$(2)$ Consider the following continuous$-$time signal

xa$($t$)=$ xa$1($t$)+$ xa$2($t$)+$ xa$3($t$)$

where,

xa$1($t$)=10$ sin$(2$f$1$t$)$ cos$(2$f$2$t$),$

xa$2($t$)=8$ cos$(2$f$3$t$)+3$ cos$(2$f$4$t$),$

xa$3($t$)=8$ cos$(2$f$5$t$)$ cos$(2$f$6$t$),$

f$1=5$ kHz$,$ f$2=10$ kHz$,$ f$3=25$ kHz$,$ f$4=35$ kHz$,,$f$5=9$ kHz$,$ and f$6=11$ kHz$,$

It is required to design a digital signal processing$-$based system to separated the two signals xa$1($t$)$ and xa$2($t$),$ and remove the third signal. Thus, the system will have one input and $2$ outputs corresponding to xa$1($t$)$ and xa$2($t$).$ The requirements of the system are as follows:

$$ The anti$-$aliasing analog filter has an order of $6,$ with p $=0\mathrm{.}2$ dB$,$ and s $60$ dB$.$

$$ Concerning the IIR filters used, the order is n $=4$ and s $=45$ dB$.$

$($a$)$ Draw the line spectrum of the signals using different colors to distinguish them from each other.

$($b$)$ Sketch the overall block diagram of the system.

$($c$)$ Specify the requirements of the anti$-$aliasing analog LPF needed.

$($d$)$ From the above requirements, determine the required sampling frequency.