Analysis of the interrelations between frequency bands of the EEG by means of the bispectrum a preliminary study

Abstract

The more or less random character of spontaneous EEG activity justifies the application of mathematical models developed in time series analysis. Among these methods numerical spectral analysis has proved to be a powerful tool for analysing and quantifying EEG data, especially background activity. The spectral decomposition of an EEG sample into its frequency components, giving (after appropriate smoothing) the power spectrum, provides complete information about the statistical properties of an EEG sample only under the assumption that the underlying process is stationary and Gaussian. If this assumption is violated, only partial information is obtained and higher order moments should be investigated. Whereas by the power spectrum the second central moment is analysed in detail, the bispectrum allows a detailed analysis of the third central moment, which is influenced either by interrelations between frequency components or by non-stationarity of the signal. The bispectrum may therefore display important additional information about the properties of a stochastic signal like the EEG. In the stationary case this information is of great value in the investigation of phase-locking between different frequency bands, e.g., between alpha and beta activities. In addition, some new insights into the non-linear aspects of the EEG generating process might be expected. Bispectra of artificial signals are shown in order to explain the basic aspects of this extension of spectral analysis and selected examples of EEG bispectra demonstrate the interesting possibilities which this method offers in the field of EEG analysis.