\begin{definition}[Definition:Odd Impulse Pair Function]
The '''odd impulse pair function''' is the real function $\operatorname {I_I}: \R \to \R$ defined as:
:$\forall x \in \R: \map {\operatorname {I_I} } x := \dfrac 1 2 \map \delta {x + \dfrac 1 2} - \dfrac 1 2 \map \delta {x - \dfrac 1 2}$
where $\delta$ denotes the Dirac delta function.
\end{definition}