The cross-correlation $c_{xy}(\tau)$ of two functions $a(t)$ and $b(t)$ is the time-averaged product of the two functions with one delayed by time $\tau$, i. e.

$$ c_{xy}(\tau) \equiv \langle a(t) \ b(t-\tau) \rangle $$

where $\langle \rangle$ represents time-average. This is also called the cross-power product.