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Math — Convolution

The convolution integral and the convolution theorem.

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(f * g)(t) = \int_{-\infty}^{\infty} f(\tau)\,g(t-\tau)\,d\tau

\mathcal{F}\{f * g\} = \mathcal{F}\{f\}\cdot\mathcal{F}\{g\}

(f * g) = (g * f)

(f * g)[n] = \sum_{m} f[m]\,g[n-m]