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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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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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