Overview

This resource examines both theoretical and practical aspects of computational signal processing using wavelets. Computationally, wavelet signal processing algorithms are presented and applied to signal compression, noise supression, and signal identification. Numerical illustrations of these computational techniques are further discussed in the text (using MATLAB) and the software M-Files are available via the World Wide Web site for the book. Starting from basic principles of signal representation with atomic functions, a mathematically well-founded theory of the discretization of analogue signals is developed. General families are specialized to wavelet families, with discrete representation specialized to generally non-orthogonal wavelet transforms. The theory leads naturally to the computer implementation of the non-orthagonal wavelet transform. Specific topics covered include general signal representation, continuous wavelet transform, multi-resolution analysis, continuous wavelet transform, non-orthagonal wavelet transform, and wavelet based signal processing algorithms for compression, noise supression, and identification. The technical discussion is at the begninning graduate level and is accessible to all signal processing professionals and practitioners.

Full Product Details

Author:   Anthony Teolis
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1998 ed.
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.480kg
ISBN:  

9780817639099

ISBN 10:   0817639098
Pages:   324
Publication Date:   15 May 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 1.1 Motivation and Objectives.- 1.2 Core Material and Development.- 1.3 Hybrid Media Components.- 1.4 Signal Processing Perspective.- 2 Mathematical Preliminaries.- 2.1 Basic Symbols and Notation.- 2.2 Basic Concepts.- 2.3 Basic Spaces.- 2.4 Operators.- 2.5 Bases and Completeness in Hilbert Space.- 2.6 Fourier Transforms.- 2.7 Linear Filters.- 2.8 Analog Signals and Discretization.- Problems.- 3 Signal Representation and Frames.- 3.1 Inner Product Representation (Atomic Decomposition).- 3.2 Orthonormal Bases.- 3.3 Riesz Bases.- 3.4 General Frames.- Problems.- 4 Continuous Wavelet and Gabor Transforms.- 4.1 What Is a Wavelet?.- 4.2 Example Wavelets.- 4.3 Continuous Wavelet Transform.- 4.4 Inverse Wavelet Transform.- 4.5 Continuous Gabor Transform.- 4.6 Unified Representation and Groups.- Problems.- 5 Discrete Wavelet Transform.- 5.1 Discretization of the CWT.- 5.2 Multiresolution Analysis.- 5.3 Multiresolution Representation.- 5.4 Orthonormal Wavelet Bases.- 5.5 Compactly Supported (Daubechies) Wavelets.- 5.6 Fast Wavelet Transform Algorithm.- Problems.- 6 Overcomplete Wavelet Transform.- 6.1 Discretization of the CWT Revisited.- 6.2 Filter Bank Implementation.- 6.3 Time-Frequency Localization and Wavelet Design.- 6.4 OCWT Examples.- 6.5 Irregular Sampling and Frames.- Problems.- 7 Wavelet Signal Processing.- 7.1 Noise Suppression.- 7.2 Compression.- 7.3 Digital Communication.- 7.4 Identification.- 7.5 Conclusion.- Problems.- 8 Object-Oriented Wavelet Analysis with MATLAB 5.- 8.1 Wavelet Signal Processing Workstation.- 8.2 MATLAB Coding.- 8.3 The sampled_signal Object.- 8.4 Wavelet Transform Implementation.- 8.5 The wavelet Object.- 8.6 Processing Example.- 8.7 Supporting Functions and Globals.- References.

Reviews

This book provides an expository treatment of wavelets from a signal processing perspective. The focus is on the expansion of signals in overcomplete wavelet systems. All illustrations of the theory are generated in the framework of the Matlab toolbox wavelet signal processing workstation (WSPW) made publicly available by the author.... The last chapter is a manual for WSPW, and the whole book serves as an extended manual. a Mathematical Reviews <p> This book provides a bridge between theory and practice of wavelet-based signal processing and is written for both students and professionals. A solid mathematical foundation is given in the beginning chapters [1a 6].... Several applications of wavelet-based signal processing including noise suppression, signal compression, signal identification and digital communication are presented in Chapter 7. Chapter 8 gives numerical illustrations and examples of wavelet methods using MATLAB 5. The accomanying MATLAB-based software is available on the world wide web. Every chapter of the book contains a collection of exercises. a Zentralblatt MATH <p> A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topica ]is a class of a ~overcomplete waveletsa (TM). These functions are not orthonormal and they lead to many useful results. a Journal of Mathematical Psychology

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