563489578934

Problems 491
6–60 Let
be a wideband FM signal, where
and m(t) is a random modulation process.
(a) Show that
s(t) = Re{g(t)e j(v c t+u c ) }
g(t) = A c e jD f 1 - t q m(l) dl
R g (t) = A 2 c [e jDftm(t) ]
t + t
when the integral t m(l) dl is approximated by tm(t).
(b) Using the results of part (a), prove that the PSD of the wideband FM signal is given by
Eq. (5–66). That is, show that
s (f) = pA c 2
cf
2D m a 2p (f - f
f D c )b + f m a 2p (-f - f
f D c )bd
f