$4.(25$ points$)$ An amplitude$-$modulated signal v$($t$)$ includes a $1$ MHz sinusoidal carrier vcarrier$($t$)=$ V$0$ cos$(0$t$)$ where V$0=10$V and $0=2(1$MHz$).$ The modulating signal s$($t$)$ is comprised of two sinusoidal musical tones at middle C $(256$ Hz$)$ and concert A $(440$ Hz$)$ of amplitude $1.$ Hence: s$($t$)=$ cos$($ Ct$)+$ cos$($ At$)$ with C $=2(256$Hz$)$and A $=2(440$Hz$).$ Anamplitudemodulatorproduces the following output signal v$($t$)$: v$($t$)=[1+$ s$($t$)]$vcarrier$($t$)$ with $=01.($a$)$ Find the Fourier transform V$()$