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Heaviside step function

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The Heaviside step function is a discontinuous function whose value is zero for negative inputs and unity elsewhere:

  s(x) = { 1 : x > 0
         { 0 : x ≥ 0

It is the integral of the Dirac delta function.

The function is used in the mathematics of signal processing to represent a signal that switches on at a specified time and stays switched on indefinitely.