31. A signal x(t) = 100cos(24π × 103)t is ideally sampled with a sampling period of 50 psec and then passed through an ideal lowpass filter with cutoff frequency of 15 kHz. Which of the following frequencies is/are present at the filter output?
32. In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval t1 ≤ t ≤ t2. This indicates that during this interval
33. A BPSK scheme operating over an AWGN channel with noise power spectral density of $$\frac{{{N_0}}}{2},$$ uses equiprobable signals
$${s_1}\left( t \right) = \sqrt {\frac{{2E}}{T}} \sin \left( {{\omega _c}t} \right)$$ and $${s_2}\left( t \right) = \sqrt {\frac{{2E}}{T}} \sin \left( {{\omega _c}t} \right)$$
over the symbol internal (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45° with respect to the received signal, the probability of error in the resulting system is
$${s_1}\left( t \right) = \sqrt {\frac{{2E}}{T}} \sin \left( {{\omega _c}t} \right)$$ and $${s_2}\left( t \right) = \sqrt {\frac{{2E}}{T}} \sin \left( {{\omega _c}t} \right)$$
over the symbol internal (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45° with respect to the received signal, the probability of error in the resulting system is
34. Consider a sample signal
\[y\left( t \right) = 5 \times {10^{ - 6}}x\left( t \right)\sum\nolimits_{ - \infty }^{ + \infty } {\delta \left( {t - n{T_s}} \right)} \]
where x(t) = 10cos(8π × 103)t and Ts =100 μsec. When y(t) is passed through an ideal lowpass filter with a cutoff frequency of 5 kHz, the output of the filter is
\[y\left( t \right) = 5 \times {10^{ - 6}}x\left( t \right)\sum\nolimits_{ - \infty }^{ + \infty } {\delta \left( {t - n{T_s}} \right)} \]
where x(t) = 10cos(8π × 103)t and Ts =100 μsec. When y(t) is passed through an ideal lowpass filter with a cutoff frequency of 5 kHz, the output of the filter is