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GATE EC 2020 || Signals & Systems || Z-Transform Quiz 1 (App update required to attempt this test)
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Question 1
The inverse z-transform of the signal 
;ROC; 
;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.
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
. 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
If
then the z-transform X(z) is Question 6
Z-Transform of a signal 
is given as 
. The Z-Transform of 
is given as 
, then find the value of 
.
is given as . The Z-Transform of is given as , then find the value of .- 597 attempts
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