GATE 2023 Electrical Engineering Q19

Question

The Z-transform of a discrete signal x[n] is

$X(z) = \frac{4z}{(z-\frac{1}{2})(z-\frac{2}{3})(z-3)}$ with ROC = R.

Which one of the following statements is true?

Answer

Discrete-time Fourier transform of x[n] converges if R is $|z| > 3$

Answer

Discrete-time Fourier transform of x[n] converges if R is $\frac{2}{3} < |z| < 3$

Answer

Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a left-sided sequence

Answer

Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a right-sided sequence