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<p>Hi Soujatta,</p>
<p><br>
</p>
<p>I hope I understand your question.</p>
<p><br>
</p>
<p>For demeaned data, the covariance is the expected value of sum(xy). For data with finite mean, we have to get the expected value of sum(x-mu(x))*sum(y-mu(y)). Removing the mean and trend doesn't have any impact on the denominators used to compute the unbiased
estimate of E{sum(xy)}. The unbiased covariance estimated between x and y for a given trial is sum(xy)/(N_times-1), where N _times is the number of time points in an epoch. When averaging covariance matrices over multiple trials the denominator becomes N_trs-1.
I hope that helps.</p>
<p><br>
</p>
<p>Best,</p>
<p><br>
</p>
<p>Alexander </p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> fieldtrip-bounces@science.ru.nl <fieldtrip-bounces@science.ru.nl> on behalf of Soujata Borbaruah <s.borbaruah@student.utwente.nl><br>
<b>Sent:</b> Thursday, June 16, 2016 10:19:12 AM<br>
<b>To:</b> fieldtrip, donders<br>
<b>Subject:</b> [FieldTrip] What is the data present in the covariance matrix after using ft_timelockanalysis</font>
<div> </div>
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<div>
<div dir="ltr">Hello,
<div><br>
</div>
<div>I want to calculate the covariance of the data I provide. In the function ft_timelockanalysis there is a portion where the covariance is being normalised over all trials by the total number of samples in all trials. </div>
<div><br>
</div>
<div><br>
</div>
<div>
<div>% normalize the covariance over all trials by the total number of samples in all trials</div>
<div>if strcmp(cfg.covariance, 'yes')</div>
<div> if strcmp(cfg.keeptrials,'yes')</div>
<div> for i=1:ntrial</div>
<div> if strcmp(cfg.removemean, 'yes')</div>
<div> covsig(i,:,:) = covsig(i,:,:) / (numcovsigsamples(i)-1);</div>
<div> else<br>
</div>
<div> covsig(i,:,:) = covsig(i,:,:) / numcovsigsamples(i);</div>
<div> end<br>
</div>
<div> end</div>
<div> else</div>
<div> if strcmp(cfg.removemean, 'yes')</div>
<div> covsig = squeeze(nansum(covsig, 1)) / (sum(numcovsigsamples)-ntrial);</div>
<div> else<br>
</div>
<div> covsig = squeeze(nansum(covsig, 1)) / sum(numcovsigsamples);</div>
<div><br>
</div>
<div> end</div>
<div> end</div>
<div>end</div>
</div>
<div><br>
</div>
<div>Please note that the cfg.removemean was selected as yes. </div>
<div><br>
</div>
<div>Can someone please explain what is the final data present in my covariance matrix? <br>
<br>
<br>
<br>
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