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:ID:       53dade38-21e1-4fa9-a552-6ceab8a75f82
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#+title: Heaviside Step Function
#+author: Preston Pan
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* Introduction
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 [[id:90574fea-88f4-4b80-9cda-32cff0bcb76d][dirac delta]] distribution by taking a [[id:31d3944a-cddc-496c-89a3-67a56e821de3][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.