digital signal processing problem Okay, so I am trying to address a biological problem here. I have asked a variant of this question here, but I was not able to get to solving it. 

The question:

Four objects are vibrating constantly with some variable frequency and amplitude. I have the X-Y coordinates of the objects w.r.t time. Now, I want to find if there is any correlation between the objects movements. 

Also, if there is any correlation between the movement of an object with itself w.r.t time.

I am not sure what to do, I have absolutely no idea about the mathematics involved, but can try to understand what needs to be done.

Thanks!
A
Since you have the x/y position for each object it should be fairly straightforward.  Call the position of each $p_1(t)$ through $p_4(t)$.  Subtract the mean from all of them since it sounds like you only care about their movement, not their position.

Once you have done that it should be a fairly simple matter of cross-correlating the position functions.  If the vibration frequencies don't change with time you will only get a strong cross-correlation if the vibration frequencies of the two objects are either the same or quite close to each other.