# Tag Info

Questions on the (continuous or discrete) convolution of two functions. It can also be used for questions about convolution of distributions (in the Schartz's sense) or measures.

Convolution is a commutative, associative, distributive operation between two functions that produces a a third function. It is defined in the continuous domain as

$$(x \ast y)(t)=\int_{-\infty}^\infty{x(\tau)\space{}y(t-\tau)}\space{}d\tau$$

And in the discrete domain as

$$(x \ast y)[n]=\sum_{k=-\infty}^\infty{x[k]\space{}y[n-k]}$$

Its identity is the Dirac delta function $\delta(t)$ in continuous domain, and the Kronecker delta function $\delta[n]$ in discrete domain.

Reference: Convolution.