Preface
Conuentions and Notation
1．Introduction to Wavelets
1.0 Introduction
1.1 The Essence of a Wavelet
Comments and Extensions to Section 1.1
1.2 The Essence of Wavelet Analysis
Comments and Extensions to Section 1.2
1.3 Beyond the CWT:the Discrete Wavelet Transform
Comments and Extensions to Section 1.3
2．Review of Fourier Theory and Filters
2.0 Introduction
2.1 Complex Variables and Complex Exponentials
2.2 Fourier Transform of Infinite Sequences
2.3 Convolution/Filtering of Infinite Sequences
2.4 Fourier Transform of Finite Sequences
2.5 Circular Convolution/Filtering of Finite Sequences
2.6 Periodized Filters
Comments and Extensions to Section 2.6
2.7 Summary of Fourier Theory
2.8 Exercises
3．Orthonormal Transforms of time Series
3.0 Introduction
3.1 Basic Theory for Orthonormal Transforms
3.2 The Projection Theorem
3.3 Complex-Valued Transforms
3.4 The Orthonormal Discrete Fourier Transform
Comments and Extensions to Section 3.4
3.5 Summary
3.6 Exercises
4．The Discrete Wavelet Transform
4.0 Introduction
4.1 Qualitative Description of the DWT
Key Facts and Definitions in Section 4.1
Comments and Extensions to Section 4.1
4.2 The Wavelet Filter
Key Facts and Definitions in Section 4.2
Comments and Extensions to Section 4.2
4.3 The Scaling Filter
Key Facts and Definitions in Section 4.3
Comments and Extensions to Section 4.3
4.4 First Stage of the Pyramid Algorithm
Key Facts and Definitions in Section 4.4
Comments and Extensions to Section 4.4
4.5 Second Stage of the Pyramid Algorithm
Key Facts and Definitions in Section 4.5
4.6 General Stage of the Pyramid Algorithm
Key Facts and Definitions in Section 4.6
Comments and Extension to Section 4.6
4.7 The Partial Discrete Wavelet Transform
4.8 Daubechies Wavelet and Scaling Filters:From and Phase
Key Facts and Definitions in Section 4.8
Comments and Extensions to Section 4.8
4.9 Coiflet Wavelet and Scaling Filters:Form and Phase
4.10 Example:Electrocardiogram Data
Comments and Extensions to Section 4.10
4.11 Practical Considerations
Comments and Extensions to Section 4.11
4.12 Summary
4.13 Exercises
5．The Maximal Overlap Discrete Wavelet Transform
6．The Discrete Wavelet Packet Transform
7．Random Variables and Stochastic Processes
8．The Wavelet Variance
9．Analysis and Synthesis of Long Memory Processes
10．Wavelet-Based Signal Estimation
11．Wavelet Analysis of Finite Energy Signals
Appendix．Answers to Embedded Exercises
References
Author Index
Subject Index
