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# GATE 2024 Communication System Foundation Quiz 38

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Question 1

An information carrying signal g(t) band limited to W Hz is received after passing through a distoring channel H(f)

The magnitude of the received signal when sampled at TS = 3 sec is_______

Question 2

A joint sample space for 2 random variable X and Y has four elements (1, 1), (2, 2), (3, 3), (4, 4) probability of these elements are 0.1, 0.2, 0.3, 0.4 respectively.

The probability of event (x ≤ 2.5, y ≤ 5) will be

Question 3

A carrier wave is frequency modulated using a sinusoidal signal of frequency fm and amplitude Am. In a certain experiment conducted with fm = 1kHz and increasing Am (Starting from 0 volts), it is found that the carrier component of the FM signal is reduced to zero for the first time when Am = 2 volts. What is the frequency sensitivity of the modulator?

Question 4

An analog signal, which is band limited to 10 KHz, is sampled at a rate of fs and the samples are applied to a 32-level PCM system. The resultant bits are separated by using a raised cosine filter with roll-off factor of 0.60 and transmitted through a baseband channel. If the channel bandwidth is 100 kHz, then the maximum allowed sampling rate (fs) for |S| free transmission, will be _______ kHz.

Question 5

If two independent random variables X and Y have variance 20 and 5 respectively. If two new random variables U = X + Y and V = X – Y are defined, then the value of correlation coefficient
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