Definition:Even Impulse Pair Function

Definition
The even impulse pair function is the real function $\operatorname {II}: \R \to \R$ defined as:


 * $\forall x \in \R: \map {\operatorname {II} } x = \dfrac 1 2 \map \delta {x + \dfrac 1 2} + \dfrac 1 2 \map \delta {x - \dfrac 1 2}$

where $\delta$ denotes the Dirac delta function.