Heaviside Function

The unit step function or Heaviside function is the function $u_{c}$ defined by

${\begin{aligned}u_{c}(t)&={\begin{cases}0&t<c\\1&t\geq c\end{cases}}&c\geq 0\end{aligned}}$

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Some systems (e.g. Wolfram|Alpha) use the following definition, in which case $u_{c}(t)=\theta (t-c)$:

$\theta (t)={\begin{cases}0&t<0\\1&t\geq 0\end{cases}}$

This more closely parallels the dirac delta function.