Modern Spectrum Analysis of Time Series: Fast Algorithms and Error Control Techniques, 1st Edition (Hardback) book cover

Modern Spectrum Analysis of Time Series

Fast Algorithms and Error Control Techniques, 1st Edition

By Prabhakar S. Naidu

CRC Press

416 pages

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Hardback: 9780849324642
pub: 1995-10-25

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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


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


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


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


Spectrum Estimation: Data Adaptive Approach

Data Adaptive Approach


Burg Spectrum

Data Matrix and Singular Value Decomposition

Adaptive Subspace


Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General