Spectral analysis for electroencephalograms: mathematical determination of neurophysiological relationships from...

Spectral analysis is a mathematical method which contains and generalizes frequency analysis. The form of spectral analysis most applicable to EEG is tutorially presented, using both algebraic formulae and four simplified illustrative examples. The examples are each converted into an autocorrelogram and auto-spectrogram, functions whose graphic presentation clarifies the structure of each example, partly by emphasizing regular at the expense of irregular components, partly by analyzing the intensity of regular activity into components at each frequency. Then the formulae for cross-correlograms and cross-spectrograms are presented, and illustrated by converting pairs of examples into functions which clarify their interrelationships. Not only are the advantages of auto-spectrograms retained by cross-spectrograms, but they also emphasize activity shared between two traces, and include the mean phase angle relating such shared activity, at each frequency. The coherence function and transfer function, calculated next, are the analogs of correlation coefficient and regression coefficient. The coherence function is applied not only to calculate the "quantity of interdependence" between pairs of illustrative examples, but also to supply probable bounds on the other calculated relationships. Finally, discussion of the assumptions underlying spectral analysis prepares the method for application to actual EEG, given in preceding papers.