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 $N_0/2$.

(iii) (8%) Suppose the signal is further corrupted by an interference \( k(t) = \text{sinc}(wt) \) and the received signal after the bandpass filter becomes \( y_2(t) = (t) + k(t) \cos 2\pi(f_c + 2W)t + n_c(t) \cos 2\pi f_c t - n_s(t) \sin 2\pi f_c t \). Design a low-pass filter for the demodulator in part ii) such that the signal-to-interference-plus-noise ratio (signal power divided by the sum of interference and noise power) is maximized.