Signals and systems/Unit step function

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


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

Source: Wikibooks on Signals and Systems