[ari003]

To have a proper understanding I started with a short dataframe where the 2nd column represensts velocity at different time-step collected from a probe (for example). And I m trying to plot the correlation function with time lag.

PHP Code:

time    U
1    10.22
2    10.54
3    10.15
4    10.87
5    10.24
6    10.35
7    10.45
8    10.75
9    10.58
10    10.4 


r(s)=⟨U(t)U(t+S)⟩/⟨⋃(t)^2 ⟩

And the above formula is my auto-correlation function where τ is my time lag.
Now as far my my knowledge it is calculated as follows (explaining with this example).
1. The denominator is just when τ =0. So

<u(1)*u(1)+u(2)*u(2)…….u(10)*u(10)>

In this way we found the mean <u2>.

2. The τ = 0 to 10

For r(0)= <u2>/<u2> =1
For r(1)= <u(1)u(2)+u(2)u(3)……+u(8)u(9)+u(9)u(10)>/ <u2>.

Similarly it will be on till 10 where finally r(10)=0

Now my questions are:-
1. Does this procedure really happen like this?
2. If so then I tried it in MATLAB and it gave results with negative( whereas my U are all positive). How is that possible?

I ve attached a word doc for better understanding of my doubt. Will be really helpful if someone helps.