Cross correlation to compute delay between two lines does not work

Question

I have zero experience with signal processing, and I am stuck in what I believe to be a very simple problem. I am trying to use the xcorr in matlab to find delay between two signals. The signals are basically two time-series that look like two lines:

I am using the function xcorr in matlab. If I try to run

[acor,lag] = xcorr(Y,X);
[~,I] = max(abs(acor));
lagDiff = lag(I);
timeDiff = lagDiff/Fs

where Y and X are the two lines I get a delay (timeDiff) equal to zero. Which is obviously not true. But if I run the same code on two delayed sinusoids like these:

I get the correct delay (-0.5).

I don't get why with two lines I can't get the right delay. What am I missing?

Here the entire code:

example_sig = 'sinusoid';
% example_sig = 'line';
switch example_sig
    case 'sinusoid'

        Fs = 10;

        t1 = (0:100-1)/Fs;
        t2 = (0:100-1)/Fs;


        X = sin(t1);
        Y= sin(t2+0.5);

    case 'line'
        Fs = 10;

        t1 = (0:100-1)/Fs;
        t2 = (0:100-1)/Fs;

        X = 1 + 4*t1;
        Y = 1 + 4*(t2-2);

end 

[acor,lag] = xcorr(Y,X);

[~,I] = max(abs(acor));
lagDiff = lag(I);
timeDiff = lagDiff/Fs
figure
plot(lag,acor)
a3 = gca;
% a3.XTick = sort([-3000:1000:3000 lagDiff]);

% figure, plot(X),hold on, plot(Y), plot(inc_surf(indx0-100+delay+1:indx))
figure, plot(X),hold on, plot(Y)

Thank you in advance!

Answer 1

If you plot the cross correlation instead of taking the maximum, then I expect you'd see the problem.

The cause is that your signals aren't centered around zero. They have an offset. The cross correlation of two signals with an offset is a kind of triangle looking thing with the peak at zero.

As far as the cross correlation is concerned, your two signal are identical except for the offset - and you normally use a high pass filter or subtract the average of the data points to remove the offset.

Your result is correct and to be expected, it's just not what you wanted.