Äärellisten (lyhyiden) sekvenssien konvoluution laskeminen

Konvoluutio:

$$y[n] = \sum_{k=-\infty}^{+\infty} {h[k] \, x[n-k]}$$

Esimerkki, $h[n] = \{ 1, 2, -1\}, \ x[n] = \{2, 1, 1, 2\}$:

$$\begin{eqnarray*}y[n] &=& \sum_{k=-\infty}^{+\infty} {h[k] \, x[n-k]} \\ &=& \u... ...\\ &=& x[n] + 2 \, x[n-1] - x[n-2]\\ &=& \{2, 5, 1, 3, 3, -2\} \end{eqnarray*}$$

Matlabilla:
h = [1 2 -1]
x = [2 1 1 2]
y = conv(h,x)
vastaus [2 5 1 3 3 -2].