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matlabpartialfaultcross-correlation

Matlab xcorr giving different values for different implementations of cross-correlation

I am trying to perform a cross-correlation but noticed that performing this in two different ways results in slightly different results.

I have a vector with some spikes ('dual_spikes') and I want to cross-correlate this with 'dips' (using xcorr in Matlab).

I noticed a difference when I perform this in two different ways:

  • perform an xcorr as normal with 'dual_spikes'
  • perform an xcorr with each individual spike, add them together, and normalise.

I do not know why there should be a difference. Use the following function below for illustration.

function [] = xcorr_fault()

dual_spikes = [zeros(1,200),ones(1,200),zeros(1,400),ones(1,100),zeros(1,100)];

dips = 1-[zeros(1,400),ones(1,1),zeros(1,599)];
plot(dips)

single_spike_1 = [zeros(1,200),ones(1,200),zeros(1,600)];
single_spike_2 = [zeros(1,800),ones(1,100),zeros(1,100)];

xcorr_dual = xcorr_div(dual_spikes,dips);
xcorr_single1 = xcorr_div(single_spike_1,dips);
xcorr_single2 = xcorr_div(single_spike_2,dips);

xcorr_single_all = (xcorr_single1+xcorr_single2)/max(xcorr_single1+xcorr_single2);
xcorr_dual_norm = xcorr_dual/max(xcorr_dual);

figure(1)
clf
hold all
plot(xcorr_dual_norm)
plot(xcorr_single_all)
legend('Single xcorr','xcorr with individual spikes')


function [xcorr_norm] = xcorr_div(lines,signal)
    xcorr_signal = xcorr(signal,lines,'none');
    xcorr_signal(xcorr_signal<1e-13) = NaN;
    xcorr_bg = xcorr(ones(1,length(signal)),lines,'none');
    xcorr_norm = xcorr_signal ./ xcorr_bg;
    xcorr_norm(isnan(xcorr_norm)) = 1;

Note, the xcorr signal must have a 'background' (bg) divided so only the dips are found. This happens in 'xcorr_div'.

IMG

Solution

  • Your function xcorr_div computes cross-correlation, then divides the result with the correlation with a uniform signal. The result is some sort of normalized cross-correlation (not the standard definition) that is not linear. Thus, you should not expect that the sum of the result is the result of the sum.

    If you want to be able to get the same result both ways, output both xcorr_signal and xcorr_norm from xcorr_div, then do the sum on those two outputs then divide.