Heaviside Function

The unit step function or Heaviside function is the function $u_c$ defined by

$\begin{array}{rlr}{u}_c(t)& =\{\begin{array}{ll}0& t<c\\ 1& t\ge c\end{array}& c\ge 0\end{array}$

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

$\theta (t)=\{\begin{array}{ll}0& t<0\\ 1& t\ge 0\end{array}$

This more closely parallels the dirac delta function.