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1
GATE ECE 2025
MCQ (More than One Correct Answer)
+1
-0
Let $x[n]$ be a discrete-time signal whose $z$-transform is $X(z)$. Which of the following statements is/are TRUE?
A
The discrete-time Fourier transform (DTFT) of $x[n]$ always exists
B
The region of convergence (RoC) of $X(z)$ contains neither poles nor zeros
C
The discrete-time Fourier transform (DTFT) exists if the region of convergence (RoC) contains the unit circle
D
If $x[n]=\alpha \delta[n]$, where $\delta[n]$ is the unit impulse and $\alpha$ is a scalar, then the region of convergence (RoC) is the entire $z$-plane
2
GATE ECE 2024
MCQ (More than One Correct Answer)
+1
-0

For a causal discrete-time LTI system with transfer function

$H(z) = \frac{2z^2 + 3}{\left(z + \frac{1}{3}\right)\left(z - \frac{1}{3}\right)}$

which of the following statements is/are true?

A

The system is stable.

B

The system is a minimum phase system.

C

The initial value of the impulse response is 2.

D

The final value of the impulse response is 0.

3
GATE ECE 2020
MCQ (Single Correct Answer)
+1
-0.33

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?

$$ y[n]=\sum_{k=0}^3(-1)^k x[n-k] $$

A

GATE ECE 2020 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 1

B

GATE ECE 2020 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 2

C

GATE ECE 2020 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 3

D

GATE ECE 2020 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 4

4
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of the following statements about the system is TRUE?
A
It has two more poles at 0.5$$\angle 30^\circ $$ and 4$$\angle 0^\circ $$.
B
It is stable only when the impulse response is two-sided.
C
It has constant phase response over all frequencies.
D
It has constant phase response over the entire z-plane.
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