A DSB$-$SC signal is given by $m(t)cos{}_{c}t.$ At the receiver, it is multiplied with a carrier $2cos({}_{c}t+15)$ and then passed through a lowpass filter with cut$-$off frequency $3$ kHz $.$ The signal spectrum, $M(f),$ is shown in the figure below, with $f_m=3kHz.$ Using the condition

$(a)$ Show that the signal $m(t)$ can $be$ recovered $at$ the output.

$(b)$ Calculate power $in$ the output signal.

Figure $1$: Figure for Question $No.3$