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Faltung

Definition

Corresponds to multiplication in the frequncy domain.

$$x(t) * h(t) = \int\limits_{-\infty}^{\infty} x(\tau) \cdot h(t-\tau) {\,\text{d}}\tau$$

with signals $x(t)$, $h(t)$.

Discrete: $$(f*g)[n] = \sum\limits_{k = -\infty}^{\infty} {f[k] g[n-k]}$$

Comparison of convolution, cross-correlation, and auto-correlation. [From Wikimedia](https://de.wikipedia.org/wiki/Datei:Comparison_convolution_correlation_de.svg)
Comparison of convolution, cross-correlation, and auto-correlation. From Wikimedia
Convolution of $f(t) * g(t)$ showing $f(\tau)$ and $g(t - \tau)$
Convolution of $f(t) * g(t)$ showing $f(\tau)$ and $g(t - \tau)$

Properties

Refrences

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