$6\mathrm{.}1-4$ A signal $\backslash ($ g$($t$)=\backslash$operatorname$\{$sinc$\}^\{2\}(5\backslash$pi t$)\backslash )$ is sampled $($using uniformly spaced impulses$)$ at a rate of $($i$)5$ Hz ;

$($ii$)10$ Hz ; $($iii$)20$ Hz $.$ For each of the three cases:

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

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

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

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