GATE ECE Discrete-time signals PYQs & Answers — Page 2

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Discrete-time signals

Questions 11–20 of 28. Imported answers require independent review unless marked reviewed.

Topic practice 28 questionsPage 2 of 3

Consider two 16-point sequences

and

. Let the linear convolution of

and

be denoted by

, while

denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point discrete Fourier transforms (DFTs) of

and

. The value(s) of

for which

is/are

Your answerChoose one option.

and

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For a unit step input

, a discrete-time LTI system produces an output signal

. Let

be the output of the system for an input

. The value of

is ________.

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Consider the signals

and

, where

is the unit step sequence. Let

and

be the discrete-time Fourier transform of

and

, respectively. The value of the integral

(rounded off to one decimal place) is ________.

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The output

of a discrete-time system for an input

The unit impulse response of the system is

Your answerChoose one option.

0 for all

1 for all

unit step signal

unit impulse signal

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Which one of the following pole-zero plots corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below?

Your answerChoose one option.

Diagram for Electronics and Communication Engineering question 14

Diagram for Electronics and Communication Engineering question 14 (figure 2)

Diagram for Electronics and Communication Engineering question 14 (figure 3)

Diagram for Electronics and Communication Engineering question 14 (figure 4)

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A finite duration discrete-time signal

is obtained by sampling the continuous-time signal

at sampling instants

. The 8-point discrete Fourier transform (DFT) of

is defined as

Which one of the following statements is TRUE?

Your answerChoose one option.

All

are non-zero.

Only

is non-zero.

Only

and

are non-zero.

Only

and

are non-zero.

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The transfer function of a stable discrete-time LTI system is

, where

and

are real numbers. The value of

(rounded off to one decimal place) with

, for which the magnitude response of the system is constant over all frequencies, is __________ .

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Let

be the z-transform of a real-valued discrete-time signal

. If

has a zero at

, and

has a total of four zeros, which one of the following plots represents all the zeros correctly?

Your answerChoose one option.

Diagram for Electronics and Communication Engineering question 3

Diagram for Electronics and Communication Engineering question 3 (figure 2)

Diagram for Electronics and Communication Engineering question 3 (figure 3)

Diagram for Electronics and Communication Engineering question 3 (figure 4)

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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

Your answerChoose one option.

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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

Your answerChoose one option.

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GATE ECE Discrete-time signals PYQs

Question 5

Question 40

Question 41

Question 5

Question 14

Question 29

Question 53

Question 3

Question 28

Question 29