Step function: Difference between revisions

Revision as of 14:51, 17 December 2020

Revision as of 17:49, 2 January 2021

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[[Image:Dirac distribution CDF.svg|325px|thumb|The [[Heaviside step function]] is an often-used step function.]]

* A [[constant function]] is a trivial example of a step function. Then there is only one interval, <math>A_0=\mathbb R.</math>

* The [[sign function]] <{{math>\|sgn(''x'')}},</math> which is −1 for negative numbers and +1 for positive numbers, and is the simplest non-constant step function.

* The [[Heaviside step function|Heaviside function]] {{math|''H''(''x'')}}, which is 0 for negative numbers and 1 for positive numbers, is equivalent to the sign function, up to a shift and scale of range (<math>H = (\sgn + 1)/2</math>). It is the mathematical concept behind some test [[Signal (electronics)|signals]], such as those used to determine the [[step response]] of a [[dynamical system (definition)|dynamical system]].

[[File:Rectangular function.svg|thumb|The [[rectangular function]], the next simplest step function.]]