Subband and Wavelet Transforms: Design and Applications / Edition 1

by Ali N. Akansu, Mark J.T. Smith

Overview

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.

Product Details

ISBN-13:	9780792396451
Publisher:	Springer US
Publication date:	10/31/1995
Series:	The Springer International Series in Engineering and Computer Science , #340
Edition description:	1996
Pages:	452
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1 Introduction and Overview.- 1 Introduction.- 2 Filter Banks and Transforms.- 3 Analysis/Synthesis Filter Banks.- 4 Two-Band Filter Banks.- 5 Tree-Structured Filter Banks.- 6 M-Band Filter Banks.- 7 Multidimensional Filter Banks.- 8 Wavelet Transforms.- 9 Historical Overview.- 2 Fundamentals and Optimal Design of Subband and Wavelet Transforms.- 1 Introduction.- 2 Fundamentals.- 3 Polyphase Decomposition.- 4 Uniform M-Band Filter Banks.- 5 The Two-Band Case and Tree Extensions.- 6 The Wavelet Transform and Dyadic Filter Banks.- 7 Time-Frequency Localization.- 8 Optimal Design and Performance.- 9 Progressive Optimality in Subband Trees and Wavelets.- 10 Discussions and Future Research.- 3 Matrix Theory for Filter Bank Analysis and Design.- 1 Introduction.- 2 Transform Domain Formulations.- 3 Time-Domain Formulation.- 4 Filter Bank Design Using the Time Domain Equations.- 4 IIR Filter Banks and Wavelets.- 1 Introduction.- 2 IIR Polyphase Networks.- 3 Two-Channel IIR Filter Banks and Wavelets.- 4 IIR Filter Design and Implementation of Two-Channel Filter Banks.- 5 M-Channel IIR Filter Banks.- 6 IIR Filter Design for M-Channel Filter Bank.- 7 2-D IIR Filter Banks.- 8 Concluding Remarks.- 5 The Continuous Wavelet Transform, from 1 to 3 Dimensions.- 1 Motivation.- 2 The Main Features of the 1-D CWT.- 3 Mathematical Analysis of the 1-D CWT.- 4 Discretization of the 1-D CWT.- 5 Implementation of the 1-D CWT.- 6 The CWT in Two Dimensions.- 7 Going to Higher Dimensions.- 8 Outcome.- 6 Time-Frequency Localization with Non-Stationary Wavelet Packets.- 1 Introduction.- 2 Non-Stationary Wavelet Packets.- 3 Frequency Localization and L1 Fourier Estimates.- 4 Estimates on the Variance of—n.- 5 Conclusion.- 7 Subband Image Coding.- 1 Theoretical Foundations of Subband Image Coding.-2 Image Subband Decomposition.- 3 Compression of Image Subband Signals.- 4 Conclusions.- 8 Subband Video Coding.- 1 Introduction.- 2 Basic Forms of Subband Video Coding.- 3 Spatially Scalable Intraframe Subband Coding.- 4 Spatially Scalable Motion-Compensated Interframe Subband Coding.- 5 Spatio-Temporally Scalable 3-D Subband Coding.- 9 Audio Coding with Filter Banks.- 1 Introduction.- 2 The Human Auditory System.- 3 The Auditory Filter Bank.- 4 The Audio Signal.- 5 Interactions Between Auditory Filter Bank and the Audio Signal.- 6 Conclusions.- 10 Wavelets and Filter Banks in Spread Spectrum Communication Systems.- 1 Introduction and Background.- 2 Transform Domain Processing Using Wavelets and Filter Banks.- 3 Data Modulation Using Filter Banks.- 4 Conclusions.- 11 Acoustic Echo Cancellation Using Subband Adaptive Filtering.- 1 Introduction.- 2 Linear FIR Adaptive Filtering.- 3 The Subband Adaptive Filtering System.- 4 Computational Complexity of the Subband Adaptive Filtering System.- 5 Experimental Setup.- 6 Critically Sampled Systems.- 7 Oversampled Systems.- 8 Conclusion.- 12 Analog Scramblers.- 1 Introduction.- 2 Four Techniques for Analog Scrambling.- 3 Filter Bank Analysis for Analog Scramblers.- 4 Conclusions.- 13 Multitone Modulation.- 1 Introduction.- 2 Information Theory.- 3 The QAM Multitone Modulation.- 4 The Twisted-Pair Channel.- 5 Decision Feedback Equalization Comparison.- 6 Discrete Multitone (DMT)—An Implementation.- 7 Summary and the Future.

Editorial Reviews

A reference on multirate signal processing and wavelets, compiling the fundamentals and surveying both mature and emerging applications. Theory and design are approached from such perspectives as matrix theory for filter bank analysis, the continuous wavelet transform, and time-frequency localization. Among the applications described are image and video coding, acoustic echo cancellation, analog scramblers, and multitone modulation. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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