2.1a.2 C-T Unit Step

Continuous-Time Unit Step

The continuous-time unit step can be defined as a signal $u$, such that
$u(t)=\{\begin{array}{ll}0& \text{if }t<0\\ 1& \text{if }t\ge 0\end{array}.$
The unit step can be written as the integral of the Dirac delta, such that
$u(t)={\int }_{-\infty }^{\infty }\delta (\tau )d\tau .$