How to determine time lag by using xcorr ?

Hello everyone,

I am trying to determine the time lag between two signals delayed with the function xcorr but I'm not sure I'm doing it the right way.

Here's the code that i am using:

[cor,lag]=xcorr(SIGNAL,SIGNAL2);
[~,I]=max(abs(cor));
lagDiff=lag(I);  
Time_Diff=lagDiff*DT;

Where DT is the sampling time in sec,

I am not sure si Time_Diff is giving the real time Lag between the two signals.

Answer 1

[David Goodmanson]

Hello Linda,

the idea is basically correct, but for two signals of the same length, zero lag is at the center of the resulting xcorr array. The following example shows two identical waveforms with a realative time shift of 4 sec, and the xcorr plot has a peak at the right location.

delt = 1e-3;
t = (-20e3:20e3)*delt;
[tt n1] = meshgrid(t,rand(1,16));
[~, n2] = meshgrid(t,rand(1,16));
y1 = sum(exp(-((tt    ).^2/10)).*(cos(77*(tt    ).*n1 + 2*pi*n2)));
tsh = 4;                            % time shift for y2
y2 = sum(exp(-((tt-tsh).^2/10)).*(cos(77*(tt-tsh).*n1 + 2*pi*n2)));

tcorr = (-40e3:40e3)*delt;              % time array for correlation function

figure(1)
plot(t,y1,t,y2)
grid on
figure(2)
plot(tcorr,xcorr(y2,y1))
grid on

[Linda]

thank you for your response but I don't really see the link between this and what i am trying to do (define the time lag between two signals of the same length) do I have to define a time array for correlation function as you did ?

What I did for the moment is to define LagDiff which refers to a lag expressed in terms of number of samples, and what I want to do is to expressed it as a real time Lag. To make it ( I m not sure), I have multiplied this LagDiff by the sampling period DT as :

Time_Diff=lagDiff*DT;

[David Goodmanson]

Hi LInda,

It's really the same thing. Using a time array I constructed two signals, where one of them lags the other by 4 sec. So in line with how you are looking at this, suppose we plot each function in terms of its array index, and look at xcorr in terms of its array index

delt = 1e-3;
t = (-20e3:20e3)*delt;
[tt n1] = meshgrid(t,rand(1,16));
[~, n2] = meshgrid(t,rand(1,16));
y1 = sum(exp(-((tt    ).^2/10)).*(cos(77*(tt    ).*n1 + 2*pi*n2)));
tsh = 4;                            % time shift for y2
y2 = sum(exp(-((tt-tsh).^2/10)).*(cos(77*(tt-tsh).*n1 + 2*pi*n2)));
% same up to this point

%tcorr = (-40e3:40e3)*delt;              % time array for correlation function
n = length(y1);
indices = 1:n;
figure(1)
plot(indices,y1,indices,y2)
grid on
indices_corr  = 1:2*n-1;                 % corellation takes 2*n-1 points
figure(2)
plot(indices_corr,xcorr(y2,y1))
grid on

The y1 and t2 arrays happen to have n = 40001 points by constuction, The correlation array has 2*n-1 = 80001 points. For correlation, zero lag is right in the center of this array, which is point 40001.

One way or another you are going to have to find the maximum of xcorr in order to determine the lag. That can be done either by finding the position of the max or by looking at the plot. Zooming in on figure 2 the max is at array point 44001. That differs from the zero lag point by exactly 4000 points. Then in accord with the way you are looking at this, DT = .001 and, 4000*DT = 4 sec.

All I did was come up with a time array that mimics this process, so you can read time delay directly off the plot. Hope this helps.

[Linda]

Thanks a lot!