How to interpret the following complex demodulation code?

Hi all,

I am still pretty new to MATLAB and using it to analyze EEG data. Following is a code passed on to me which performs complex demodulation on EEG data. However, I am trying to really understand what this code does based on the set paramters so can someone please help me by explaining what exactly is this piece of code doing with my EEG data?

[b, a] = butter(PARAM.cdemod_forder, PARAM.cdemod_filter_lowpass / EEG.srate, 'low');
carArray = exp(-2*pi * li * PARAM.cdemod_freq * (0:size(EEG.data,2) - 1)) / EEG.srate);
x = double(EEG.data(iChan, :, iTrial)) .* carArray;
x = filtfilt(b, a, x);

Following are the paramter info:

PARAM.cdemod_forder = 4

PARAM.cdemod_filter_lowpass = 5

EEG.srate = 250

PARAM.cdemod_freq = 13.5

iChan and iTrial are just variables within a for loop basically the selected channels and trials from the EEG data.

Your help is very much appreciated. Please let me know if the question is not clear or if you require further information on it.

Thanks,

Mo

Answer 1

[dfl]

Hi Mo, here's what is happening:

line 1 makes a butterworth lowpass filter

line 2 makes a complex sinusoid at the demodulation frequency

line 3 multiplies the EEG signal with the complex sinusoid (multiplication in the time domain is convultion in the frequency domain... resulting in a frequency shift). This shifts the spectral components at the demodulation frequency down to zero (DC).

line 4 uses the demodulation filter (from line 1) to lowpass filter the signal (removing the high frequency components) around the positive and negative frequencies near the band edge.

The filtfilt command does forward/backward filtering, which ends up filtering twice (essentially doubling the filter order) but ends up with no phase shift.