Unit Step Function

Topics: Function

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(definition)

The unit step function is defined as:

$$u(t)=\{\begin{array}{ll}0& \text{if }t\le 0\\ 1& \text{if }t>0\end{array}$$

In other words, the unit step function is a function that returns $0$ when its argument is non-positive, and $1$ when it is positive. Sometimes $<,\ge$ are used instead of $\le ,>$.

We can shift this function so that it’s centred around a number other than $0$.