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   -> Volume 4, Issue 2

Book: Wavelets and subband coding
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Author Message "Jelena Kovacevic"

PostPosted: Mon Dec 02, 2002 5:42 pm    
Subject: Book: Wavelets and subband coding
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Book: Wavelets and subband coding


Martin Vetterli Jelena Kovacevic
UC Berkeley AT&T Bell Labs
Berkeley, CA 94720 Murray Hill, NJ 07974

1995, 483 pp, ISBN: 0-13-097080-8
PRENTICE HALL, Englewood Cliffs, NJ 07632

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

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

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

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
1.1 Series Expansions of Signals
1.2 The Multiresolution Concept
1.3 Overview of the Book

2 Fundamentals of Signal Decompositions
2.1 Notations
2.2 Hilbert Spaces
2.3 Linear Algebra
2.4 Fourier Theory and Sampling
2.5 Signal Processing
2.6 Time-Frequency Representations
2.A Bounded Linear Operators on Hilbert Spaces
2.B Parametrization of Unitary Matrices
2.C Convergence and Regularity of Functions

3 Discrete-Time Bases and Filter Banks
3.1 Series Expansions of Discrete-Time Signals
3.2 Two-Channel Filter Banks
3.3 Tree-Structured Filter Banks
3.4 Multichannel Filter Banks
3.5 Pyramids and Overcomplete Expansions
3.6 Multidimensional Filter Banks
3.7 Transmultiplexers and Adaptive Filtering in Subbands
3.A Lossless Systems
3.B Sampling in Multiple Dimensions and Multirate Operations

4 Series Expansions using Wavelets and Modulated Bases
4.1 Definition of the Problem
4.2 Multiresolution Concept and Analysis
4.3 Construction of Wavelets Using Fourier Techniques
4.4 Wavelets Derived from Iterated Filter Banks and Regularity
4.5 Wavelet Series and Its Properties
4.6 Generalizations in One Dimension
4.7 Multidimensional Wavelets
4.8 Local Cosine Bases
4.A Proof of Theorem 4.5

5 Continuous Wavelet and Short-Time Fourier Transforms and Frames
5.1 Continuous Wavelet Transform
5.2 Continuous Short-Time Fourier Transform
5.3 Frames of Wavelet and Short-Time Fourier Transforms

6 Algorithms and Complexity
6.1 Classic Results
6.2 Complexity of Discrete Bases Computation
6.3 Complexity of Wavelet Series Computation
6.4 Complexity of Overcomplete Expansions
6.5 Special Topics

7 Signal Compression and Subband Coding
7.1 Compression Systems Based on Linear Transforms
7.2 Speech and Audio Compression
7.3 Image Compression
7.4 Video Compression
7.5 Joint Source-Channel Coding
7.A Statistical Signal Processing
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