P$5$: $[4$pts$]$ Two signals $f_1(t)$ and $f_2(t)$ are transmitted simultaneously by using quadrature multiplexer. Let $(t)$ be the resulting modulated signal.

$($a$)[2$ pts$]$ Sketch a synchronous detector for $(t).$

$($b$)[2$ pts$]$ Analyze the effect of a phase error $()$ in the local carrier generated at the receiver on the output of your synchronous detector.