How do you calculate a correlation function in MATLAB?

I am trying to calculate the correlation function given by

where I sum over all i ("part" in the following). Do I just choose time zero arbitrarily as t1 like in the following? I am not sure how to do this. vbar is calculated separately and is just a constant here..

for t1 = 1:tmax
    for t2 = t1:tmax
        for part = 1:tot_part
            a0(t2-t1,part) = a0(t2-t1,part) + (v(t1,part)+vbar)*(v(t2,part)+vbar)
            n0(t1,part) = (v(t1,part)+vbar) + 1
        end
    end
end

for t = 0:tmax-1
    for part = 1:tot_part
        corr0(t) = corr0(t) + a0(t,part)/n0(t,part)
    end
end

Answer 1

[Hiro Yoshino]

If you want to calculate "auto correlation", see xcorr.

You may need to devide the result by var.

[Hiro Yoshino]

Just a few lines of code server for this problem.

[L'O.G.]

@Hiro Not quite, it's essentially an autocorrelation function with a constant subtracted from each x(t)

[Hiro Yoshino]

so what about using xcorr with a single argument?

You should take a look at the documentation carefully. I would do it like:

x = rand(10,1)

x = 10×1

0.6315 0.4384 0.3091 0.8854 0.2887 0.0139 0.3035 0.0960 0.7033 0.1798

[r,lag] = xcorr(x)

r = 19×1

0.1136 0.5230 0.4245 0.6103 0.8461 0.5727 1.0507 1.0046 1.1730 2.1822

lag = 1×19

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

stem(lag,r/var(x))

[Hiro Yoshino]

Does this make sense to you?

[L'O.G.]

Thanks, yes, it would nice though if it would be possible to understand this without resorting first things first to the xcorr function, which is why I had the clunky for loops in my post.

[Hiro Yoshino]

Totally understood. When I was in school, I didn't realize there had been this function for ages and crafted my own from scratch but good thing about MATLAB is that you can avoid "re-inventing wheels".