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 $N_0/2$.

(i) (5%) Pass the received signal through an ideal bandpass filter centered at $ f_{c} $ with bandwidth $ B \geq 2W $. The noise then becomes $ n_{c}(t) \cos 2\pi f_{c}t - n_{s}(t) \sin 2\pi f_{c}t $ narrowband noise. Draw $ S_{n_c}(f) $ the PSD of $ n_{c}(t) $.

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題組內容

(i) (5%) Pass the received signal through an ideal bandpass filter centered at \( f_{c} \) with bandwidth \( B \geq 2W \). The noise then becomes \( n_{c}(t) \cos 2\pi f_{c}t - n_{s}(t) \sin 2\pi f_{c}t \) narrowband noise. Draw \( S_{n_c}(f) \) the PSD of \( n_{c}(t) \).

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