GATE ECE topic:signals-and-systems PYQs & Answers — Page 50

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Questions 491–500 of 715. Imported answers require independent review unless marked reviewed.

Topic practice 715 questionsPage 50 of 72

Consider a differentiable function

on the set of real numbers such that

and

. Given these conditions, which one of the following inequalities is necessarily true for all

Your answerChoose one option.

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Consider the line integral

, the integral being taken in a counterclockwise direction over the closed curve

that forms the boundary of the region

shown in the figure below. The region

is the area enclosed by the union of a

rectangle and a semi-circle of radius 1. The line integral evaluates to

Diagram for Electronics and Communication Engineering question 27

Your answerChoose one option.

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Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to

is shown in the figure. Let

. In the figure, what should be the values of the coefficients

in terms of

so that

is obtained correctly?

Diagram for Electronics and Communication Engineering question 28

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It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

, where

and

are arbitrary real numbers. The desired three-tap filter is given by

and

for

. What are the values of the filter taps

and

if the output is

for all

, when

is as given above?

Diagram for Electronics and Communication Engineering question 29

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In the circuit shown, if

volts,

and

, then the steady-state current

, in milliamperes (mA), is

Diagram for Electronics and Communication Engineering question 30

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Consider a causal second-order system with the transfer function

with a unit-step

as an input. Let

be the corresponding output. The time taken by the system output

to reach 94% of its steady-state value

, rounded off to two decimal places, is

Your answerChoose one option.

5.25

4.50

3.89

2.81

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The block diagram of a system is illustrated in the figure shown, where

is the input and

is the output. The transfer function

Diagram for Electronics and Communication Engineering question 32

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Let the state-space representation of an LTI system be

where

are matrices,

is a scalar,

is the input to the system, and

is its output. Let

and

. Which one of the following options for

and

will ensure that the transfer function of this LTI system is

Your answerChoose one option.

and

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A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density

. Binary signaling, with

and

, is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let

form an orthonormal signal set. If we choose

and

, we would obtain a certain bit-error probability

. If we keep

, but take

, for what value of

would we obtain the same bit-error probability

Your answerChoose one option.

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The quantum efficiency (

) and responsivity (

) at a wavelength

(in

) in a p-i-n photodetector are related by

Your answerChoose one option.

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GATE ECE topic:signals-and-systems PYQs

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35