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Wavelets and Filter Banks

Wavelets and Filter Banks - 96 edition

ISBN13: 978-0961408879

Cover of Wavelets and Filter Banks 96 (ISBN 978-0961408879)
ISBN13: 978-0961408879
ISBN10: 0961408871
Cover type:
Edition/Copyright: 96
Publisher: Wellesley-Cambridge Press
Published: 1996
International: No
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Wavelets and Filter Banks - 96 edition

ISBN13: 978-0961408879

Gilbert Strang

ISBN13: 978-0961408879
ISBN10: 0961408871
Cover type:
Edition/Copyright: 96
Publisher: Wellesley-Cambridge Press

Published: 1996
International: No
Summary

This new textbook by Gilbert Strang and Truong Nguyen offers a clear and easy-to-understand introduction to two central ideas -- filter banks for discrete signals, and wavelets. The connections are fully explained -- the wavelet is determined by a choice of filter coefficients. All important wavelet properties (orthogonality or biorthogonality, symmetry, accuracy of approximation, and smoothness) come from specific properties of the filters. The text shows how to construct those filters and wavelets.

The applications are very widespread -- and they continue to develop rapidly. The book gives a direct approach to signal processing and image processing through filter banks that iterate on the lowpass filter (this is the wavelet idea). Blocking and ringing artifacts are analyzed, along with many MATLAB applications. Wavelets and Filter Banks is written for the very broad audience that uses these ideas:

  • Digital Signal Processing and Speech Processing
  • Image Processing including Medical Imaging
  • Scientific and Engineering Applications
  • Students and Professionals (wanting to understand wavelets!)

Table of Contents

Preface

Chapter 1 Introduction

1.1 Overview and Notation
1.2 Lowpass Filter = Moving Average
1.3 Highpass Filter = Moving Difference
1.4 Filter Bank = Lowpass and Highpass
1.5 Scaling Function and Wavelets
1.6 Wavelet Transforms by Multiresolution

Chapter 2 Filters

2.1 Signals, Samples, and Time-Invariance
2.2 Ideal Filters, Shannon Sampling, Sinc Wavelets
2.3 Lowpass and Highpass Filter Design
2.4 Fourier Analysis
2.5 Bases and Frames
2.6 Time, Frequency, and Scale


Chapter 3 Downsampling and Upsampling

3.1 Matrices for Downsampling and Upsampling
3.2 Subsampling in the Frequency Domain
3.3 Sampling Operations in the z-Domain
3.4 Filters Interchanged with Samplers


Chapter 4 Filter Banks

4.1 Perfect Reconstruction
4.2 The Polyphase Matrix
4.3 Efficient Filter Banks
4.4 Polyphase for Upsampling and Reconstruction
4.5 Lattice Structure


Chapter 5 Orthogonal Filter Banks

5.1 Paraunitary Matrices
5.2 Orthonormal Filter Banks
5.3 Halfband Filters
5.4 Spectral Factorization
5.5 Maxflat (Daubechies) Filters


Chapter 6 Multiresolution

6.1 The Idea of Multiresolution
6.2 Wavelets from Filters
6.3 Computing the Scaling Function
6.4 Infinite Product Formula
6.5 Biorthogonal Wavelets


Chapter 7 Wavelet Theory

7.1 Accuracy of Approximation
7.2 The Cascade Algorithm for the Dilation Equation
7.3 Smoothness of Scaling Functions and Wavelets
7.4 Splines and Semiorthogonal Wavelets
7.5 Multifilters and Multiwavelets


Chapter 8 Finite Length Signals

8.1 Circular Convolution and the DFT
8.2 Symmetric Extension for Symmetric Filters
8.3 Cosine Bases and the DCT
8.4 Smooth Local Cosine Bases
8.5 Boundary Filters and Wavelets


Chapter 9 M-Channel Filter Banks

9.1 Freedom Versus Structure
9.2 Polyphase Form: M Channels
9.3 Symmetry, Orthogonality, and PR
9.4 Cosine-Modulated Filter Banks
9.5 Multidimensional Filters and Wavelets


Chapter 10 Design Methods

10.1 Distortions in Image Compression
10.2 Design Methods - General Perspective
10.3 Design of PR Filter Banks
10.4 Design of Two-Channel Filter Banks
10.5 Design of Cosine-Modulated Filter Banks


Chapter 11 Applications

11.1 Digitized Fingerprints and the FBI
11.2 Image and Video Compression
11.3 Speech, Audio, and ECG Compression
11.4 Shrinkage, Denoising, and Feature Detection
11.5 Communication Applications and Adaptive Systems
11.6 Wavelet Integrals for Differential Equations


Glossary
Appendix 1 Wavelets (American Scientist)
Appendix 2 Wavelets and Dilation Equations (SIAM Review)
MATLAB and the Wavelet Toolbox
References
Index

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