GATE ECE concept:power-spectral-density PYQs & Answers

Questions 1–8 of 8. Imported answers require independent review unless marked reviewed.

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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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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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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Consider a white Gaussian noise process

with two-sided power spectral density

W/Hz as input to a filter with impulse response

(where t is in seconds) resulting in output Y(t). The power in Y(t) in watts is

Your answerChoose one option.

0.1

0.22

0.33

0.44

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Let

be a wide sense stationary random process with the power spectral density

as shown in Figure (a), where

is in Hertz (Hz).

Diagram for Electronics and Communication Engineering question 51

The random process

is input to an ideal lowpass filter with the frequency response

as shown in Figure (b).

Diagram for Electronics and Communication Engineering question 51 (figure 2)

The output of the lowpass filter is

Let

be the expectation operator and consider the following statements:

II.

III.

Select the correct option:

Your answerChoose one option.

only I is true

only II and III are true

only I and II are true

only I and III are true

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GATE ECE concept:power-spectral-density PYQs

How to practice concept:power-spectral-density

Question 20

Question 30

Question 59

Question 23

Question 24

Question 45

Question 28

Question 51