Definition:Odd Impulse Pair Function

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Definition

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.


Graph of Odd Impulse Pair Function

The graph of the odd impulse pair function is illustrated below:


Odd-impulse-pair-function.png


It is to be understood that the blue arrows represent rays from the $x$-axis for constant $n \in \set {-\dfrac 1 2, \dfrac 1 2}$.


Sources