A baseband signal $m(t)$ is transmitted using DSB$-$SC$,$ let the modulated signal be $x_c(t)=m(t)cos(2f_{c}t+).$ Let $W$ be the bandwidth of $m(t).$ The input signal power $\frac{?}{\text{b}\text{a}\text{r}}(m^2(t))=10$ Watts. Suppose the white noise superimposed on the DSB$-$SC signal has a two$-$sided power spectral density of $\frac{N_0}{2}.$

$($a$)(3$ pts$)$ What is the output signal power of the receiver?

$($b$)(4$ pts$)$ Sketch the power density of Predection noise and the postdection noise.

$($c$)(8$ pts$)$ What are the input SNR $($Predetection SNR$)SN{R}_i,$ output SNR $($Postdetection $SNR$ and channel $SN{R}^{-}SN{R}_c?$ What are the Detection gain and Figure of Merit?