Modern Spectrum Analysis of Time Series: Fast Algorithms and Error Control Techniques
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Summary
Spectrum analysis can be considered as a topic in statistics as well as a topic in digital signal processing (DSP). This book takes a middle course by emphasizing the time series models and their impact on spectrum analysis.
The text begins with elements of probability theory and goes on to introduce the theory of stationary stochastic processes. The depth of coverage is extensive. Many topics of concern to spectral characterization of Gaussian and non-Gaussian time series, scalar and vector time series are covered. A section is devoted to the emerging areas of non-stationary and cyclostationary time series.
The book is organized more as a textbook than a reference book. Each chapter includes many examples to illustrate the concepts described. Several exercises are included at the end of each chapter. The level is appropriate for graduate and research students.
Table of Contents
Stochastic Characterization of Time Series
Time Series as a Stochastic Process
A Review of Stochastic Process
Stationary Stochastic Process: Second Order
Spectral Representation
Stationary Stochastic Process: Third Order
Vector Stochastic Process
Nonstationary Process
Exercises
Mathematical Models of Time Series
Time Series Models
Filter Model
Discrete Fourier Transform (DFT)
Parametric Models: MA/AR
Parametric Models: ARMA
Parametric Bispectral Model
Deterministic Chaos
Exercises
Spectrum Estimation: Low Resolution Methods
An Overview
Covariance Function
Estimation of Spectrum and Cross-Spectrum
Estimation of Coherence
Spectrum of Window Function
Estimation of Bicovariance and Bispectrum
Estimation of Time Varying Spectrum
Exercises
Spectrum Estimation: High Resolution Methods
An Overview
Maximum Likelihood (ML) Spectrum
Maximum Entropy (ME) Spectrum
Parametric Spectrum
Subspace Methods
Nonlinear Transformation
Extrapolation of Band Limited Time Series
Exercises
Spectrum Estimation: Data Adaptive Approach
Data Adaptive Approach
Prewhitening
Burg Spectrum
Data Matrix and Singular Value Decomposition
Adaptive Subspace
Exercises
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