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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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.