GATE ECE Random processes PYQs & Answers

Questions 1–10 of 14. Imported answers require independent review unless marked reviewed.

Consider a real-valued random process

where

and

is a positive integer. Here,

for

and 0 otherwise. The coefficients

are pairwise independent, zero-mean unit-variance random variables.

Read the following statements about the random process and choose the correct option.

(i) The mean of the process

is independent of time

(ii) The autocorrelation function

is independent of time

for all

(Here,

is the expectation operation.)

Your answerChoose one option.

(i) is TRUE and (ii) is FALSE

Both (i) and (ii) are TRUE

Both (i) and (ii) are FALSE

(i) is FALSE and (ii) is TRUE

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A white Gaussian noise

with zero mean and power spectral density

, when applied to a first-order RC low pass filter produces an output

. At a particular time

, the variance of the random variable

is ______.

Your answerChoose one option.

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Let

be a random process, where amplitude

and phase

are independent of each other, and are uniformly distributed in the intervals

and

, respectively.

is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of

, the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is __________.

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For a real signal, which of the following is/are valid power spectral density/densities?

Your answerSelect all correct options. You can choose more than one.

Diagram for Electronics and Communication Engineering question 30

Diagram for Electronics and Communication Engineering question 30 (figure 2)

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Let

be a white Gaussian noise with power spectral density

W/Hz. If

is input to an LTI system with impulse response

. The average power of the system output is ________ W (rounded off to two decimal places).

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The frequency response

of a linear time-invariant system has magnitude as shown in the figure.

Statement I: The system is necessarily a pure delay system for inputs which are bandlimited to

Statement II: For any wide-sense stationary input process with power spectral density

, the output power spectral density

obeys

for

Which one of the following combinations is true?

Diagram for Electronics and Communication Engineering question 23

Your answerChoose one option.

Statement I is correct, Statement II is correct

Statement I is correct, Statement II is incorrect

Statement I is incorrect, Statement II is correct

Statement I is incorrect, Statement II is incorrect

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A state transition diagram with states

, and

, and transition probabilities

is shown in the figure (e.g.,

denotes the probability of transition from state A to B). For this state diagram, select the state(s) which is/are universally true.

Diagram for Electronics and Communication Engineering question 48

Your answerSelect all correct options. You can choose more than one.

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The autocorrelation function

of a wide-sense stationary random process

is shown in the figure. The average power of

is ______.

Diagram for Electronics and Communication Engineering question 21

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The random variable

and

is a real white Gaussian noise process with two-sided power spectral density

W/Hz, for all

. The variance of Y is ______.

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Let a random process

be described as

, where

is a white noise process with power spectral density

. The filter

has a magnitude response given by

for

, and zero elsewhere.

is a stationary random process, uncorrelated with

, with power spectral density as shown in the figure. The power in

, in watts, is equal to ______ W (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 45

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GATE ECE Random processes PYQs

How to practice Random processes

Question 42

Question 20

Question 57

Question 30

Question 59

Question 23

Question 48

Question 21

Question 24

Question 45