GATE ECE Discrete-time signals PYQs & Answers

Questions 1–10 of 28. Imported answers require independent review unless marked reviewed.

The response of a discrete time system

obeys the following relation:

The input to the system is

Which of the following options is TRUE for

Your answerChoose one option.

Stable and causal response

Stable and non-causal response

Unstable and causal response

Unstable and non-causal response

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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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Let

be a discrete-time signal whose z-transform is

. Which of the following statements is/are TRUE?

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

The discrete-time Fourier transform (DTFT) of

always exists

The region of convergence (RoC) of

contains neither poles nor zeros

The discrete-time Fourier transform (DTFT) exists if the region of convergence (RoC) contains the unit circle

, where

is the unit impulse and

is a scalar, then the region of convergence (RoC) is the entire z-plane

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The radian frequency value(s) for which the discrete time sinusoidal signal

has a period of 40 is/are _____.

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

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The relation between any N-length sequence

and its corresponding N-point discrete Fourier transform

is defined as

Another sequence

is formed as below

For the sequence

, the value of

is ______.

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In the table shown below, match the signal type with its spectral characteristics.

Signal type	Spectral characteristics
(i) Continuous, aperiodic	(a) Continuous, aperiodic
(ii) Continuous, periodic	(b) Continuous, periodic
(iii) Discrete, aperiodic	(c) Discrete, aperiodic
(iv) Discrete, periodic	(d) Discrete, periodic

Your answerChoose one option.

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Consider a discrete-time period signal with period

. Let the discrete-time Fourier series (DTFS) representation be

, where

and

. The value of the sum

Your answerChoose one option.

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Let an input

have discrete time Fourier transform

be passed through an LTI system. The frequency response of the LTI system is

. The output

of the system is

Your answerChoose one option.

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For a vector

, the 8-point discrete Fourier transform (DFT) is denoted by

, where

Here,

. If

and

, then the value of

is ________ (rounded off to one decimal place).

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GATE ECE Discrete-time signals PYQs

How to practice Discrete-time signals

Question 16

Question 47

Question 17

Question 27

Question 56

Question 59

Question 29

Question 47

Question 48

Question 55