One Sided Z Transform

Digital Communications Systems

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

1. The z-transform of a signal x(n) whose definition is given by X(z)=∑∞n=0x(n)z−n is known as _____________
a) Unilateral z-transform
b) Bilateral z-transform
c) Rational z-transform
d) None of the mentioned

2. For what kind of signals one sided z-transform is unique?
a) All signals
b) Anti-causal signal
c) Causal signal
d) None of the mentioned

3. What is the one sided z-transform X+(z) of the signal x(n)={1,2,5,7,0,1}?
a) z2+2z+5+7z-1+z-3
b) 5+7z+z3
c) z-2+2z-1+5+7z+z3
d) 5+7z-1+z-3

4. What is the one sided z-transform of x(n)=δ(n-k)?
a) z-k
b) zk
c) 0
d) 1

5. What is the one sided z-transform of x(n)=δ(n+k)?
a) z-k
b) 0
c) zk
d) 1

6. If X+(z) is the one sided z-transform of x(n), then what is the one sided z-transform of x(n-k)?
a) z-k X+(z)
b) zk X+(z-1)
c) z-k [X+(z)+∑kn=1x(−n)zn]; k>0
d) z-k [X+(z)+∑kn=0x(−n)zn]; k>0

7. If x(n)=an, then what is one sided z-transform of x(n-2)?
a) z−21−az−1+a−1z−1+a−2
b) z−21−az−1–a−1z−1+a−2
c) z−21−az−1+a−1z−1–a−2
d) z−21+az−1+a−1z−1+a−2

8. If x(n)=an, then what is one sided z-transform of x(n+2)?
a) z−21−az−1 + a-1z-1 + a-2
b) z−21−az−1 – a-1z-1 + a-2
c) z21−az−1 + a z + z2
d) z21+az−1 – z2 – az

9. If X+(z) is the one sided z-transform of the signal x(n), then limn→∞x(n)=limz→1(z−1)X+(z) is called Final value theorem.
a) True
b) False

10. The impulse response of a relaxed LTI system is h(n)=anu(n), |a|<1. What is the value of the step response of the system as n→∞?
a) 11+a
b) 11−a
c) a1+a
d) a1−a

11. What is the step response of the system y(n)=ay(n-1)+x(n) -1<a<1, when the initial condition is y(-1)=1?
a) 11−a(1+an+2)u(n)
b) 11+a(1+an+2)u(n)
c) 11−a(1-an+2)u(n)
d) 11+a(1-an+2)u(n)

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