Spectral analysis of EEG's by autoregressive decomposition of time series

Abstract

A technique for scalar and multidimensional spectral analysis based on the autoregressive representation of the observed data records is presented and illustrated. In an autoregressive representation the observed data set is regressed on its own past history. This results in a formula that expresses the observed data as the output of a linear filter excited by an uncorrelated sequence (“discrete white noise”). Energy spectral densities, transfer functions, and coherences are computed from the autoregressive formula. The results of this technique are compared with the older windowed periodogram methods of spectral analysis. Two potential advantages over the latter methods are observed. For spectral estimates of comparable statistical performance, the autoregressive method analysis appear smoother and easier to interpret than the older windowed periodogram analysis. Also, in contrast with the expertise required to apply the windowed periodogram analysis, use of the autoregressive representation spectral analysis method appears to require little or no subjective judgment.