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# GATE 2025 Communication Systems Foundation Quiz 34

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Question 1

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 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

Question 2

In PCM signal m(t) = [2 sin (100 πt )+ 2 cos (100 πt)]V is sampled at Nyquist rate samples are processed by a uniform quantizer with step size .5V minimum data rate of PCM system in bits per second.

Question 3

Four signals g1(t), g2(t), g3(t) and g4(t) are to be multiplexed and transmitted. g1(t) and g4(t) have a bandwidth of 4 kHz, and the remaining two signals have bandwidth of 8 kHz. Each sample requires 8 bit for encoding. What is the minimum transmission bit rate of the system.

Question 4

In a PCM system, if the code word length is increased form 6 to 8 bits, the signal to quantization noise ratio improves by the factor

Question 5

In a DPCM system, signal m (t) = 2cos2 (50t) V is sampled at Nyquist Rate. The samples are processed by a uniform quantizer with step size 0.5. Then the bit rate of the system is ___________bits/sec.
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