The result given below is incorrect. The AM-free signal that has the same shift in zero crossings as A0*cos(wot) + a*cos (wo+dw t + φ) is
A0*cos(wot) + a/2*cos (wo+dw t + φ) + a/2*cos (wo-dw t + π - φ), for a≪A0. There is no factor of 1/2 for the carrier. Putting either of these signals through a limiter produces the same signal. The limiter's output around the fundamental will be proportional to the latter signal and depends on the limiting amplitude.
iVenky wrote on Mar 29th, 2016, 8:42am:Hi,
... he considers
x(t)=A cos(wot)+a cos(wo+Δw)t
Where the second term is the additive noise component.
He says that after passing the above signal through a limiter (so that amplitude noise component gets suppressed), we get the following FM (or PM) signal at the output of the limiter.
xlim(t) = (A/2) cos wot - (a/2) cos(wo+Δw)t + (a/2) cos(wo-Δw)t