Figure P$4\mathrm{.}5-2.$

P$4\mathrm{.}7-3$ Let s$($t$)$ be an angle$-$modulated signal that arrives at a receiver,

$s(t)=2cos[1^{107}t+2sin{(}^{1000}t+{03}_{})-3cos{(}^{2000}t)]$

a$)$ Find the bandwidth of this FM signal.

b$)$ If $s(t)$ is sent to an $($ideal$)$ envelope detector, find the detector output signal.

c$)$ If $s(t)$ is first differentiated before the envelope detector, find the delector output signal.

d$)$ Explain which detector output can be processed to yield the message signal $m(t)$ and find the message signal $m(t)$ if $kf=200.$