# Unit Impulse Function
> [!Unit impulse function]
> The *unit impulse function*, $\delta(x)$, also known as the *Dirac delta function*, is zero for all values except at $t=0$, where it is undefined. Its integral over the *entire real line* is equal to $1$.
> $\int_{-\infty}^{\infty}\delta(x)\;dx=1$
The function is noted for its *sampling* or *sifting* property.
$\int_{a}^{b}f(x)\delta(x-x_{0})\;dx=f(x_0)$
![[UnitImpulseFunction.svg]]