cross-spectrum to cross-correlogram

Jasper Poort j.poort at NIN.KNAW.NL
Mon Sep 29 09:54:50 CEST 2008

```Dear all,

I'd like to convert the cross-spectrum to a cross-correlogram. My first
approach would be simply to ifft the output of freqanalysis with output
option 'complex'.

However, I have difficulty understanding the result of this procedure and in
particular how I can get output comparable to the matlab function xcorr
using FieldTrip. Below I inserted a small test script.

Best, Jasper

% using the fake data from the FieldTrip tutorial 'Fourier analysis of

% oscillatory power and coherence'

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%get many repetitions of two signals with somewhat consistent phase
difference

clear all

close all

frq = 10; % Hz

len = 1; % seconds

smpfrq = 100; % Hz

numrpt = 1000;

circulran = mod(randn(2.*numrpt,2).*phsspreadfac + pi, 2.* pi) - pi;

ranphs = circulran ./ (2 .* pi);

phsdif = 45 ./ 360;

noifac = 1./50;

for rptlop = 1:numrpt

wav(:,rptlop,1) =
sin(((0:(len.*smpfrq-1))./(len.*smpfrq).*(frq.*2.*pi))+(ranphs(rptlop,1).*2.
*pi)) + ...

randn(1,len.*smpfrq).*noifac;

wav(:,rptlop,2) =
sin(((0:(len.*smpfrq-1))./(len.*smpfrq).*(frq.*2.*pi))+((ranphs(rptlop,2)+ph
sdif).*2.*pi)) + ...

randn(1,len.*smpfrq).*noifac;

end

% get the FFT of the waves

for rptlop = 1:numrpt

fftwav(:,rptlop,1) = fft(wav(:,rptlop,1));

fftwav(:,rptlop,2) = fft(wav(:,rptlop,2));

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% make FieldTrip structure

dum.label   = {'1','2'};

dum.fsample = smpfrq;

for i=1:size(wav,2), % for every trial

dum.trial{i}=squeeze(wav(:,i,:))';

dum.time{i} =[0:(len.*smpfrq-1)]./smpfrq;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%fft:

cfg.method     = 'mtmfft';

cfg.output     = 'fourier';

cfg.taper      = 'hanning';

cfg.tapsmofrq  = 1;

[freq] = freqanalysis(cfg, dum)

% cross-spectrum

CS=freq.fourierspctrm(:,1,:).*conj(freq.fourierspctrm(:,2,:));

y = real((squeeze(mean(CS))));

figure;plot(y)

% inverse fft of cross-spectrum

y = real(ifft(squeeze(mean(CS))));

figure;plot(y)

% compare to cross-correlation function

[c,lags] = xcorr(mean(squeeze(wav(:,:,1)),2),mean(squeeze(wav(:,:,2)),2));

figure;plot(lags,c)

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