Problem of finding lag when using xcorr

Hi everyone,

Thank ou for your watching! I have some problem in using xcorr. Basically I have two groups of data, group1 follows the function sin(x) and group2 follows the function sin(x+3/50). The x region is from 0 to 2 and sampling frequency is 100 (201 dots in total). I can see the lags clearly through the function equation and the plot out, but when I try to use the xcorr to find the lags, the maximum always occurs at the center of the output matrix, which means the lag equals to zero. Is there anyway to solve this problem?

I find someone who has the same problem with me, but his data is a group of data close to a mean value, the method mentions in that page doesn'r work in my case.

Here is the link for his problem:https://www.mathworks.com/matlabcentral/answers/431015-cross-correlation-of-two-signal-always-shows-unexpected-0-lag

Thanks for your reading and wish you have a nice day!

Best,

Zhikun

Answer 1

[Daniel M]

Yes, running this gives a max lag at 0. That is indicating that y matches x the best in their current positions. Shifting y by any value will make it agree less. You're expecting to see a lag of 3/50 = 0.06 right? (This is equal to 6 samples).

clearvars
clc
close all

fs = 100;
t = 0:1/fs:2;
x = sin(t);
y = sin(t + 3/50);

[r1,lagsy] = xcorr(x,y);
[mr1,locmaxy] = max(r1);
lagsy(locmaxy)/fs
% ans = 0

y2 = circshift(y,6); % shift it by 6 samples

[r2,lagsy2] = xcorr(x,y2);
[mr2,locmaxy2] = max(r2);
lagsy2(locmaxy2)/fs
% ans = 0

% Plot the results
figure
plot(t,x,t,y,t,y2,'k--')
legend('x','y','y2','location','southeast')

Notice that mr1 > mr2. Look at the plot of y2. It's easy to see that any shift of y would lead to less correlation with x than the original signal.

HOWEVER, if you allow the oscillations to go through one full period, then yes, you get the correct value of 0.06.

clearvars
clc
close all

fs = 100;
t = 0:1/fs:2*pi;
x = sin(t);
y = sin(t + 3/50);

[r1,lagsy] = xcorr(x,y);
[mr1,locmaxy] = max(r1);
lagsy(locmaxy)/fs
% ans = 0.06

[Zhikun Wang]

Hi Daniel,

Thanks for your answer! I know that way can help me to get the correct lags. But the problem is that my actual experimental result can only get the groups of data that close to the segment periods. Do you have any other idea that can solve this problem without the period expansion?

Thanks again for your kind reply!

Best,

Zhikun

[Daniel M]

It depends on how specific your problem is then. Are you really just trying to measure the phase difference between two sinusoids of the same frequency and amplitude? That's very trivial (you could just use asin()), which is why I suspect your actual problem to be more sophisticated than that.

You can detect the phase by using the functions fft() and then angle(). Here is a thread you may find useful. https://www.mathworks.com/matlabcentral/answers/378174-how-to-find-phase-shift-and-do-phase-shift-correction-between-two-signals-in-frequency-domain

Here are some other functions of interest:

https://www.mathworks.com/help/signal/ref/dtw.html

https://www.mathworks.com/help/signal/ref/edr.html

https://www.mathworks.com/help/signal/ref/findsignal.html

I didn't check, but I suspect these functions rely on xcorr internally.

[Zhikun Wang]

Yes. Actually that segment of real data just "looks like" a sin wave but not. What I want to figure out it's the time delay from two diffraction intensity result. I will see the link you attached to figure out if it helps or not. Thanks again for your kindness and wish you have good at the rest of the day!

Best,

Zhikun

[Daniel M]

Well I can't provide a more specific answer unless you ask a more specific question. If you uploaded some data along with some examples of your expected outputs then I can try to help.

Answer 2

[Linas Svilainis]

Yes, essential problem is that signal is sampled wrong. Majority of signal processing techniques assume periodical signal (especially xcorr). Try to make several copies of your signal fragment and put them next to each other-does your real signal looks like this? Probably not.

1.Try to increase the sampling range.

2. Try using subsample delay estimation:

GetTOFfftPhase GetTOFcos(MySignal,RefSignal)

if you will combine 1 and 2 results should be acceptable

[Zhikun Wang]

Thanks for your advice! I will try that to see if it works.

Answer 3

[Linas Svilainis]

Of course, it would be helpfull to increase the record length first, if possible.