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