25 + Mcqs in Inverse Z Transform Page 1 McqOptions

1.	The value of inverse Z-transform of log($\frac{z}{z+1}$) is _______________
A.	(-1)n/n for n = 0; 0 otherwise
B.	(-1)n/n
C.	0, for n = 0; (-1)n/n, otherwise
D.	0
Answer» D. 0

Discussion

2.	Given the z-transform pair$X[n] \leftrightarrow \frac{32}{z^2-16}$, \|z\|
A.	$\frac{(z+1)^2}{(z+1)^2-16} + \frac{(z-1)^2}{(z-1)^2-16}$
B.	$\frac{z^2 (1+z)}{z^2-16}$
C.	$\frac{z^2 (z-1)}{z^2-16}$
D.	$\frac{(z+2)^2}{(z+2)^2-16}$
Answer» C. $\frac{z^2 (z-1)}{z^2-16}$

Discussion

3.	The value of $Z^{-1}\Big\{\frac{z^2}{(z-a)(z-b)}\Big\}$ is ____________
A.	$\frac{a^{n+1} – b^{n+1}}{a+b}$
B.	}\Big\}\) is ____________a) $\frac{a^{n+1} – b^{n+1}}{a+b}$ b) $\frac{a^{n+1} – b^{n+1}}{a-b}$
C.	$\frac{a^{n+1} + b^{n+1}}{a-b}$
D.	$\frac{a^{n+1} + b^{n+1}}{a+b}$
Answer» C. $\frac{a^{n+1} + b^{n+1}}{a-b}$

Discussion

4.	The system described by the difference equation y(n) – 2y(n-1) + y(n-2) = X(n) – X(n-1) has y(n) = 0 and n
A.	2
B.	1
C.	0
D.	-1
Answer» D. -1

Discussion

5.	Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to {X(z)}2 is ___________
A.	{x[n]}2
B.	x[n]*x[n]
C.	x[n]*x[-n]
D.	x[-n]*x[-n]
Answer» C. x[n]*x[-n]

Discussion

6.	Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to $\frac{z^2-z^{-2}}{2}$ X(z) is ___________
A.	$\frac{1}{2}$(x[n+2]-x[n-2])
B.	(x[n+2]-x[n-2])
C.	$\frac{1}{2}$(x[n-2]-x[n+2])
D.	(x[n-2]-x[n+2])
Answer» B. (x[n+2]-x[n-2])

Discussion

7.	Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to $\frac{dX(z)}{dz}$ is ___________
A.	(n-1)33n-1u[n-1]
B.	n33nu[n-1]
C.	(1-n)33n-1u[n-1]
D.	(n-1)33n-1u[n]
Answer» D. (n-1)33n-1u[n]

Discussion

8.	Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to X(z-1) is ___________
A.	n23-nu[n]
B.	n23-nu[-n]
C.	$\frac{1}{n^2} 3^{\frac{1}{n}} u[n]$
D.	$\frac{1}{n^2} 3^{\frac{1}{n}} u[-n]$
Answer» C. $\frac{1}{n^2} 3^{\frac{1}{n}} u[n]$

Discussion

9.	What is the causal signal x(n) having the z-transform X(z)=$\frac{1}{(1+z^{-1})(1-z^{-1})^2}$?
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)
Answer» E.

Discussion

10.	What is the inverse z-transform of X(z)=$\frac{1}{1-1.5z^{-1}+0.5z^{-2}}$ if ROC is 0.5
A.	-2u(-n-1)+(0.5)nu(n)
B.	-2u(-n-1)-(0.5)nu(n)
C.	-2u(-n-1)+(0.5)nu(-n-1)
D.	2u(n)+(0.5)nu(-n-1)
Answer» C. -2u(-n-1)+(0.5)nu(-n-1)

Discussion

11.	What is the inverse z-transform of X(z)=$\frac{1}{1-1.5z^{-1}+0.5z^{-2}}$ if ROC is \|z\|
A.	[-2-0.5n]u(n)
B.	[-2+0.5n]u(n)
C.	[-2+0.5n]u(-n-1)
D.	[-2-0.5n]u(-n-1)
Answer» D. [-2-0.5n]u(-n-1)

Discussion

12.	What is the partial fraction expansion of the proper function X(z)=$\frac{1}{1-1.5z^{-1}+0.5z^{-2}}$?
A.	$\frac{2z}{z-1}-\frac{z}{z+0.5}$
B.	$\frac{2z}{z-1}+\frac{z}{z-0.5}$
C.	$\frac{2z}{z-1}+\frac{z}{z+0.5}$
D.	$\frac{2z}{z-1}-\frac{z}{z-0.5}$
Answer» E.

