Unit step function

Created

Created

2023 Sep 27 2:6

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Editor

Creator

Creator

Edited

Edited

2025 Feb 19 23:27

Refs

Refs

Indicator function

Heaviside step function

u(t)

Discrete representation

u[n] = \begin{cases} 1, & n=0,1,\dots \\ 0, & n=-1, -2 \dots \end{cases} = \sum_{k=0}^\infty \delta[n-k] = \sum_{k=-\infty}^n\delta[k]

Continuous representation

u(t) = \begin{cases} 0, & t < 0 \\ 1, & t > 0 \\ undefined, & t=0 \end{cases} = \int_{-\infty}^t \delta(\tau)d\tau

Sign Function representation

u(t) = 1/2 + \frac{1}{2}sgn(t) = \frac{1}{2}[1 + sgn(t)]

u(t) + u(-t) = 1

Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by H or θ, is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.

Heaviside step function

https://en.wikipedia.org/wiki/Heaviside_step_function

Heaviside step function

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