Multichannel Systems NeuroExplorer - Manual (Page 89)

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intervals.
For each interval:
The rate histogram is calculated.
The histogram is detrended (its linear regression is subtracted)
The Hann window w[i] = (1 - cos(2*PI*i/(NumBer_Of_Bins-1)))/2
is applied to the histogram.
FFT of the result is calculated.
Raw power spectrum is formed from the FFT.
Spectral Densities for Continuous Variables
If Maximum_Frequency = M and Number_of_Frequency_Values = N, we need to calculate the
spectrum for frequency values 0, M/N, 2*M/N, ..., M.
For a continuous variable with digitizing frequency F, a standard power spectrum with K values in the
FFT transform would produce the spectrum values for frequencies 0, F/K, 2*F/K, ..., F/2.
If a continuous variable digitizing frequency F equals to Maximum_Frequency*2, we can set K =
Number_of_Frequency_Values*2 and calculate the standard power spectrum to get the spectrum
values for the desired frequencies. That is, in the algorithm described above, instead of rate
histogram we simply use continuous variable values in milliVolts.
If a continuous variable digitizing frequency is not equal to Maximum_Frequency*2, we cannot
directly calculate the spectrum for the specified frequencies. Instead, we find a value K such that the
frequency step for continuous variable spectrum is less than the specified step (i.e. F/K < M/N, so that
we should get a more detailed spectrum than specified) and calculate the spectrum for this value of
K. Then, we resample the resulting spectrum to get the spectrum values for the specified frequencies.
Normalization
If Normalization is Raw PSD, the power spectrum is normalized so that the sum of all the spectrum
values equals to the mean squared value of the rate histogram.
If Normalization is % of Total PSD, the power spectrum is normalized so that the sum of all the
spectrum values equals 100.
If Normalization is Log of PSD, the power spectrum is calculated using the formula:
power_spectrum[i] = 10.*log10(raw_spectrum[i])
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