Convolution
1. of functions
Given a pair of functions \(f\) and \(g\) their convolution, written \(f \ast g\), is given by the integral
Given a pair of sequences \(f\) and \(g\) their convolution, written \(f \ast g\), is given by the series
Given a pair of functions \(f\) and \(g\) their convolution, written \(f \ast g\), is given by the integral
\[
(f \ast g)(x) = \int f(t)\,g(x-t)\,\mathrm{d}t
\]
2. of sequencesGiven a pair of sequences \(f\) and \(g\) their convolution, written \(f \ast g\), is given by the series
\[
(f \ast g)_j = \sum_i f_i\,g_{j-i}
\]
Gallimaufry
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