Spectral analysis and its applications
Aims and means in time series analysis; Fourier analysis; probability theory; Introduction to statistical inference; Introduction to time series analysis; The spectrum; Examples of univariate spectral analysis; The cross correlation function and cross spectrum; Estimation of cross spectra; Estimation of frequency response functions; Multivariate spectral analysis.
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AIMS AND MEANS IN TIME SERIES ANALYSIS
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acvf approximately autocovariance function autoregressive process bandwidth bias bivariate coherency spectrum computed confidence interval corresponding covariance function covariance matrix cross amplitude cross correlation cross covariance cross spectrum Cxx(f data of Figure degrees of freedom delta function derived described discrete equation example filter Fourier transform frequency response frequency response function gain and phase Hence impulse response input least squares likelihood function linear process linear system marginal likelihood mean square error multivariate Normal pdf obtained output parameters Parzen window peak phase spectrum plotted properties random variables residual rv's rxx(f sample space sample spectrum sampling distribution sampling distribution approach second-order shown in Figure shown in Section shows smoothed spectral estimators spectral analysis spectral estimators spectral window squared coherency statistical stochastic process sum of squares Table tends to infinity theoretical theory truncation point uncorrelated values white noise Xu X2 zero