Heaviside step function

Remarks

The function $t \mapsto H(t - a)$ switches a signal on at the time $a$. For example, $f(t) H(t - a)$ is $0$ before $a$ and $f(t)$ after $a$. For $g : [0, \infty) \to \mathbb{C}$ with a Laplace transform $G$ and $a \ge 0$, the shifted function $t \mapsto H(t - a)\, g(t - a)$ has the transform $e^{-a s} G(s)$. In the sense of distributions, the derivative of $H$ is the Dirac delta. It is named after Oliver Heaviside.