Statistical methods for investigating phase relations in stationary stochastic processes

Harmonically related peaks in the spectrum of a stationary stochastic process may indicate the presence or wave components that are not sine-shaped, i.e., whose Fourier expansions contain phase-locked higher order terms. But the spectrum itself suppresses phase relations, and more refined methods are needed to decide such questions. Moreover, phase relations might also exist outside of the peaks. We discuss proposals for testing the presence of phase relations and for extracting them quantitatively by means of numerical bispectrum analysis, and we derive their statistical properties and compare their relative merits. Applications of these methods to EEG signals will be presented.