Modern Spectrum Analysis of Time Series: Fast Algorithms and Error Control Techniques
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.
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ARMA model assumed autocorrelation function backward prediction errors bandwidth bicovariance bispectrum chaotic component computed consider correlation covariance function covariance matrix cross entropy Cx(l Cx(q Cx(T data vectors defined DFT coefficients diagonal dimension discrete eigenvalues eigenvectors End of Example equal evaluated expressed extended covariance matrix extrapolation finite Fourier transform frequency Gaussian given hence IEEE IEEE Trans input inside the unit lags linear matrix form method minimum phase ML spectrum non-Gaussian nonlinear Note obtain output parameters poles polynomial probability density function Proc properties random sinusoids random variable result s-plane samples segments sequence shown in Figure spectral estimate spectral matrix spectral peak spectral representation spectrum analysis stationary process stationary stochastic process STFT subspace Sx(co time-frequency time-varying transfer function uncorrelated unit circle variance Welch method white noise white noise process window function WV distribution x(co z-transform zero mean