$($CTFT$)$ With continuous$-$time signals $x(t)=\frac{sin(\frac{9}{2}t)}{2t}$ and $p(t)=cos(2t),$ calculate the followings:

$($a$)(10$ pts$)$ Sketch the Fourier transform $x(j)$ of $x(t).$

$($b$)(10$ pts$)$ Sketch the Fourier transform $P(j)$ of $p(t).$

$($c$)(10$ pts$)$ Write the Fourier transform $Y(j)$ of $y(t)=x(t)p(t)$ in terms of $x(j)$ and $P(j).$

$($d$)(15$ pts$)$ Sketch the Fourier transform $Y(j).$