$1$ A signal $\backslash (\backslash$mathrm$\{$g$\}(\backslash$mathrm$\{$t$\})=\backslash$operatorname$\{$sinc$\}^\{2\}(5\backslash$pi $\backslash$mathrm$\{$t$\})\backslash )$ is sampled $($using uniformly spaced impulses$)$ at a rate of:

$(1)5$ Hz

$(2)10$ Hz

and

$(3)20$ Hz $.$ For each of the three cases:

a$.$ Sketch the sampled signal.

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

c$.$ Explain for each of the three cases, whether you can recover the signal $\backslash ($ g$($t$)\backslash )$ from the sampled signal.

$[10][$CO$01][$BTL$2]$