Discussion

13.	What is the proper fraction and polynomial form of the improper rational transformX(z)=$\frac{1+3z^{-1}+\frac{11}{6} z^{-2}+\frac{1}{3} z^{-3}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}$?
A.	1+2z-1+$\frac{\frac{1}{6}z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}$
B.	1-2z-1+$\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}$
C.	1+2z-1+$\frac{\frac{1}{3} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}$
D.	1+2z-1–$\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}$
Answer» B. 1-2z-1+$\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}$

Discussion

14.	What is the inverse z-transform of X(z)=log(1+az-1) \|z\|>\|a\|?
A.	x(n)=(-1)n+1 $\frac{a^{-n}}{n}$, n≥1; x(n)=0, n≤0
B.	x(n)=(-1)n-1 $\frac{a^{-n}}{n}$, n≥1; x(n)=0, n≤0
C.	x(n)=(-1)n+1 $\frac{a^{-n}}{n}$, n≥1; x(n)=0, n≤0
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

15.	What is the inverse z-transform of X(z)=$\frac{1}{1-1.5z^{-1}+0.5z^{-2}}$ 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…..}
Answer» C. {0,0,2,6,14,30,62…..}

Discussion

16.	What is the inverse z-transform of X(z)=$\frac{1}{1-1.5z^{-1}+0.5z^{-2}}$ 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
Answer» B. {1,2/3,4/7,8/15,16/31,….}

Discussion

17.	WHAT_IS_THE_INVERSE_Z-TRANSFORM_OF_X(Z)=_1/(1-1.5Z-1+0.5Z2-2_)_IF_ROC_IS_\|Z\|>1??$
A.	(2-0.5<sup>n</sup>)u(n)
B.	(2+0.5<sup>n</sup>)u(n)
C.	(2<sup>n</sup>-0.5<sup>n</sup>)u(n)
D.	None of the mentioned
Answer» B. (2+0.5<sup>n</sup>)u(n)

Discussion

18.	What_is_the_inverse_z-transform_of_X(z)=_1/(1-1.5z-1+0.5z-2_)_if_ROC_is_\|z\|
A.	[-2+0.5<sup>n</sup>]u(n)
B.	[-2+0.5<sup>n</sup>]u(-n-1)
C.	[-2-0.5<sup>n</sup>]u(-n-1)
Answer» D.

Discussion

19.	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)<sup>n</sup>+3/4-n/2]u(n)
B.	[1/4(-1)<sup>n</sup>+3/4-n/2]u(-n-1)
C.	[1/4+3/4(-1)<sup>n</sup>-n/2]u(n)
D.	[1/4(-1)<sup>n</sup>+3/4+n/2]u(n)
Answer» E.

Discussion

20.	What is the partial fraction expansion of X(z)=1/((1+z-1 )(1-z-1)2)?
A.	z/(4(z+1)) + 3z/(4(z-1)) + z/(2‚Äö√Ñ√ª‚àö√ë‚àö¬±(z+1)‚Äö√Ñ√ª‚àö√ë‚àö‚â•<sup>2</sup> )
B.	z/(4(z+1)) + 3z/(4(z-1)) ‚Äö√Ñ√∂‚àö√ë‚àö¬® z/(2‚Äö√Ñ√ª‚àö√ë‚àö¬±(z+1)‚Äö√Ñ√ª‚àö√ë‚àö‚â•<sup>2</sup> )
C.	z/(4(z+1)) + 3z/(4(z-1)) + z/(2‚Äö√Ñ√ª‚àö√ë‚àö¬±(z-1)‚Äö√Ñ√ª‚àö√ë‚àö‚â•<sup>2</sup> )
D.	z/(4(z+1)) + z/(4(z-1)) + z/(2‚Äö√Ñ√ª‚àö√ë‚àö¬±(z+1)‚Äö√Ñ√ª‚àö√ë‚àö‚â•<sup>2</sup> )
Answer» D. z/(4(z+1)) + z/(4(z-1)) + z/(2‚Äö√Ñ√ª‚àö√ë‚àö¬±(z+1)‚Äö√Ñ√ª‚àö√ë‚àö‚â•<sup>2</sup> )

