio_signal

This book concerns a new method of image data compression which weil may supplant the well-established block-transfonn methods that have been state-of-the art for the last 15 years. Subband image coding or SBC was first perfonned as such in 1985, and as the results became known at first through conference proceedings, and later through journal papers, the research community became excited about both the theoretical and practical aspects of this new approach. This excitement is continuing today, with many major research laboratories and research universities around the world investigating the subband approach to coding of color images, high resolution images, video- including video conferencing and advanced tele vision, and the medical application of picture archiving systems. Much of the fruits of this work is summarized in the eight chapters of this book which were written by leading practitioners in this field. The subband approach to image coding starts by passing the image through a two- or three-dimensional filter bank. The two-dimensional (2-D) case usually is hierarchical' consisting of two stages of four filters each. Thus the original image is split into 16 subband images, with each one decimated or subsampled by 4x4, resulting in a data conservation. The individual channel data is then quantized ·for digital transmission. In an attractive variation an octave-like approach, herein tenned subband pyramid, is taken for the decomposition resulting in a total of just eleven subbands.

Methods of signal analysis represent a broad research topic with applications in many disciplines, including engineering, technology, biomedicine, seismography, eco nometrics, and many others based upon the processing of observed variables. Even though these applications are widely different, the mathematical background be hind them is similar and includes the use of the discrete Fourier transform and z-transform for signal analysis, and both linear and non-linear methods for signal identification, modelling, prediction, segmentation, and classification. These meth ods are in many cases closely related to optimization problems, statistical methods, and artificial neural networks. This book incorporates a collection of research papers based upon selected contri butions presented at the First European Conference on Signal Analysis and Predic tion (ECSAP-97) in Prague, Czech Republic, held June 24-27, 1997 at the Strahov Monastery. Even though the Conference was intended as a European Conference, at first initiated by the European Association for Signal Processing (EURASIP), it was very gratifying that it also drew significant support from other important scientific societies, including the lEE, Signal Processing Society of IEEE, and the Acoustical Society of America. The organizing committee was pleased that the re sponse from the academic community to participate at this Conference was very large; 128 summaries written by 242 authors from 36 countries were received. In addition, the Conference qualified under the Continuing Professional Development Scheme to provide PD units for participants and contributors.