Dirac-impulse (δ-function) #
The dirac-impulse is a function that is zero everywhere except at \(x=0\) . The integral of the dirac-impulse is one.
\[\delta(x) = 0 \text{ for } x \neq 0\\ \delta(x) = \infty \text{ for } x = 0\\ \int_{-\infty}^{\infty} \delta(x) dx = 1\]