$(20$ points$)$ Natural sampling. Suppose the signal $f(t)$ is band$-$limited with $Ff(s)=0$ for $|s|B.$ Instead of sampling with a train of $\text{'}$s we sample $f(t)$ with a train of very narrow pulses. The pulse is given by a function $p(t),$ we sample at a rate $T,$ and the sampled signal

then has the form

$g(t)=f(t)({\displaystyle \underset{k=-}{\overset{}{}}}Tp(t-kT))$

$($a$)$ Is it possible to recover the original signal $f$ from the signal $g?$

$($b$)$ If not, why not. If it is possible, what conditions on the parameters $T$ and $B,$ and on the pulse $p(x)$ make it possible.