Spectral Analysis and Its ApplicationsAims 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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a₁ acvf approximately bandwidth bias bivariate coherency spectrum computed confidence interval corresponding covariance function covariance matrix cross amplitude cross correlation cross covariance cross spectrum cxx(u degrees of freedom delta function derived described discrete equations example filter Fourier transform frequency response frequency response function fx(x gain and phase given 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 sample space sample spectrum sampling distribution sampling distribution approach shown in Figure shown in Section smoothed spectral estimators spectral analysis spectral estimators spectral window squared coherency statistical stochastic process Table tends to infinity theoretical truncation point Txx(f u₁ uncorrelated values variance white noise X₁ X₁(t Y₁ Yxx(u Z₁ zero