Can anyone tell me how to simplify this recursive equation?
$$h(n) = \alpha h(n-1) + (1-\alpha)\delta(n)$$
$\delta(n)$ is Dirac delta function.
I have got to this so far:
$$h(n) = (1-\alpha)\delta(n) + (1-\alpha)\alpha\delta(n-1) + (1-\alpha)\alpha^2\delta(n-2) + \dots\\ =(1-\alpha)\sum_{i=0}^{\infty}\alpha^i \delta(n-i)$$
I guess this is a pretty common equation to simplify, and I know the solution has something to do with the step function, but I don't know how to get to that and can't find anything useful.