You know this all went above my head but I can tell you one thing. You have been one of the few people who know how to ask a question and I encourage others to do the same.
Anyway, I can say that you look into your text book and try to figure this out, or refer some books on communication circuits ( using OP-AMPS / Schmidt trigger etc) and looking at the mathematic involved there.
Another thing you can have a look at is this, BUT believe me, I hope you know what you are talking about. Here is a white paper I found on
The MAP and cumulative distribution function equalization methods for the speech spectral estimation with application in noise suppression filtering.
LINK --> http://www.eurasip.org/content/Eusip...papers/N15.pdf
And I have no idea how probability works here, go figure!