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.
This tutorial was presented during the 1986 training course of the International Pharmaco-EEG Group (IPEG) in Santa Margherita Ligure, Italy. During recent years spectral analysis has been increasingly used in experimental EEG. However, to avoid misinterpretations of results, its limitations must still be carefully considered. The tutorial starts with revisiting the fundamentals of the technique, emphasizes the practical estimation of auto- and cross-spectra, discusses the assumptions underlying the spectral analysis of stochastic processes, and ends with a brief discussion concerning the postprocessing of spectral data
Power and coherence spectra were computed from all-night sleep EEG records in 6 healthy adult subjects. Derivations were from F3, F4, P3, P4, O1, 02, T3, and T4 to the vertex (Cz). Records were conventionally scored into sleep stages. Average power per sleep stage was maximal at frequencies 0.4–6 c/s in stage 4, at 6–10 c/s in either stage 3 or stage 4, at 12–14 c/s in stage 2 and at 14–30 c/s in stage 1. The average power range from highest values in the lowest frequency band to lowest values in the highest frequency band showed marked differences between sleep stages: It was lowest (12–14 dB) in stage 1, followed by stage 2 (20–22 dB), and stage 3 (16–28 dB), and largest in stage 4 (29–32 dB). REM sleep (15–16 sB) was between stage 1 and 2. The waking state showed an average power range of 11–15 dB. Alpha power at 8–10 c/s in occipital and parietal leads was remarkably constant during sleep, i.e. independent of sleep stage. Coherence showed maximal values at 2–8 c/s in REM sleep, at 8–12 c/s in stage 4, at 12–17 c/s in either stage 3 or 4, and at 17–30 c/s again in stage REM. There was significant coherence increase at 2–8 and 17–30 c/s from NREM to REM sleep, most pronounced between parietal to vertex derivations. Overall coherence between both occipital-to-vertex, or between occipital and parietal-to-vertex derivations, was essentially higher than in the other derivations. The results, essentially, give a comprehensive phenomenology of the dynamic spectral structure of all-night sleep EEG. They suggest that the different brain states during sleep (e.g. stage 1 NREM vs. REM) which are associated with different functions (e.g. hypnagogic hallucinations vs. dreams) differ in EEG spectral parameters if coherence is considered. Likewise, they suggest that studies of automatic sleep staging based exclusively on EEG spectral parameters appear promising.
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