Heaviside step function

Definition

One definition (depends on convention of definition at $0$ is: $$1(t) = \begin{cases}1 \quad \text{for } t \geq 0 \\ 0 \quad \text{for } t <0 \end{cases}$$

Discrete form

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Further notes

See Singularity functions, $\mu_1(t) = 1(t)$

Related to Delta function, $\mu_0(t) = \delta(t)$,

relationship between delta function and unit function

$$1(t) = \int_{-\infty}^t \delta(\tau) d\tau$$

References

1. https://lpsa.swarthmore.edu/BackGround/ImpulseFunc/ImpFunc.html
2. https://mathworld.wolfram.com/HeavisideStepFunction.html
3. https://en.wikipedia.org/wiki/Heaviside_step_function