Definition:Sampling Function/2 Dimensional

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Definition

Let $\operatorname {III}: \R \to \R$ denote the sampling function.

The $2$-dimensional form of $\operatorname {III}$ is defined and denoted:

$\forall x, y \in \R: \map {\operatorname { {}^2 III} } {x, y} := \map {\operatorname {III} } x \map {\operatorname {III} } y$


Also known as

The sampling function $\operatorname {III}$ can also be seen referred to as:

the replicating function
the Dirac comb.

It can be referred to and voiced as shah.


Also see

  • Results about the sampling function can be found here.


Linguistic Note

The name shah for the sampling function derives from its similarity in shape and appearance to the Russian ะจ, whose name is itself pronounced shah.


Sources

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