$($a$)$ A signal $m(t)$ is first sampled by an impulse train $p(t)$ and then transmitted as shown in Figure Q$4$a$.$ Let the sampling period be $T=100ns.$ Determine and sketch $Y().$

$[4$ marks$]$

$($b$)$ Explain how we can recover the original signal from $y(t).$

$[4$ marks$]$

$($c$)$ In practice, we are not able to generate impulse trains to form $p(t).$ Instead, trains of short rectangular pulse $q(t)$ as shown in Figure Q$4$b are used to obtain imperfect samples $z(t)=m(t)q(t).$ In this case, one can express $q(t)=p(t)**r(t).$ Determine $r(t).$

$[4$ marks$]$

$($d$)$ Explain how we can recover the original signal $y(t)$ from $z(t).$

$[5$ marks$]$