## 31. A signal x(t) = 100cos(24π × 10^{3})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?

^{3})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 t_{1} ≤ t ≤ t_{2}. This indicates that during this interval

_{1}≤ t ≤ t

_{2}. 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 × 10^{3})t and T_{s} =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 × 10

^{3})t and T

_{s}=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 × 10^{4}sinC^{3}(400t) ∗ 10^{6}sinC^{3}(100t) is

^{4}sinC

^{3}(400t) ∗ 10

^{6}sinC

^{3}(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(ω_{m}t) is

_{m}t) is