Asignal g$($t$)=$ sinc $(5$xt$)$ si sampled $($using uniformly spaced impulses$)$ at arate of: $($i$)5$Hz; $($ii$)10$ Hz; $($iii$)20$ Hz$.$ For each of the three case:

$($a$)$ Sketch the sampled signal.

$($b$)$ Sketch the spectrum of the sampled signal.

$($c$)$ Explain whether you can recover the signal g$($t$)$ from the sampled signal.

$($d$)$ If the sampled signal si passed through an ideal low$-$pass filter of bandwidth $5$ Hz$,$ sketch the spectrum of the output signal.