Contents

Index

• Getting Started

• Wavelet Applications

• Wavelets in Action: Examples and Case Studies

• Using Wavelet Packets

• Advanced Concepts

Mathematical Conventions

• General Concepts

Wavelets: A New Tool for Signal Analysis

Wavelet Decomposition: A Hierarchical Organization

Finer and Coarser Resolutions

Wavelets and Associated Families

Wavelet Transforms: Continuous and Discrete

Local and Global Analysis

Synthesis: An Inverse Transform

Details and Approximations

• Fast Wavelet Transform (FWT) Algorithm

Filters Used to Calculate the DWT and IDWT

Why Does Such an Algorithm Exist?

One-Dimensional Wavelet Capabilities

Two-Dimensional Wavelet Capabilities

• Dealing with Border Distortion

Signal Extensions: Zero-Padding, Symmetrization, and Smooth Padding

• Discrete Stationary Wavelet Transform (SWT)

e-Decimated DWT

How to Calculate the e-Decimated DWT: SWT

Inverse Discrete Stationary Wavelet Transform (ISWT)

• Lifting Method for Constructing Wavelets

Lifting Background

Lifting Functions

• Frequently Asked Questions

Continuous or Discrete Analysis?

Why Are Wavelets Useful for Space-Saving Coding?

• Wavelet Families: Additional Discussion

Daubechies Wavelets: dbN

Symlet Wavelets: symN

Coiflet Wavelets: coifN

Biorthogonal Wavelet Pairs: biorNr.Nd

Meyer Wavelet: meyr

Battle-Lemarie Wavelets

Mexican Hat Wavelet: mexh

Morlet Wavelet: morl

Additional Real Wavelets

Complex Wavelets

Summary of Wavelet Families and Associated Properties (Part 1)

Summary of Wavelet Families and Associated Properties (Part 2)

• Wavelet Applications: More Detail

Suppressing Signals

Splitting Signal Components

Noise Processing

Data Compression

Function Estimation: Density and Regression

Available Methods for De-Noising, Estimation, and Compression Using GUI Tools

True Compression for Images

• Wavelet Packets

From Wavelets to Wavelet Packets: Decomposing the Details

Wavelet Packets in Action: An Introduction

Building Wavelet Packets

Wavelet Packet Atoms

Organizing the Wavelet Packets

Choosing the Optimal Decomposition

Some Interesting Subtrees

Wavelet Packets 2-D Decomposition Structure

Wavelet Packets for Compression and De-Noising

• Adding Your Own Wavelets

• Function Reference

• GUI Reference

• Object-Oriented Programming

• Release Notes

Advanced Concepts

This chapter presents a more advanced treatment of wavelet methods, and focuses on real wavelets, except in the two sections dedicated to wavelet families.

Mathematical Conventions

General Concepts

Fast Wavelet Transform (FWT) Algorithm

Dealing with Border Distortion

Discrete Stationary Wavelet Transform (SWT)

Lifting Method for Constructing Wavelets

Frequently Asked Questions

Wavelet Families: Additional Discussion

Wavelet Applications: More Detail

Wavelet Packets

References

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