GATE ECE concept:impulse-response PYQs & Answers

Questions 1–9 of 9. Imported answers require independent review unless marked reviewed.

Consider the discrete time system (S) with input

and output

as shown in the Figure. The two sub-systems represented by their impulse responses

and

are linear and time invariant.

Which of the following statements is necessarily TRUE?

Diagram for Electronics and Communication Engineering question 47

Your answerChoose one option.

S is causal.

S is linear and time invariant.

S is linear and time varying.

S is non-linear.

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Consider the discrete-time system below with input

and output

. In the figure,

and

denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also,

is the unit impulse, and

. Assuming

, the overall system (denoted by the dashed box) is _____.

Diagram for Electronics and Communication Engineering question 17

Your answerChoose one option.

linear and time invariant

linear and time variant

nonlinear and time invariant

nonlinear and time variant

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A causal and stable LTI system with impulse response

produces an output

for an input signal

. A signal

is applied to another causal and stable LTI system with impulse response

. The resulting output is ______.

Your answerChoose one option.

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For a causal discrete-time LTI system with transfer function

which of the following statements is/are true?

Your answerSelect all correct options. You can choose more than one.

The system is stable.

The system is a minimum phase system.

The initial value of the impulse response is 2.

The final value of the impulse response is 0.

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A continuous time signal

is sampled at a rate of 15 Hz. The sampled signal

when passed through an LTI system with impulse response

produces an output

. The expression for

is ______.

Your answerChoose one option.

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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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Let

be a length-7 discrete-time finite impulse response filter, given by

, and

is zero for

. A length-3 finite impulse response approximation

has to be obtained such that

is minimized, where

and

are the discrete-time Fourier transforms of

and

, respectively. For the filter that minimizes

, the value of

, rounded off to 2 decimal places, is ______.

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A discrete-time all-pass system has two of its poles at

and

. Which one of the following statements about the system is TRUE?

Your answerChoose one option.

It has two more poles at

and

It is stable only when the impulse response is two-sided.

It has constant phase response over all frequencies.

It has constant phase response over the entire z-plane.

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Let

be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by

Let

be the discrete-time Fourier transform (DTFT) of

, where

is the normalized angular frequency in radians. Given that

and

, the value of

(in radians) is equal to __________.

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GATE ECE concept:impulse-response PYQs

How to practice concept:impulse-response

Question 47

Question 17

Question 21

Question 24

Question 48

Question 5

Question 44

Question 13

Question 33