Table of Contents for WMTSA
Wavelet Methods for Time Series Analysis has a total of 594+xxvi pages.
The main part of the book
consists of eleven chapters and an appendix
that gives full solutions
to the 114 exercises that are embedded within Chapters 2 to 11.
The first chapter provides an introduction to wavelets
via the continuous wavelet transform (CWT).
The next two chapters go over background material
on Fourier theory and orthonormal transforms,
after which there are three chapters devoted to developing
the discrete wavelet transform (DWT)  and two variations thereof 
from the ground level and up.
Chapter 7 gives the necessary statistical background
for the material covered in Chapter 8, 9 and 10.
The final chapter discusses the connections between the CWT and the DWT.

Preface (3 pages)
 Conventions and Notation (9 pages)

Chapter 1: Introduction to Wavelets (19 pages)
 Introduction
 The Essence of a Wavelet
 The Essence of Wavelet Analysis
 Beyond the CWT: the Discrete Wavelet Transform

Chapter 2: Review of Fourier Theory and Filters (21 pages)
 Introduction
 Complex Variables and Complex Exponentials
 Fourier Transform of Infinite Sequences
 Convolution/Filtering of Infinite Sequences
 Fourier Transform of Finite Sequences
 Circular Convolution/Filtering of Finite Sequences
 Periodized Filters
 Summary of Fourier Theory
 Exercises

Chapter 3: Orthonormal Transforms of Time Series (15 pages)
 Introduction
 Basic Theory for Orthonormal Transforms
 The Projection Theorem
 ComplexValued Transforms
 The Orthonormal Discrete Fourier Transform
 Summary
 Exercises

Chapter 4: The Discrete Wavelet Transform (103 pages)
 Introduction
 Qualitative Description of the DWT
 The Wavelet Filter
 The Scaling Filter
 First Stage of the Pyramid Algorithm
 Second Stage of the Pyramid Algorithm
 General Stage of the Pyramid Algorithm
 The Partial Discrete Wavelet Transform
 Daubechies Wavelet and Scaling Filters: Form and Phase
 Coiflet Wavelet and Scaling Filters: Form and Phase
 Example: Electrocardiogram Data
 Practical Considerations
 Summary
 Exercises

Chapter 5: The Maximal Overlap Discrete Wavelet Transform (47 pages)
 Introduction
 Effect of Circular Shifts on the DWT
 MODWT Wavelet and Scaling Filters
 Basic Concepts for MODWT
 Definition of jth Level MODWT Coefficients
 Pyramid Algorithm for the MODWT
 MODWT Analysis of `Bump' Time Series
 Example: Electrocardiogram Data
 Example: Subtidal Sea Level Fluctuations
 Example: Nile River Minima
 Example: Ocean Shear Measurements
 Practical Considerations
 Summary
 Exercises

Chapter 6: The Discrete Wavelet Packet Transform (49 pages)
 Introduction
 Basic Concepts
 Example: DWPT of Solar Physics Data
 The Best Basis Algorithm
 Example: Best Basis for Solar Physics Data
 Time Shifts for Wavelet Packet Filters
 Maximal Overlap Discrete Wavelet Packet Transform
 Example: MODWPT of Solar Physics Data
 Matching Pursuit
 Example: Subtidal Sea Levels
 Summary
 Exercises

Chapter 7: Random Variables and Stochastic Processes (40 pages)
 Introduction
 Univariate Random Variables and Probability Density Functions (PDFs)
 Random Vectors and PDFs
 A Bayesian Perspective
 Stationary Stochastic Processes
 Spectral Density Estimation
 Definition and Models for Long Memory Processes
 Nonstationary 1/fType Processes
 Simulation of Stationary Processes
 Simulation of Stationary Autoregressive Processes
 Exercises

Chapter 8: The Wavelet Variance (45 pages)
 Introduction
 Definition and Rationale for the Wavelet Variance
 Basic Properties of the Wavelet Variance
 Estimation of the Wavelet Variance
 Confidence Intervals for the Wavelet Variance
 Spectral Estimation via the Wavelet Variance
 Example: Atomic Clock Deviates
 Example: Subtidal Sea Level Fluctuations
 Example: Nile River Minima
 Example: Ocean Shear Measurements
 Summary
 Exercises

Chapter 9: Analysis and Synthesis of Long Memory Processes (53 pages)
 Introduction
 Discrete Wavelet Transform of a Long Memory Process
 Simulation of a Long Memory Process
 Maximum Likelihood Estimators (MLEs) for Stationary Fractionally Differenced (FD) Processes
 MLEs for Stationary or Nonstationary FD Processes
 Least Squares Estimation for FD Processes
 Testing for Homogeneity of Variance
 Example: Atomic Clock Deviates
 Example: Nile River Minima
 Summary
 Exercises

Chapter 10: WaveletBased Signal Estimation (63 pages)
 Introduction
 Signal Representation via Wavelets
 Signal Estimation via Thresholding
 Stochastic Signal Estimation via Scaling
 Stochastic Signal Estimation via Shrinkage
 IID Gaussian Wavelet Coefficients
 Uncorrelated NonGaussian Wavelet Coefficients
 Correlated Gaussian Wavelet Coefficients
 Clustering and Persistence of Wavelet Coefficients
 Summary
 Exercises

Chapter 11: Wavelet Analysis of Finite Energy Signals (43 pages)
 Introduction
 Translation and Dilation
 Scaling Functions and Approximation Spaces
 Approximation of Finite Energy Signals
 TwoScale Relationships for Scaling Functions
 Scaling Functions and Scaling Filters
 Wavelet Functions and Detail Spaces
 Wavelet Functions and Wavelet Filters
 Multiresolution Analysis of Finite Energy Signals
 Vanishing Moments
 Spectral Factorization and Filter Coefficients
 Summary
 Exercises
 Appendix: Answers to Embedded Exercises (51 pages)
 References (13 pages)
 Author Index (4 pages)
 Subject Index (26 pages)
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