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For use when discussing the commutative and linear, but not associative operator interpreted on functions and distributions.

The convolution of the functions $f(t)$, $g(t)$ (interpreted on $]-\infty,\infty[$) is defined as

$$(f * g)(t)=\int_{-\infty}^{\infty} f(t)g(x-t)dt$$

Or in the discrete case,

$$(f * g)(n) = \sum_{k \in D} f(k) g(n - k)$$

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