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 is known as:

a) Unilateral z-transform

b) Bilateral z-transform

c) Rational z-transform

d) None of the mentioned

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Explanation: The z-transform of the x(n) whose definition exists in the range n=-∞ to +∞ is known as bilateral or two sided z-transform. But in the given question the value of n=0 to +∞. So, such a z-transform is known as Unilateral or one sided z-transform.

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

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Explanation: One sided z-transform is unique only for causal signals, because only these signals are zero for n<0.

3. What is the one sided z-transform X^{+}(z) of the signal x(n)={1,2,**5**,7,0,1}?

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

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

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

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

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Explanation: Since the one sided z-transform is valid only for n>=0, the z-transform of the given signal will be X

^{+}(z)= 5+7z

^{-1}+z

^{-3}.

4. What is the one sided z-transform of x(n)=δ(n-k)?

a) z^{-k}

b) z^{k}

c) 0

d) 1

View Answer

Explanation: Since the signal x(n)= δ(n-k) is a causal signal i.e., it is defined for n>0 and x(n)=1 at z=k

So, from the definition of one sided z-transform X

^{+}(z)=z

^{-k}.

5. What is the one sided z-transform of x(n)=δ(n+k)?

a) z^{-k}

b) 0

c) z^{k}

d) 1

View Answer

Explanation: Since the signal x(n)= δ(n+k) is an anti causal signal i.e., it is defined for n<0 and x(n)=1 at z= -k. Since the one sided z-transform is defined only for causal signal, in this case X

^{+}(z)=0.

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)?

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7. If x(n)=a^{n}, then what is one sided z-transform of x(n-2)?

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8. If x(n)=a^{n}, then what is one sided z-transform of x(n+2)?

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9. If X+(z) is the one sided z-transform of the signal x(n), then lim┬(n→∞)x(n)=lim┬(z→1)(z-1) X^{+} (z) is called Final value theorem.

a) True

b) False

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Explanation: In the above theorem, we are calculating the value of x(n) at infinity, so it is called as final value theorem.

10. The impulse response of a relaxed LTI system is h(n)=a^{n}u(n),|a|<1. What is the value of the step response of the system as n→∞?

a) 1/(1+a)

b) 1/(1-a)

c) a/(1+a)

d) a/(1-a)

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Explanation: The step response of the system is y(n)=x(n)*h(n) where x(n)=u(n)

On applying z-transform on both sides, we get

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?

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**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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