$($Fawwaz Signal and system; SSB modulation $)***$Please complete the complete solution according to the text of the problem solving process. $***$ Solution:

$($a$)$ The spectrum of y$($t$),$ the SSB$-$modulated x$($t$)$ :

The spectrum of y$($t$)$ consists of only the lower sidebands of x$($t$).$ This explains the

name "single$-$sideband" modulation.

$($b$)$ To recover x$($t$)$ from y$($t$),$ compute and then lowpass filter

the result. This is the same as DSB demodulation. However, if there are multiple SSB

signals present, the receiver is more complex.

$($c$)$ Since the upper sidebands of x$($t$)$ are eliminated in SSB$,$ the power and

spectrum used in SSB are half those used in DSB$.$