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