The 𝑍-transform of a discrete signal 𝑥[𝑛] is X ( z ) = 4 z ( z − 1 5 ) ( z − 2 3 ) ( z − 3 ) with ROC = R. Which one of the following statements is true?

Correct Answer is : Discrete-time Fourier transform of x[n] converges if R is 23<|.z|.<3

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

Discrete-time Fourier transform of x[n] converges if R is 2 3 < | . z | . < 3

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

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

Test Index

GATE Electrical Engineering (EE) 2023 Solved Paper

Question : 19

Total: 65

Discrete-time Fourier transform of x[n] converges if R is |𝑧| > 3
Discrete-time Fourier transform of x[n] converges if R is ‌
2
3
<|.z|.<3
Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a left-sided sequence
Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a right-sided sequence

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