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