Documentation Table of Contents

Part 1. Fundamentals of Wavelets

1.2 Multiresolution Analysis

• Definition of a Multiresolution Analysis
• Examples of Multiresolution Analysis
• Approximation Spaces, Scaling Function, and the Dilation Equation
• Detail Spaces, Mother Wavelet, and the Wavelet Equation
• A view from the Frequency Domain

1.3 Orthogonal Wavelets

• Battle-Lemarie Wavelets
• Other Examples

1.4 Orthogonal Wavelets II: Daubechies Wavelets

• Solving for Daubechies Filter Coefficients
• Daubechies' Extremal Phase Filters
• Scaling Function and Mother Wavelet
• Daubechies' Least Asymmetric Filters
• Coiflets
• Scaling Function and Mother Wavelet in Fourier Space and the Derivatives of the Scaling Function and the Mother Wavelet

1.5 Discrete Wavelet Transforms and Wavelet Packet Transforms

• Wavelet Transforms
• Inverse Wavelet Transforms
• Connection to Subband Filtering
• Wavelets and Wavelet Transforms in Two Dimensions
• Mathematica Functions for Doing Wavelet Transforms
• Wavelet Packets and Wavelet Packet Transforms
• Generating Wavelet Packets
• Zooming in on Details of the Scaling Function and Mother Wavelet

1.6 Biorthogonal Wavelets

• Dual Bases
• Biorthogonal Wavelets
• Biorthogonal Spline Wavelets
• Biorthogonal Wavelet Transforms

1.7 Local Trigonometric Bases and Transforms

• Windowed Fourier Transforms
• Discrete Sine and Cosine Transforms
• Local Sine and Cosine Bases of Coifman and Meyer
• Local Trigonometric Transforms
• Local Sine and Cosine Packet Transforms

Part 2. Further Examples and Applications

• Shock Solution of Burgers Equation
• Denoising
• Wavelet Packet Analysis of a Speech Signal
• Local Cosine Packet Analysis of a Sound Signal

2.2 Analysis of Two-Dimensional Images

• Analysis of an Image Using Wavelet Basis
• Analysis of an Image Using Local Trigonometric Basis

Part 3. Summary of Functions

• Filters
• Scaling Functions, Wavelets, and Wavelet Packets
• Viewing Details of the Scaling Function and Mother Wavelet
• Derivatives of the Scaling Function and Mother Wavelet

3.2 Various Transforms

• Wavelet Transforms
• Wavelet Packet Transforms
• Local Sine and Cosine Transforms
• Sine and Cosine Packet Transforms

3.3 Other Utilities