Heaviside step function: Difference between revisions

Revision as of 17:03, 27 July 2021

Revision as of 05:05, 28 July 2021

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<math display="block">H[n]=\begin{cases} 0, & n < 0, \\ \tfrac12, & n = 0,\\ 1, & n > 0, \end{cases} </math>

where {{mvar|n}} is an [[integer]]. If {{mvar|n}} is an integer, then {{mvarmath|''n}}'' < 0}} must imply that {{mvarmath|''n}}'' ≤ −1&minus;1}}, while {{mvarmath|''n}}'' > 0}} must imply that the function attains unity at {{mvarmath|1=''n}}'' = 1}}. Therefore the "step function" exhibits ramp-like behavior over the ___domain of [−1{{closed-closed|&minus;1, 1]}}, and cannot authentically be a step function, using the half-maximum convention.

Unlike the continuous case, the definition of {{math|''H''[0]}} is significant.