$7\mathrm{.}21.$ A signal x$($t$)$ with Fourier transform X$($jw$)$ undergoes impulse$-$train sampling to

generate

$00$

xp$($t$)=$ :L$,$ x$($nT$)$o$($t $-$ nT$)$

n$=-$ oo

where T $=$ w$-4.$ For each of the following sets of constraints on x$($t$)$ and$/$or X$($jw $),$

does the sampling theorem $($see Section $7\mathrm{.}1\mathrm{.}1)$ guarantee that x$($t$)$ can be recovered

exactly from Xp$($t$)?$

$($a$)$ X$($jw$)=0$ for lwl $>50001$T

$($b$)$ X$($jw$)=0$ for lwl $>150001$T

$($c$)$ CR$.$e$\{$X$($jw$)\}=0$ for lwl $>50001$T

$($d$)$ x$($t$)$ real and X$($jw$)=0$ for w $>50001$T

$($e$)$ x$($t$)$ real and X$($jw$)=0$ for w $<-150001$T

$($f$)$ X$($jw$)*$ X$($jw$)=0$ for lwl $>150001$T

$($g$)$ IX$($Jw $)$I $=0$ for w $>50001$T