Heaviside step function: Difference between revisions

Revision as of 15:47, 29 May 2021

Revision as of 15:48, 29 May 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 {{mvar|n}} < 0 must imply that {{mvar|n}} \le<= -1, whilst {{mvar|n}} > 0 must imply that the function attains unity at {{mvar|n}} = 1. Therefore the "step function" exhibits ramp-like behaviour over the range of [-1,1], and can not authentically be a step function, using the half-maximum convention.

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