GATE ECE 2025 EC Q27: Discrete-time signals

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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