zero lag when using xcorr on 2 near-similar, shifted timeseries

Hi all,

I try to cross correlate two signals which are from 2 different instruments.

I use xcorr to find the lag between signal A (blue) and signal B (red). However, I keep getting 0 lag which should not be the case. As can be seen from the figure, the lag should be around ~ 110 where it gives a quit nice fit.

Attached are the signals A & B.

I'm using xcorr as the following:

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

Thanks in advance for you help.

Kind regards,

Jos

[Adam Danz]

load A.mat
whos

  Name              Size             Bytes  Class     Attributes

  PIV_mag_test      1x623             2492  single              
  ans               1x30                60  char                
  cmdout            1x33                66  char                

load B.mat
whos

  Name              Size             Bytes  Class     Attributes

  ADV_sampled       1x623             4984  double              
  PIV_mag_test      1x623             2492  single              
  ans               1x30                60  char                
  cmdout            1x33                66  char                

Which variables are A and which are B?

[Jos Muller]

Hi Adam,

Thanks for you comment. This was a bit messy from my side. Indeed as below, it is PIV_mag_test for A.mat and ADV_sampled for B.mat.

Sorry for the inconvenience.

Best,

Jos

Answer 1

[dpb]

load A, load B
whos

  Name              Size             Bytes  Class     Attributes

  ADV_sampled       1x623             4984  double              
  PIV_mag_test      1x623             2492  single              
  ans               1x30                60  char                
  cmdout            1x33                66  char                

subplot(2,1,1)
plot(ADV_sampled)
hold on
plot(PIV_mag_test)
xlim([300 inf])
subplot(2,1,2)
plot(ADV_sampled)
hold on
plot(PIV_mag_test)
xlim([1 200])
legend('B','A','location','northwest')

The two are perfectly in phase over almost 90% of the total signal length; that the lag between the two is zero is what I would expect. From about sample 80 on, the peaks align almost perfectly.

Only the ramp up stage of B before any regular fluctuating behavior was achieved won't correlate highly, and there there simply isnt any significant similar behavior yet to even try to compare. I suppose B is somehow driven by A and you're trying to find where the two become phase locked, maybe?

The only area that appears to have a small phase shift is that A seems to lag B some in that initial startup section between 100 and 200+ samples, but other than within that small segment of the overall signal, there's simply so little lag that a lag shift by even one sample would appear to make the overall worse -- which is what xcorr() is telling you.

A subset section might show something...

[Jos Muller]

Hi DPB,

Thanks for your comment and effort.

The signals are from 2 different instruments measuring the same sinusodial pattern and then made absolute. There is a spinup time indeed. Signal A was started logging a bit earlier (indeed ~100 samples) than signal B. So indeed i'm looking for this lag of signal A to B of expected ~100 samples.

Should I try cross-correlating this spinup period of both signals instead of the full series, to help xcorr finding a more distinct difference?

Best,

Jos

[dpb]

There simply isn't a phase lag to speak of anywhere there's a defined sinsoidal component so I don't think correlation is the tool that will help.

Making the best first match to the amplitude of the initial peak in A by subsequent peaks in B, might serve to give a way to align them; that might then need a bit of a lag adjustment after the initial guess.

With some creativity, it should be possible to use lsqnonlin to minimize the error between the two traces by adjusting the offset of B relative to A as the parameter to solve for -- the error function would have to account for the changing length for B as it is shifted in some manner; updating the indices to match lengths between the two as pieces are lopped off the front of B.