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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6 years, 9 months ago by Hendrik |
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3 years, 9 months ago |
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