Initial EEG feature extraction, spectra, and synthesis.

I have only just begun to study EEG signal features using the 2d frequency-delay spectrum and individual feature extraction. As noted previously, since the EEG is non-periodic and a generally more complicated signal than the EKG, it is expected that the analysis of this signal will also be more involved. Nevertheless, some of the same analyses can be performed immediately. Below are frequency-delay spectra of two similar EEG signals, with the scale of each image set high enough to posterize the plot into two colors which show the location and frequency distributions of several features.

At present, about all that can be said for the qualitative differences between these two spectra is that one appears simpler and more regular:

and the other appears more complicated, both in terms of number of features and in branching phenomena:

although the signals themselves appear very similar. The ability to read more quantitative information from these spectra is obviously necessary. Several ideas come to mind, but they will have to wait for another installment of this research.

Two aspects of these plots that are readily apparent are (1) that there appears to be much more prevalent bifurcation of features into additional features at both lower and higher frequencies than there was in the EKG, and (2) that there does not appear to be a convergent time center or "trigger" which is asymptotic to all features as there was in the EKG, although there do appear to be clusters of features which do converge to a common center.

Here is the spectrum of a single feature extracted from the 2d EEG spectrum. This feature was chosen at random and is indicated in yellow. Note that since the EEG signal is not periodic, the upper and lower branches of the spectrum indicated in yellow may not actually represent the same feature. However, the frequency-delay analysis component makes the input signal periodic.

Note that, like the individual EKG features, the spectrum magnitude is again that of a band-pass filter, and the phase is completely linear.

Here is a component software system which can be used to extract individual feature spectra from an EEG signal, create a Hermitian filter from a spectrum, and then invert the filter response to generate the feature in the time domain, independently of the rest of the signal.

Shown below is the 2d frequency-delay spectrum of the same signal as above, but this time from 0-128 Hz (the Nyquist limit for this signal). The spectrum of one feature has been extracted and used to create a Hermitian filter. That filter is then inverted by the inverse Fourier transform to generate the feature itself, in its correct location within the overall signal.

Note that in this case, the actual spectrum of the feature has been used to synthesize the feature in the time domain. This spectrum has not been modeled by a mathematical function. The entire signal is the superposition of all individual features. As with the EKG, it may be possible to extract a finite and small number of primary features and to use these to reconstruct the signal to a good degree of accuracy. Although the brain is a much more complicated dynamic system than the heart, it still may be the case that a relatively small number of cononical features, or "principle modes", may be used to accurately reflect the enormous (but finite) variation in the overall EEG signal.

©Copyright Sky Coyote, 2001.