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Heaviside Step Function

Table of Contents

1. Introduction

1. Introduction

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

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

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

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

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