Signals and systems/Unit step function

Unit Step Function

Shifted Unit Step function

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

$u(t)=\{\begin{array}{cc}0,& \text{if }t<0\\ 1,& \text{if }t>0\\ \text{undefined},& \text{if }t=0\end{array}$

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

Source: Wikibooks on Signals and Systems