WAVELETS AND FILTER BANKS

Gilbert Strang and Truong Nguyen
Wellesley-Cambridge Press (1996)



TABLE OF CONTENTS

  Preface

  Guide to the Book

  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