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
35. The Nyquist sampling frequency (in Hz) of a signal given by 6 × 104sinC3(400t) ∗ 106sinC3(100t) is
36. In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantization noise ratio improves by the factor
37. Three analog signals, having bandwidths 1200 Hz, 600 Hz and 600 Hz, are sampled at their respective Nyquist rates, encoded with 12-bit words, and time division multiplexed. The bit rate for the multiplexed signal is
38. The peak-to-peak input to an 8-bit PCM coder is 2 Volts. The signal power-to-quantization noise power ratio (in dB) for an input of 0.5cos(ωmt) is
39. The Nyquist sampling rate for the signal $$s\left( t \right) = \frac{{\sin \left( {500\pi t} \right)}}{{\pi t}} \times \frac{{\sin \left( {700\pi t} \right)}}{{\pi t}}$$ is given by
40. The bit rate of digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for |S| free transmission is
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