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# GATE EC 2022: Subject Revision Quiz

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Question 1

A periodic signal m(t) angle modulates a very high frequency carrier. Let modulated signal be given by

s(t) = ACcos[2π × 108t + KP m(t)]

If (fi)max – (fi)min is to be 500 KHz, find KP in rad/V.

Question 2

The PSD of random process x(t) is shown below

If fo = 1 Hz, then the value of AC power of x(t) = __________W.

Question 3

Consider a discrete memoryless source with alphabet and respective probabilities of occurrence. The entropy of the source (in bits) is

Question 4

A signal is band limited to 7.2 KHz and three other signals are band-limited to 2.4 KHz each. The signals are to be transmitted by means of TDM. If each signal is sampled at, its Nyquist rate, find the speed of commutator in rpm.

Question 5

Which of the following is correct?
(i) In QAM each signal can be recovered by synchronous detection of the received signal by using two local carriers of same frequency but in phase quadrature.
(ii) QAM is similar to DSB-SC, the only difference is that QAM sends two message signal over the same spectrum.

Question 6

A message signal with bandwidth 10 kHz is Lower-Side Band SSB modulated with carrier frequency . The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency . The bandwidth of the output would be:

Question 7

A satellite receiver with noise figure of 5.6 dB has a bandwidth of 16 kHz and consist of a preamplifier with noise temperature 147 K and a gain of 30 dB. If the reference temperature is 297 K the equivalent noise temperature of the receiver is

Question 8

An analog voltage signal with highest frequency of 1 kHz is digitally encoded with a resolution of 0.02% covering the voltage range-50 V to 50 V to avoid the loss of information, the rms value of quantization noise is

Question 9

Which of the following is true about a Cumulative Distribution Function (CDF)
A) CDF is bounded between -1 to +1.
B) CDF is a monotone non-decreasing function.
C) Fx () = 0
D) CDF is bound between 0 and 1.

Question 10

A DSB-SC signal is to be generated with a carrier frequency fc=1MHz using non-linear device with the input-output characteristic

Vo = a0vi + a1vi3

where a0 and a1 are constants .the output of the non linear device can be filtered by an appropriate band-pass filter.

Let

Vi = Aci cos (2π fc’t)  +m(t)

where m(t) is the message signal, the value of fc'(in MHz).

Question 11

In a binary PCM system, the output signal to noise ratio is maintained at minimum of 40 dB. Then find number of levels required  and the corresponding SNR.

Question 12

The two binary FSK signals are given by

The minimum frequency separation of these two signals to be orthogonal is

Question 13

The figure shows the distribution function of random variable X the probability of random variable X having value between 3 to 4 will be __________

Question 14

If transmitted power,
WL is 90 dB, n is 10-15 W/Hz and Pe is 10-4
Then maximum allowable bit rate using non coherent FSK will be

Question 15

A random process given by where θ is the random variable uniformly distributed in the interval (0, 2π).

Find Autocorrelation

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