How Matched filter is transformed due to frequency modulation? Intro:

Consider a signal source S which emits a PAM modulated signal, bits encoded as +g(t) and -g(t) pulses. 

The matched filter for S is f - f is a function of g.

Then S is fed to an FM modulator and yields a modulated signal, S', let's call the corresponding matched filter of the modulated signal f'.

Question:

If f is known how can f' be computed ?
Normally you wouldn't try to do the match filter directly on the received FM signal.  Typically the receiver path would look something like this-

Received Signal -> Noise/Interference Filter -> FM Demod -> Matched Filter