MATLAB: Time delay – Cross Correlation Situation

cross correlationtime delay

Hi everyone…

I'm trying to calculate time delay using cross correlation but i don't know why i'm having this problem:

a=rand(1,10); %random excitation

x1=[a zeros(1,90)]; %Input signal

x2=[zeros(1,90) 0.8.*a]; %Output signal is a delayed version of x1 attenuated

Delay is equal to 90? right?

Well i should be able to calculate this delay from xc=xcorr(x1,x2);

but once i do this the peak is at xc(10) instead of be positioned at xc(190) now when i do xc=xcorr(x2,x1) peak is right positioned.

I don't know if I made myself clear, but i think that xc=xcorr(x1,x2) should be the correct way to do it….

Please help me here…

Best Answer

The order basically determines which one is the reference, but you need to set your lag right. The delay between the two is basically 90, so one will give you 90 and the other one is -90. Try the following:

[xc,lags] = xcorr(x2,x1);
plot(lags,xc)
[xc,lags] = xcorr(x1,x2);
plot(lags,xc)

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MATLAB: Delay using Cross correlation

The output of xcorr is an array of values of how one array is similar to the other. The maximum value is when two arrays match the most. Find the place (position) of the maximum value in the array (you can look it up from the variable editor, or use built-in functions such as 'find' and 'max', I don't remember exactly). So, if your max value is at position 25, it means that the delay is 25. Also, I am not sure if it matters, but make sure to feed the xcorr function, so the shorter array slides against longer (at least it make sense analytically). Not sure if this will work, but the idea is here:

cor=xcorr(shortArray,longArray);
[~,index]=max(cor);

where 'index' should be the position of the max value as well as the delay index. So, first 25 values must be skipped from the longer array

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Do you have the Signal Processing Toolbox? If so, you can use xcorr()

I'll give you an example

load mtlb;
[xc,lags] = xcorr(mtlb,100,'coef');

xc above is 201 samples long with the autocorrelation out to lags of +/- 100 (plus 0)

You can just extract the positive lags with

stem(lags(101:end),xc(101:end))

Best Answer

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