Correlation

Correlation between $f$ and $g$, 2 piecewise continuous functions absolutely integrable over $(-\infty, \infty)$:

$$(f⋆g)(t)=\int_{-\infty}^{\infty}f(\lambda)g(\lambda-t)\,\text{d}\lambda$$

Relation with Convolution

$$(f⋆g)(t)=(-f*g)(t) = (f * -g)(t)$$