Here is an example of using the component software to extract an alpha band signal from the FIFO containing 30 seconds of recorded EEG data which is shown at the end of the simple EEG page. In this example, a slider is used to index through the set of 30 one second EEG data records one at a time and send these to a Fourier filter. This Fourier filter performs a complete DFT (using a semi-open range of [0, 2 Pi)) on the input signal and multiplies it by a narrow Gaussian band-pass filter centered at 11 Hz before perfoming an inverse DFT to reconstruct the alpha filtered signal. This signal is then accumulated in another FIFO for further analysis and display.
Here is the complete band-pass filter used to extract the alpha signal. Note that this filter is magnitude only, and does not affect the phase of the signal.
Here is a detail of the band-pass filter comparing it to the spectrum average of the input dataset. The shape of the filter was chosen so as to closely approximate the alpha band peak in the average spectrum. The filter is centered at 11 Hz, has a base width of +/- 5 Hz, half max width of about +/- 1.8 Hz, and -3db width of about +/- 1.2 Hz.
Here is a comparison of the original input data set and the extracted alpha signal. Each plot line is one second of data at 256 samples/sec. The most recent data is at the top of each plot.
(Click for larger image)
Here is an example of using the component software to estimate the time varying strength of the extracted alpha signal. In this example, the absolute value of each extracted alpha record of data is integrated to produce a single number indicating the area under the alpha signal curve without regard to sign. These values are then accumulated in another FIFO and displayed as a graph. In the plot, the integral of the most recent data record is at the left.
Another way to estimate the strength of the alpha signal is to compare the integral of the alpha band spectrum with that of the entire spectrum (in this case, from 0-32 Hz). Here is a component example which performs this analysis. A slider is used to index through each of the spectrum records for the original input dataset. Two integrals are then performed on each spectrum record: one for the entire 0-32 Hz range, and one for the alpha band from 8-14 Hz. The ratio of the alpha band integral to the full integral is then an estimate of the alpha signal strength within that particular second of recorded EEG data. Again, the results are plotted as a graph with the most recent data at the left. Note that a downsampling of 2x is used to filter the results, since the two integral paths of the component flow diagram produce two data points for each record. Downsampling throws away the spurious intermediate results.
Each point of the resulting strength plot is a percentage of the alpha band strength with respect to the entire signal spectrum (in this case, from about 20-40%). Note that this result is confirmed by the simple ratio of the maximum alpha signal magnitude (~0.09 VPP) to that of the maximum entire signal magnitude (~0.22 VPP), or about 41%, as shown in the two side-by-side comparison plots above.
It is clear from both the alpha-extracted signal and the alpha strength analyses that the magnitude of the alpha signal varies over time, waxing and waning. The magnitude of this component also varies over the surface of the scalp as well, as can be seen from the following frames of an animation created by the Prolate1 program at a frequency of 10 Hz:
Several researchers (Haken, Fuchs, etc...) have attempted to model this time/space variation of the alpha signal with Bessel functions or other principle component expansions. Although I do not agree with their techniques or results, it does appear clear that the alpha band signal varies in a non-random and systematic way in both time and space. Presumably this is also true of other components of the overall EEG signal.
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