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 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.
3
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the sequence
$$x\left[ n \right]$$= $${a^n}u\left[ n \right] + {b^{\partial n}}u\left[ n \right]$$ , where u[n] denotes the unit step sequence and 0<$$\left| a \right| < \left| b \right| < 1.$$
The region of convergence (ROC) of the z-transform of $$\left[ n \right]$$ is
A
$$\left| z \right| > \left| a \right|$$
B
$$\left| z \right| > \left| b \right|$$
C
$$\left| z \right| < \left| a \right|$$
D
$$\left| a \right| < \left| z \right| < \left| b \right|$$
4
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z) is the z-transform of another signal y$$\left[ n \right]$$, then
A
$$y\left[ n \right] = x\left[ n \right]$$
B
$$y\left[ n \right] = x\left[ { - n} \right]$$
C
$$y\left[ n \right] = - x\left[ n \right]$$
D
$$y\left[ n \right] = - x\left[ { - n} \right]$$
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