Correlation between two differently sized data sets

Assume that I have solved a System with an ODE-Solver. The results [T1,Y1] (time and corresponding solution vector) I obtained for specific tolerances.

Now I have changed the tolerances and have [T2,Y2]. Although the time span for simulation remains the same these data sets have different lengths.

For example these lengths:

T1: 200x1, Y1: 200x3

T2: 500x1, Y2: 500x3

Now i can plot these sets easily for each component of Y into one plot, so I can see the differences. What I would like to do now is calculate the correlation coefficient to see how well these data sets match. My problem is this:

I can only correlate them, if the vectors of Y have the same length. So how do I expand the vector Y1 to match the size of Y2, obviously while keeping the same relation to the times T1 and T2 (which should then actually be the same)?

I tried interp() and resample(), but that does not work for me...

[Walter Roberson]

Please post your interp1() attempt.

[Jan Wingens]

So I have:

T1: 37544x1 and Y1: 37544x14

as well as

T2: 4684x1 and Y2: 4684x1

In order to bring, say the first component of Y2 to a length of 37544 I write:

NewY2_1=interp(Y2(:,1),r)

where r is the factor by which the sampling rate is increased. In my case it should be r=37544/4684=8.015....

However r must be an integer, so this doesn't work.

Then I found resample(): y = resample(x,p,q) resamples the input sequence, x, at p/q times the original sample rate. This would work in my case. But at the end of the sampling strange errors occur. Also it does not resample to my desired length of 7 seconds but to 7.51 or so seconds. I suppose that is beacuse: resample applies an antialiasing FIR lowpass filter to x and compensates for the delay introduced by the filter.

Answer 1

[Walter Roberson]

NewY2 = interp1(T2,Y2,T1);

[Jan Wingens]

Thank you very much, I did not realize that there was interp1(). I just read the entry about interp().