Given the received signal x$($t$)=5$cos$(1900$t$)+5$cos$(2100$t$)+10$cos$(2200$t$)$x$($t$)=5$cos$(1900$t$)+5$cos$(2100$t$)+10$cos$(2200$t$)$ is demodulated using a DSB$-$SC demodulator that uses a carrier frequency of $1000$Hz$1000$Hz$,$ and a low pass filter with a cutoff frequency of $1500$Hz$1500$Hz$,$ which of the following could be the output of the demodulator?

Question $25$Answer

a$.$

x$($t$)=30$cos$(100$t$)+10$cos$(100$t$)$x$($t$)=30$cos$(100$t$)+10$cos$(100$t$)$

b$.$

x$($t$)=5$cos$(50$t$)+5$cos$(100$t$)+10$cos$(200$t$)$x$($t$)=5$cos$(50$t$)+5$cos$(100$t$)+10$cos$(200$t$)$

c$.$

x$($t$)=10$cos$(100$t$)+10$cos$(200$t$)$x$($t$)=10$cos$(100$t$)+10$cos$(200$t$)$

d$.$

x$($t$)=5$cos$(100$t$)+5$cos$(200$t$)+10$cos$(150$t$)$