Unit Step Function

Shifted Unit Step function

The unit step function, also known as the Heaviside function, is defined as such:

${\displaystyle u(t)=\left\{{\begin{matrix}0,&{\mbox{if }}t<0\\1,&{\mbox{if }}t>0\\{\mbox{undefined}},&{\mbox{if }}t=0\end{matrix}}\right.}$

Sometimes, u(0) is given the value of ${\displaystyle {\frac {1}{2}}}$ (and sometime also 0 or 1). For many applications, it is irrelevant what the value at zero is.

Source: Wikibooks on Signals and Systems