You are selected to design a DSB$-$SC modulator to generate a modulated signal km$($t$)$cos$(2\backslash$pi f$\_($c$)$t$+\backslash$theta $),$ where

m$($t$)$ is a signal band$-$limited to BHz$.$ The following figure shows a DSB$-$SC modulator available in the

stockroom. The carrier signal generator available generates not cos$(2\backslash$pi f$\_($c$)$t$),$ but $($cos$2\backslash$pi f$\_($c$)$t$)^(3).$ You may use any

kinf of filter you like.

$($a$)$ What kind of filter is required.

$($b$)$ Determine the signal spectra at points b and c and indicates the frequency bands occupied by these spectra.

$($c$)$ What is the minimum usable value of f$\_($c$)$

$($d$)$ Would this scheme work if the carrier generator output were sin$^(3)2\backslash$pi f$\_($c$)$t$.$ Explain.

$($e$)$ Would this scheme work if the carrier generator output were $($cosn$\backslash$pi f$\_($c$)$t$)^(3)$ for any integer n$>=2?$