BIO-465: The Firing rate function

I have a question regarding the Average firing rate function.

$A(t)$

In this week it is mentioned that for a high noise model we get

$A(t) = F(h(t))$ . This kind of feels unintuitive considering that

$A(t)$ is a sum of delta functions while

$F(h(t))$ is a function of the almost smooth function membrane potential. can / does the

$F(.)$ function turn

$h(t)$ into a sum of delta function ?

Also what would be an example of a

$F(.)$ function ? how is it calculated ?