EC > GATE 2025 > Z-Transform
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]=αδ[n], where δ[n] is the unit impulse and α is a scalar, then the region of convergence (RoC) is the entire Z-plane

Correct : c

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