Heaviside Step Function

the Heaviside Step Function \(H(t)\) is an important function in signal analysis. It is defined as follows:

\begin{align} \label{} H(t) = \[ \left\{ \begin{array}{ll} 0 & t \leq 0 \\ 1 & t > 0 \end{array} \right. \] \end{align}

and it is related to the distribution by taking a derivative:

\begin{align} \label{} \frac{dH}{dt} = \delta(t) \end{align}

Note that this definition of the derivative may be different than that of the regular derivative definition.