GATE ECE Continuous-time signals PYQs & Answers — Page 3

Questions 21–30 of 36. Imported answers require independent review unless marked reviewed.

The exponential Fourier series representation of a continuous-time periodic signal

is defined as

where

is the fundamental angular frequency of

and the coefficients of the series are

. The following information is given about

and

is real and even, having a fundamental period of 6 II. The average value of

is 2 III.

The average power of the signal

(rounded off to one decimal place) is ________.

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is the Fourier transform of

shown below. The value of

(rounded off to two decimal places) is __________ .

Diagram for Electronics and Communication Engineering question 52

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Consider the signal

, where

is in seconds. Its fundamental time period, in seconds, is _____.

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Let the input be

and the output be

of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

Your answerChoose one option.

(with initial rest conditions)

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Let

be a periodic function with period

. The Fourier series coefficients for this series are denoted by

, that is

The same function

can also be considered as a periodic function with period

. Let

be the Fourier series coefficients when period is taken as

. If

, then

is equal to

Your answerChoose one option.

256

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The input

is fed to a Hilbert transformer to obtain

, as shown in the figure below:

Diagram for Electronics and Communication Engineering question 39

Here

. The value (accurate to two decimal places) of

is ______.

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A band limited low-pass signal

of bandwidth 5 kHz is sampled at a sampling rate

. The signal

is reconstructed using the reconstruction filter

whose magnitude response is shown below:

Diagram for Electronics and Communication Engineering question 54

The minimum sampling rate

(in kHz) for perfect reconstruction of

is ______.

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Consider the following statements for continuous-time linear time invariant (LTI) systems.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

Your answerChoose one option.

Both I and II are true

Both I and II are not true

Only I is true

Only II is true

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A periodic signal

has a trigonometric Fourier series expansion

, we can conclude that

Your answerChoose one option.

are zero for all

and

are zero for

even

are zero for all

and

are zero for

odd

are zero for

even and

are zero for

odd

are zero for

odd and

are zero for

even

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The input

and the output

of a continuous-time system are related as

. The system is

Your answerChoose one option.

linear and time-variant

linear and time-invariant

non-linear and time-variant

non-linear and time-invariant

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GATE ECE Continuous-time signals PYQs

Question 39

Question 52

Question 21

Question 4

Question 14

Question 39

Question 54

Question 5

Question 8

Question 8