Symbols:I/Sampling Function

Sampling Function

$\map {\operatorname {III} } x$

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

When $T = 1$, it is usually omitted:

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

The $\LaTeX$ code for $\map {\operatorname {III} } x$ is \map {\operatorname {III} } x .