Time-dependent frequency domain principal components analysis of multichannel non-stationary signals

摘要: High dimensional multi-channel signals often exhibit multi-collinearities. This suggests that such can be decomposed into uncorrelated principal components with possibly lower dimension than of the original signal. A time-localized frequency domain analysis method is proposed for locally stationary behavior. The first step to form a mean square consistent estimate time-varying spectrum matrix by smoothing periodograms using kernel defined on axis whose span selected automatically generalized cross-validation procedure based asymptotic gamma distribution. eigenvalues spectral density are then computed which estimated spectra components. In addition, one may apply formal statistical testing whether weights (components an eigenvector) at particular channel change over time. easily implemented because it only requires fast Fourier transform (FFT) and eigenvalue-eigenvector decomposition routines. An illustration presented brain waves data set recorded during epileptic seizure.