Definition:Sampling Function

Definition
The sampling function is the distribution $\operatorname {III}_T: \map \DD \R \to \R$ defined as:


 * $\forall x \in \R: \forall T \in \R : \map {\operatorname {III}_T } x := \displaystyle \sum_{n \mathop \in \Z} \map \delta {x - T n}$

where $\delta$ denotes the Dirac delta distribution.

Whenever $T = 1$, it can be omitted.