June 12, 2021

Z Transform MCQ’s

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This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Z Transform”.

1. Which of the following series has a ROC as mentioned below?

a) α-nu(n)
b) αnu(n)
c) α-nu(-n)
d) αnu(n)

2. What is the z-transform of the following finite duration signal?
a) 2 + 4z + 5z2 + 7z3 + z4
b) 2 + 4z + 5z2 + 7z3 + z5
c) 2 + 4z-1 + 5z-2 + 7z-3 + z-5
d) 2z2 + 4z + 5 +7z-1 + z-3

3. What is the z-transform of the signal x(n)=(0.5)nu(n)?
a) 11−0.5z−1;ROC|z|>0.5
b) 11−0.5z−1;ROC|z|<0.5
c) 11+0.5z−1;ROC|z|>0.5
d) 11+0.5z−1;ROC|z|<0.5

4. What is the set of all values of z for which X(z) attains a finite value?
a) Radius of convergence
b) Radius of divergence
c) Feasible solution
d) None of the mentioned

5. The Z-Transform X(z) of a discrete time signal x(n) is defined as ____________
a) ∑∞n=−∞x(n)zn
b) ∑∞n=−∞x(n)z−n
c) ∑∞n=0x(n)zn
d) None of the mentioned

6. What is the ROC of a causal infinite length sequence?
a) |z|<r1
b) |z|>r1
c) r2<|z|<r1
d) None of the mentioned

7. What is the ROC of z-transform of finite duration anti-causal sequence?
a) z=0
b) z=∞
c) Entire z-plane, except at z=0
d) Entire z-plane, except at z=∞

8. The ROC of the z-transform of any signal cannot contain poles.
a) True
b) False

9. What is the z-transform of the signal x(n) = -αnu(-n-1)?
a) 11−αz−1;ROC |z|<|α|
b) −11+αz−1;ROC |z|<|α|
c) −11−αz−1;ROC |z|>|α|
d) −11−αz−1;ROC |z|<|α|

10. What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)?
a) |a|<|z|<|b|
b) |a|>|z|>|b|
c) |a|>|z|<|b|
d) |a|<|z|>|b|

11. The z-transform of a sequence x(n) which is given as X(z)=∑∞n=−∞x(n)z−n is known as _____________
a) Uni-lateral Z-transform
b) Bi-lateral Z-transform
c) Tri-lateral Z-transform
d) None of the mentioned

12. Is the discrete time LTI system with impulse response h(n)=an(n) (|a| < 1) BIBO stable?
a) True
b) False

13. What is the ROC of z-transform of a two-sided infinite sequence?
a) |z|>r1
b) |z|<r1
c) r2<|z|<r1
d) None of the mentioned

14. What is the ROC of the system function H(z) if the discrete-time LTI system is BIBO stable?
a) Entire z-plane, except at z=0
b) Entire z-plane, except at z=∞
c) Contain unit circle
d) None of the mentioned

15. What is the ROC of the signal x(n)=δ(n-k), k>0?
a) z=0
b) z=∞
c) Entire z-plane, except at z=0
d) Entire z-plane, except at z=∞

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