A binary symmetric channel (BSC) has a transition probability of If the binary transmit symbol X is such that then the probability of error for an optimum receiver will be
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Digital Communication
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Choose the correct one from among the alternatives a, b, c, dafter matching an item from Group 1 with the most appropriate item in Group 2.
| Group 1 | Group 2 |
| 1. FM | P. Slope overload |
| 2. DM | Q. H-law |
| 3. PSK | R. Envelope detector |
| 4. PCM | S. Capture effect |
| T. Hilbert transform | |
| U. Matched filter |
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A source emits bit 0 with probability and bit 1 with probability The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R as
\begin{gathered} {f_{R|0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{4},}&{ - 3 \leqslant r \leqslant 1} \\ {0,}&{{\text{otherwise;}}} \end{array}} \right. \hfill \\ {f_{R|1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{6},}&{ - 1 \leqslant r \leqslant 5} \\ {0,}&{{\text{otherwise;}}} \end{array}} \right. \hfill \\ \end{gathered}
The minimum decision error probability is
\begin{gathered} {f_{R|0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{4},}&{ - 3 \leqslant r \leqslant 1} \\ {0,}&{{\text{otherwise;}}} \end{array}} \right. \hfill \\ {f_{R|1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{6},}&{ - 1 \leqslant r \leqslant 5} \\ {0,}&{{\text{otherwise;}}} \end{array}} \right. \hfill \\ \end{gathered}
The minimum decision error probability is
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The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion
would be
would be
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The number of bits in a binary PCM system is increased from n to n + 1. As a result, the signal to quantization noise ratio will improve by a factor
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A signal is sampled at 8 kHz and is quantized using 8-bit uniform quantizer. Assuming SNRq for a sinusoidal signal, the correct statement for PCM signal with a bit rate of R is
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The Nyquist sampling interval, for the signal sin c(700t) + sin c(500t) is
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The bit stream 01001 is differentially encoded using 'Delay and Ex-OR' scheme for DPSK transmission. Assuming the reference bit as a '1' and assigning phases of '0' and 'π' for 1's and 0's respectively, in the encoded sequence, the transmitted phase sequence becomes
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For a given data rate, the bandwidth Bp of a BPSK signal and the bandwidth B0 of the OOK signal are related as
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A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantized into 128 levels using a mid-rise uniform quantizer. The quantization noise power is
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Four independent messages have bandwidths of 100 Hz, 100 Hz, 200 Hz, and 400 Hz, respectively. Each is sampled at the Nyquist rate, and the samples are Time Division Multiplexed (TDM) and transmitted. The transmitted sample rate (in Hz) is
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In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by a factor of
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The line code that has zero dc component for pulse transmission of random binary data is
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In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is
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An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is
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The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function)
x(t) = 125t(u(t) - u(t - 1)) + (250 - 125t)(u(t - 1) - u(t - 2)) so that slope-overload is avoided, would be
x(t) = 125t(u(t) - u(t - 1)) + (250 - 125t)(u(t - 1) - u(t - 2)) so that slope-overload is avoided, would be
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Consider the signal x(t) shown in the figure. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interval 0 to 4 sec. The slope of h(t) in the interval 3 < t < 4 sec is
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Compression in PCM refers to relative compression of
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If S represents the carrier synchronization at the receiver and p represents the bandwidth efficiency, then the correct statement for the coherent binary PSK is
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In a digital communication system, transmissions of successive bits through a noisy channel are assumed to be independent events with error probability p. The probability of at most one error in the transmission of an 8-bit sequence is
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