Definition:Sampling Function

Definition
The sampling function is the real function $\operatorname {III}: \R \to \R$ defined as:


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

where $\delta$ denotes the Dirac delta function.

Also known as
The sampling function can also be seen referred to as the replicating function.