GATE EE topic:signals-and-systems PYQs & Answers — Page 6

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Questions 51–59 of 59. Imported answers require independent review unless marked reviewed.

Topic practice 59 questionsPage 6 of 6

The transfer function of a system is given by,

. Let the output of the system be

for the input,

. Then the minimum and maximum values of

(in radians) are respectively

Your answerChoose one option.

and

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Consider the system with following input-output relation

where,

is the input and

is the output. The system is

Your answerChoose one option.

invertible and time invariant

invertible and time varying

non-invertible and time invariant

non-invertible and time varying

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Consider

where

. Here,

represents the largest integer less than or equal to

and

denotes the smallest integer greater than or equal to

. The coefficient of the second harmonic component of the Fourier series representing

is ________.

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The mean square value of the given periodic waveform

is ________.

Diagram for Electrical Engineering question 23

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Let a causal LTI system be characterized by the following differential equation, with initial rest condition

where

and

are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

Your answerChoose one option.

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Let the signal

be passed through an LTI system with frequency response

, as given in the figure below. The Fourier series representation of the output is given as

Diagram for Electrical Engineering question 31

Your answerChoose one option.

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The output

of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

Your answerChoose one option.

1000 samples/s

1500 samples/s

2000 samples/s

3000 samples/s

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A cascade system having the impulse responses

and

is shown in the figure below, where symbol ↑ denotes the time origin.

The input sequence

for which the cascade system produces an output sequence

Diagram for Electrical Engineering question 32

Your answerChoose one option.

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Consider a causal and stable LTI system with rational transfer function

, whose corresponding impulse response begins at

. Furthermore,

. The poles of

are

for

. The zeros of

are all at

. Let

. The value of

equals ________. (Give the answer up to three decimal places.)

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GATE EE topic:signals-and-systems PYQs

Question 6

Question 7

Question 16

Question 23

Question 30

Question 31

Question 31

Question 32

Question 51