Determine time lag from xcorr?

Hello everyone,

I am still trying to interpret the lag/timings of my own data.

My two vectors e.g A and B are both of length 26, since each data point corresponds to my time vector (in seconds)[0.18:0.01:0.43] also containing a total of 26 time points.

If conducting xcorr(A,B) gives me a peak R correlation at a lag e.g 8, then would my actual lag in the timeseries in seconds be 8*0.01 i.e a lag of 80 ms?

Thank you very much!

Answer 1

[Chunru]

doc xcorr for details.

[r,lags] = xcorr(___)

% Find the peak or r
[pk, idx] = max(r);   % for example
lags(idx)/fs          % time lag in sec

[Alba Peris]

If, for example, my data is as following:

clearvars; close all; clc

time = [0.18:0.01:0.43]; %my time vector in seconds i.e every time I have taken a data sample 
%and obtained a corresponding value stored in vectors A and B. 
n =1:26;

A = 0.84.^n; 
B = circshift(A,5);

[c,lags] = xcorr(A,B);

figure; stem(lags,c)

[pk, idx] = max(c);   

timelag = lags(idx); %My lag is -5 

Would now my lag in seconds be -5*0.01 = 0.05 seconds?

I understand my fs for my vector time is 100 in the example I have given?

Sorry for the confusion. Thank you very much.

Answer 2

[Chunru]

circshift with a positive shift number is to delay the signal A to form B.

Now exeamine the defination of xcorr in MATLAB:

Rxy(m)=E{x(n+m)y'(n)}=E{x(n)'y(n−m)},

If the second signal y=B (or m is negative) is advanced, then it match with the first signal. So the tag at peak is negative.

clearvars; close all; clc
time = [0.18:0.01:0.43]; %my time vector in seconds i.e every time I have taken a data sample 
%and obtained a corresponding value stored in vectors A and B. 
n =1:26;
A = 0.84.^n; 
B = circshift(A,5);
plot(time, A, 'r', time, B, 'b')

figure
[c,lags] = xcorr(A,B);
figure; stem(lags,c)

[pk, idx] = max(c);   
timelag = lags(idx) %My lag is -5 

timelag = -5