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Am new to signal processing and was wondering when given two signals, what are the widely used statistical analysis methods to understand the relationship between them?

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What sort of relationship are we talking about? Input-output relationship? In terms of pure statistical similarity, take a look at cross-correlation. – Phonon Sep 15 '11 at 21:02
@Phonon: ya , that is the only thing I found so I wanted to see if anyone was aware of more methods. – blueskin Sep 15 '11 at 21:33
If you could elaborate more on what kinds of signals you are trying to compare and on what their nature is (are they audio, radar medical, etc.?), we will be able to help you further. – Phonon Sep 15 '11 at 21:48
@Phonon, its movement of particles in space. the signal represents a particle's movement over time in space – blueskin Sep 16 '11 at 13:23

There are for instance coherence and (cross)correlation which are commonly used mostly because of their computational/practical attractiveness. If you need to go beyond second order relationship, that is higher order dependencies, you can look at (cross)cumulants. From information theory you may want to look at (cross)entropy and mutual information.

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