$7\mathrm{.}22.$ The signal y$($t$)$ is generated by convolving a band$-$limited signal XI $($t$)$ with another

band$-$limited signal x$2($t$),$ that is$,$

where

y$($t$)=$ XI $($t$)*$ X$2($t$)$

X$1($jw$)=0$

X$2($jw$)=0$

for lw I $>10007$T

for lw I $>20007$T$.$

Impulse$-$train sampling is performed on y$($t$)$ to obtain

$+$oo

Yp$($t$)=$ L y$($nT$)$o$($t $-$ nT$).$

n$=-$oo

Specify the range of values for the sampling period T which ensures that y$($t$)$ is

recoverable from Yp$($t$).$