P$3.$ Consider the modulated signal expressed as below, where the carrier frequency is $f_c=2kHz$

$s(t)=14cos(4000t)+2\mathrm{.}8cos(500t)cos(4000t)$

$($a$)$ Find the quadrature modulation components $x(t)$ and $y(t)$ for this modulated signal.

$($b$)$ Plot the spectrum of the modulated signal.

$($c$)$ Find the normalized average power of $s(t).$

$($d$)$ What is the type of modulation

$($e$)$ Find the information signal $m(t)$

$($f$)$ Find the overall modulation percentage