# Z Transform Inversion MCQ’s

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

1. What is the partial fraction expansion of X(z)=1+z−11−z−1+0.5z−2?

a) z(0.5−1.5j)z−0.5−0.5j–z(0.5+1.5j)z−0.5+0.5j

b) z(0.5−1.5j)z−0.5−0.5j+z(0.5+1.5j)z−0.5+0.5j

c) z(0.5+1.5j)z−0.5−0.5j–z(0.5−1.5j)z−0.5+0.5j

d) z(0.5+1.5j)z−0.5−0.5j+z(0.5−1.5j)z−0.5+0.5j

2. What is the inverse z-transform of X(z)=11−1.5z−1+0.5z−2 if ROC is |z|<0.5?

a) [-2-0.5^{n}]u(n)

b) [-2+0.5^{n}]u(n)

c) [-2+0.5^{n}]u(-n-1)

d) [-2-0.5^{n}]u(-n-1)

3. What is the inverse z-transform of X(z)=11−1.5z−1+0.5z−2 if ROC is |z| < 0.5?

a) {….62,30,14,6,**2**}

b) {…..62,30,14,6,2,0,**0**}

c) {0,0,2,6,14,30,62…..}

d) {2,6,14,30,62…..}

4. Which of the following method is used to find the inverse z-transform of a signal?

a) Counter integration

b) Expansion into a series of terms

c) Partial fraction expansion

d) All of the mentioned

5. What is the proper fraction and polynomial form of the improper rational transform

X(z)=1+3z−1+116z−2+13z−31+56z−1+16z−2?

a) 1+2z^{-1}+16z−11+56z−1+16z−2

b) 1-2z^{-1}+16z−11+56z−1+16z−2

c) 1+2z^{-1}+13z−11+56z−1+16z−2

d) 1+2z^{-1}–16z−11+56z−1+16z−2

6. What is the inverse z-transform of X(z)=11−1.5z−1+0.5z−2 if ROC is |z|>1?

a) {1,3/2,7/4,15/8,31/16,….}

b) {1,2/3,4/7,8/15,16/31,….}

c) {1/2,3/4,7/8,15/16,31/32,….}

d) None of the mentioned

7. What is the partial fraction expansion of the proper function X(z)=11−1.5z−1+0.5z−2?

a) 2zz−1−zz+0.5

b) 2zz−1+zz−0.5

c) 2zz−1+zz+0.5

d) 2zz−1−zz−0.5

8. What is the inverse z-transform of X(z)=11−1.5z−1+0.5z−2 if ROC is 0.5<|z|<1?

a) -2u(-n-1)+(0.5)^{n}u(n)

b) -2u(-n-1)-(0.5)^{n}u(n)

c) -2u(-n-1)+(0.5)^{n}u(-n-1)

d) 2u(n)+(0.5)^{n}u(-n-1)

9. What is the inverse z-transform of X(z)=11−1.5z−1+0.5z−2 if ROC is |z|>1?

a) (2-0.5^{n})u(n)

b) (2+0.5^{n})u(n)

c) (2^{n}-0.5^{n})u(n)

d) None of the mentioned

10. What is the causal signal x(n) having the z-transform X(z)=1(1+z−1)(1−z−1)2?

a) [1/4(-1)^{n}+3/4-n/2]u(n)

b) [1/4(-1)^{n}+3/4-n/2]u(-n-1)

c) [1/4+3/4(-1)^{n}-n/2]u(n)

d) [1/4(-1)^{n}+3/4+n/2]u(n)

11. What is the inverse z-transform of X(z)=log(1+az^{-1}) |z|>|a|?

a) x(n)=(-1)n+1 a−nn, n≥1; x(n)=0, n≤0

b) x(n)=(-1)n-1 a−nn, n≥1; x(n)=0, n≤0

c) x(n)=(-1)n+1 a−nn, n≥1; x(n)=0, n≤0

d) None of the mentioned

12. What is the partial fraction expansion of X(z)=1(1+z−1)(1−z−1)2?

a) z4(z+1)+3z4(z−1)+z2(z+1)2

b) z4(z+1)+3z4(z−1)–z2(z+1)2

c) z4(z+1)+3z4(z−1)+z2(z−1)2

d) z4(z+1)+z4(z−1)+z2(z+1)2

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