Application of the 2d frequency/phase and frequency/delay spectra to EEG signals.

The previous frequency/phase and frequency/delay analyses can be applied to EEG data as well. However, one fact that aggravates the difficulty of analyzing the EEG is that it is not periodic. Thus it should have no discrete or finite Fourier series representation. And, although it may consist of a finite and small number of other components, they may not be constant in time, nor may they be the result of the responses of a simple arrangement of filters.

Here is a component software system which computes the frequency-phase and frequency-delay convolution arrays as in the previous EKG analyses.

Here is a subset of some occipital EEG data (I forget which side, but I believe it is bipolar data) which was recorded a few months ago. The data is arranged into 100 records (epochs) of 1 sec each acquired at 256 Hz. The EEG electronics have an active 4th order lowpass filter at 32 Hz, so there is no aliasing and the spectrum is flat almost to that frequency.

Here are some example data sets and their f/p f/d 2d spectra. The left image shows the response to a continuous sine wave at the frequency (horizontal axis, 0-32 Hz) and phase (vertical axis from top, 0-2 pi) indicated by the color of that point. Frequency components and their phase responses appear as vertical lines in the image. The right image shows the response to a single sine pulse at a specific frequency and delay. The color of the point shows the response to both a frequency and a location within the signal. In both plots the strongest effects are seen as the endpoint colors, here red (+) and blue (-).

Note that while the differences in the signal may appear subtle, they are readily visible in the frequency-phase plot. Although some differences are also apparent in the frequency-delay plot, they require further research. Some analysis of a feature plot is the subject of the next page.

1. Strong single-line alpha band, slight 2x harmonic.

2. Alpha with 2x harmonic.

3. Multi-line alpha.

4. No alpha.

5. A slow wave at about 2 Hz, with a little alpha.

6. Two slow waves at about 2 and 4 Hz, with a little alpha and harmonic.

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