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GATE ECE (Electronics) Test: Digital Communications - 1 Free Online Test


MCQ Practice Test & Solutions: Test: Digital Communications - 1 (15 Questions)

You can prepare effectively for Electronics and Communication Engineering (ECE) GATE ECE (Electronics) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Digital Communications - 1". These 15 questions have been designed by the experts with the latest curriculum of Electronics and Communication Engineering (ECE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 45 minutes
  • - Number of Questions: 15

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Test: Digital Communications - 1 - Question 1

has P.S.D. Sxx f then y has P.S.D

Detailed Solution: Question 1

Test: Digital Communications - 1 - Question 2

Consider Y= ax+b, a>0. If the density and distribution functions of x are F. (x) and fx (x), then Fy (y) is equal to

Detailed Solution: Question 2

Test: Digital Communications - 1 - Question 3

Consider a random process x(t). Which of the following can represent Rx. (r)?

Detailed Solution: Question 3

*Answer can only contain numeric values
Test: Digital Communications - 1 - Question 4

It is required to transmit at 100 Kbit/s and a bandwidth of 2 MHz is used. The

minimum S/N ratio is ___________________


Detailed Solution: Question 4

*Answer can only contain numeric values
Test: Digital Communications - 1 - Question 5

SNR when the system is uncoded is 4 dB, when it is coded is 2 dB then the coding gain is ________________  (dB)


Detailed Solution: Question 5

Coding gain =  SNR encoded - SNR. coded = 4.dB-2dB = 2dB

Test: Digital Communications - 1 - Question 6

In the set up shown below, determine the number of bits required to encode each sample of x (t) such that bandwidth of signal y(t) is greater than 5 MHz.


Detailed Solution: Question 6

Nyquist sampler is a sampler that samples a given signal at a rate twice the highest frequencies

fs = 2 fm, f5 = 2 x 350 kHz = 0.7MHz

Band width of output of PCM =



 

Test: Digital Communications - 1 - Question 7

A sinusoidal signal whose peak-peak amplitude is 6 V is modulated using deltamodulator. At what rate should be sinusoidal signal sampled such that slope over load distortion is prevented with step size of 0.942 V?

Detailed Solution: Question 7

2A = 6V ⇒ A = 3V

In order to overcome slope over load distortion in delta modulator

Test: Digital Communications - 1 - Question 8

The probability of the five possible outcomes of an experiment are given as

Determine the informationrate, if there are 8 outcomes per second.

Detailed Solution: Question 8



= 1.875 bits / sec; r=8 outcomes/sec
Information rate R=r.

=15bits / sec

 

Test: Digital Communications - 1 - Question 9

Probability of picking 3 symbols are P0, P1 and P2 respectively. The maximum entropy is achieved, when P0, P1, P2 are

Detailed Solution: Question 9

PO =P1 =P2 =P; PO + P1 + P2 = 1; 3P=1 ⇒ P= 1/3

Test: Digital Communications - 1 - Question 10

Hartley's law can be defined as r = 2 Blog2 M . When compared to Shannon Hartley theorem, C, M are

Detailed Solution: Question 10

Comparing C=B log ; r = C;

Test: Digital Communications - 1 - Question 11

The probability of a bit decoded correctly at receiver is `p'. If n bits are sent, what is the probability that one bit is decoded correctly?

Detailed Solution: Question 11

correct : p; error: 1-p

out of n bits, only one bit is decoded correctly=

Test: Digital Communications - 1 - Question 12

A stationary random process x(t) has the following correlation function is constant) . Find the psd of random signal x(t).

Detailed Solution: Question 12

PSD of input is expressed as




 

Test: Digital Communications - 1 - Question 13

If random variable 'x' has Gaussian pdf with mean M, then y=2x has PDF andmean respectively

Detailed Solution: Question 13

so y has pdf N(2m,402) which is Gaussian

Test: Digital Communications - 1 - Question 14

If x has P.S.D Sxx (f), then y has P.S.D of ( Assume H(f) is the Fourier Transform

Detailed Solution: Question 14

Test: Digital Communications - 1 - Question 15

 A Gaussian random variable 'x' has mean 1 and variance√2. If y = x2, then the mean of y is

Detailed Solution: Question 15

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