# Z Transform MCQ’s

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^{-n}u(n)

b) α^{n}u(n)

c) α^{-n}u(-n)

d) α^{n}u(n)

2. What is the z-transform of the following finite duration signal?

a) 2 + 4z + 5z^{2} + 7z^{3} + z^{4}

b) 2 + 4z + 5z^{2} + 7z^{3} + z^{5}

c) 2 + 4z^{-1} + 5z^{-2} + 7z^{-3} + z^{-5}

d) 2z^{2} + 4z + 5 +7z^{-1} + z^{-3}

3. What is the z-transform of the signal x(n)=(0.5)^{n}u(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|<r_{1}

b) |z|>r_{1}

c) r_{2}<|z|<r_{1}

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) = -α^{n}u(-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)= a^{n}u(n)+b^{n}u(-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)=a^{n}(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|>r_{1}

b) |z|<r_{1}

c) r_{2}<|z|<r_{1}

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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