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# ESE 2021 Technical Quiz 57 ||Z Transform

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Question 1

The inverse z-transform of the signal ;ROC; Question 2

Which of the following are true regarding ROC:
i. If x (n) is a finite duration two – sided (non causal) signal, the ROC lies between z=0 and z= .
ii. If X (z) is rational, then ROC includes all poles of X (z).
iii. If X (z) is rational, and if x (n) is two sided, then ROC is the region between two circles whose radius corresponds to the pole of the causal part with the largest magnitude and the pole of the anticausal part with smallest magnitude.
iv. If x (n) is infinite duration two – sided (non causal) signal, the ROC lies on the entire z – plane except the region between two circles of radius r1 and r2.

Question 3

Given a signal . If the z -transform of signal is X(z) then which of the following diagram can represent pole location of X (z) on the z -plane

Question 4

Let The quantities p, q, r are real numbers.

Consider If the zero of H(z) lies on the unit circle, then

Question 5

Consider the signal given below, If then the z-transform X(z) is
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