BandPower of EEG Signal from PSD
sumit
India
Hello All,
Iam looking for a general concept to understand how to calculate the BandPower of EEG Signal from it's PSD? Should I just take the simple average of a particular frequency interval (eg. 1-4 Hz) by summing up all the power values at their respective frequency bins and divide by number of frequency bins in that particular band? Is there any other specific formula? I was going through the OpenBCI code & I found that a simple average formula(Total uV value/count) is used for calculating average bandpower of alpha,theta.etc.
Comments
Yes, it is the average of the sum of absolute value of the data points divided by N, the number of data points. The absolute value is so that for example 20 data points that are -10 and 10 points that are 10 do not result in an average of 0.
I should clarify this-- usually the band power is done by filtering the raw signal with a bandpass filter and doing the average of absolute value of the filtered data.
From the PSD, you need the integral of the PSD over that interval, so you would get a weighted average of the signal bins, weighted by the width of each interval. If each interval is 1, the weighting is just 1 though.
Hi Billh,
Thanks for your reply. So in case of PSD I should take the Integral of the interval. Let us say I have frequency Bin Resolution of 0.25 Hz. That means my 4th bin no. corresponds to 1 HZ , then 8th Bin Number will correspond to 2 Hz and similarly 12th Bin 3 Hz ,16th bin 4 Hz. Now, Should I consider the power value at only these 4 frequency Bins and calculate the integral OR I need to consider all the power values of 1-16th Bins?
Also, my understanding of Integration is that summation of all the values of the interval is multiplied by the difference of last bin value & first bin value of the interval. Is this correct?
One complicating factor is that the PSD amplitude is proportional to the square of the average signal, because it goes with the energy of the signal which goes up as the square of the amplitude. Are you looking for an average power or an average amplitude?
https://en.wikipedia.org/wiki/Spectral_density#Properties
Iam looking for average Power represented in uV^2/Hz units.
Then I believe you want the area under the curve of the PSD you have over the frequency interval, divided by the overall frequency interval, which can be calculated as a weighted average.