\begin{definition}[Definition:Sampling Function]
The '''sampling function''' is the distribution $\operatorname {III}_T: \map \DD \R \to \R$ defined as:
:$\forall x \in \R: \map {\operatorname {III}_T } x := \ds \sum_{n \mathop \in \Z} \map \delta {x - T n}$
where:
:$T \in \R_{\ne 0}$ is a non-zero real number
:$\delta$ denotes the Dirac delta distribution.
When $T = 1$, it is usually omitted:
:$\forall x \in \R: \map {\operatorname {III} } x := \ds \sum_{n \mathop \in \Z} \map \delta {x - n}$
\end{definition}