41. A source generates four messages with probability $$\frac{1}{8},\,\frac{1}{8},\,\frac{1}{4}$$ and $$\frac{1}{2}.$$ What is the entropy of the source (bits/message)?
42. A source has two symbols x1 and x2 with probabilities P1 and P2 respectively. If a new source, with four symbols is generated from the above source, then the new symbol probabilities will be (ε is a number such that 0 < ε < 1)
43. A digital communication system transmits a block of N bits. The probability of error in decoding a bit is α. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of the its bits is decoded wrongly. The probability that the received block is erroneous is
44. An Ideal power limited communication channel with additive white Gaussian noise with 1 MHz band width and Signal to Noise ratio of 15 is transmitting the information at theoretical maximum rate. If the Signal to Noise ratio is reduced to 7, how much bandwidth is required to maintain same rate:
45. The input to a channel is a band-pass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by Y(t) = $$\left( {\frac{1}{{100}}} \right)$$ cos(100t - 10-6)cos(106t - 1.56)
The group delay (tg) and the phase delay (tp) in seconds, of the channel are
The group delay (tg) and the phase delay (tp) in seconds, of the channel are
46. Consider a discrete memory-less source with source alphabet, S = {S0, S1, S2, S3, S4} with respective probabilities of P = {0.4, 0.2, 0.2, 0.1, 0.1}. Find the average code word length
47. Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below:
If the detection threshold is 1, the BER will be
If the detection threshold is 1, the BER will be
48. The channel capacity is measured in terms of:
49. As per Shannon's channel capacity theorem, if samples are transmitted in 'T' seconds over a noisy channel which is bandlimited to 'B' Hz. The number of samples 'n' is given by (Symbols/notations carry their usual meaning)
50. In communication system a trade-off can be made between transmission bandwidth and
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