How to determine delay between a signal and a truncated shifted version of itself

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Martin Chavez
Martin Chavez on 9 Sep 2016
Commented: Martin Chavez on 9 Sep 2016
Hi guys,
I'm trying to sync two signals of different length. For now, I just use the same signal, truncate it (make some points zero) and shift it on time. I'd like to find the time delay to be able to sync both, but since signals are not equal anymore (because of truncation) I get a wrong value for the delay when using xcorr. Here we have an example code to sync x and y:
close all
% Create example signals
N2 = 10;
N1 = N2*5;
k = 0:200-1;
z = k.*(k>=0 & k<N1);
x = z+ N1*(k>=N1 & (k<=N1+N2)) - 5*(k-N1).*((k>=N1) & (k<=N1+N2)); % original signal
% plot original signal
subplot(2,1,1);
stem(k,x); hold all
Nshift = 0; % Delay between signals (you can play with this parameter)
y = [zeros(1,Nshift), z(1:end-Nshift)]; % create second delayed and truncated signal
stem(k,y); % and plot it
subplot(2,1,2); %plot also sum of products
stem(k,y.*x); hold all
legend(num2str(sum(y.*x)));
% determine max to detect delay and print in legend
[XC,LAGS] = xcorr(x,y); % Correlation
[maxXC,I] = max(abs(XC)); % index for maxima
figure; stem(LAGS,abs(XC)); legend(num2str(LAGS(I)));
Even in the simplest case you have no delay (Nshift=0) you get the wrong estimation (in that case 5 instead of 0). Does anyone have an idea how to solve this problem to get the correct delay?
Regards, Martin

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Answers (1)

Star Strider
Star Strider on 9 Sep 2016
See if the alignsignals function will do what you want. There is a link to the finddelay function at the end of that page, so consider it as well.
  1 Comment
Martin Chavez
Martin Chavez on 9 Sep 2016
Thanks for your answer. I can't test that function since I don't have the toolbox. Still, I don't think this will work because this function bases on finddelay and finddelay uses also correlation. Moreover, the following is also written in the help:
As specified for the finddelay function, the pair of signals need not be exact delayed copies of each other. However, the signals can be successfully aligned only if there is sufficient correlation between them.
Since signals are not equal after truncation, I guess I will run into the same problem.

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