題組內容

2. Consider sending a message $m(t)$ whose power spectral density (PSD) is $S_m(f) = f^4$ for $|f| \le W$ and $S_m(f) = 0$ otherwise. The transmitted signal is given by $x(t) = m(t) \cos 2\pi f_c t$. The signal is corrupted by an additive white Gaussian noise with PSD $N_0/2$.

(ii) (8%) The output signal now is \( y(t) = x(t) + n_c(t) \cos 2\pi f_c t - n_s(t) \sin 2\pi f_c t \). Use a coherent demodulator followed by a low-pass filter with bandwidth \( W \) to demodulate it. Derive the demodulation signal and the SNR at the demodulator output.