Discussion

21.	What is the partial fraction expansion of X(z)= (1+z-1)/(1-z-1+0.5z-2 )?
A.	(z(0.5-1.5j))/(z-0.5-0.5j) ‚Äö√Ñ√∂‚àö√ë‚àö¬® (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) ‚Äö√Ñ√∂‚àö√ë‚àö¬® (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)
Answer» C. (z(0.5+1.5j))/(z-0.5-0.5j) ‚Äö√Ñ√∂‚àö√ë‚àö¬® (z(0.5-1.5j))/(z-0.5+0.5j)

Discussion

22.	What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2 )?
A.	2z/(z-1)-z/(z+0.5)
B.	2z/(z-1)+z/(z-0.5)
C.	2z/(z-1)+z/(z+0.5)
D.	2z/(z-1)-z/(z-0.5)
Answer» E.

Discussion

23.	What is the proper fraction and polynomial form of the improper rational transform
A.	= (1+3z<sup>-1</sup>+11/6 z<sup>-2</sup>+1/3 z<sup>-3</sup>)/(1+5/6 z<sup>-1</sup>+1/6 z<sup>-2</sup> )?
B.	1+2z -1+(1/6 z<sup>-1</sup>)/(1+5/6 z<sup>-1</sup>+1/6 z<sup>-2</sup> )
C.	1-2z -1+(1/6 z<sup>-1</sup>)/(1+5/6 z<sup>-1</sup>+1/6 z<sup>-2</sup> )
D.	1+2z -1+(1/3 z<sup>-1</sup>)/(1+5/6 z<sup>-1</sup>+1/6 z<sup>-2</sup>)
Answer» B. 1+2z -1+(1/6 z<sup>-1</sup>)/(1+5/6 z<sup>-1</sup>+1/6 z<sup>-2</sup> )

Discussion

24.	What is the inverse z-transform of X(z)=1/(1-1.5z-1+0.5z-2 ) if ROC is \|z\|>1?
A.	{1,3/2,7/4,15/8,31/16,‚Äö√Ñ√∂‚àö√ë¬¨‚àÇ.}
B.	{1,2/3,4/7,8/15,16/31,‚Äö√Ñ√∂‚àö√ë¬¨‚àÇ.}
C.	{1/2,3/4,7/8,15/16,31/32,‚Äö√Ñ√∂‚àö√ë¬¨‚àÇ.}
D.	None of the mentioned
Answer» B. {1,2/3,4/7,8/15,16/31,‚Äö√Ñ√∂‚àö√ë¬¨‚àÇ.}

Discussion

25.	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
Answer» E.

Discussion

2.	Given the z-transform pair\(X[n] \leftrightarrow \frac{32}{z^2-16}\), \|z\|
A.	\(\frac{(z+1)^2}{(z+1)^2-16} + \frac{(z-1)^2}{(z-1)^2-16}\)
B.	\(\frac{z^2 (1+z)}{z^2-16}\)
C.	\(\frac{z^2 (z-1)}{z^2-16}\)
D.	\(\frac{(z+2)^2}{(z+2)^2-16}\)
Answer» C. \(\frac{z^2 (z-1)}{z^2-16}\)

3.	The value of \(Z^{-1}\Big\{\frac{z^2}{(z-a)(z-b)}\Big\}\) is ____________
A.	\(\frac{a^{n+1} – b^{n+1}}{a+b}\)
B.	}\Big\}\) is ____________a) \(\frac{a^{n+1} – b^{n+1}}{a+b}\) b) \(\frac{a^{n+1} – b^{n+1}}{a-b}\)
C.	\(\frac{a^{n+1} + b^{n+1}}{a-b}\)
D.	\(\frac{a^{n+1} + b^{n+1}}{a+b}\)
Answer» C. \(\frac{a^{n+1} + b^{n+1}}{a-b}\)

13.	What is the proper fraction and polynomial form of the improper rational transformX(z)=\(\frac{1+3z^{-1}+\frac{11}{6} z^{-2}+\frac{1}{3} z^{-3}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)?
A.	1+2z-1+\(\frac{\frac{1}{6}z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)
B.	1-2z-1+\(\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)
C.	1+2z-1+\(\frac{\frac{1}{3} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)
D.	1+2z-1–\(\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)
Answer» B. 1-2z-1+\(\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)

Explore topic-wise MCQs in Digital Signal Processing.

The value of inverse Z-transform of log(\(\frac{z}{z+1}\)) is _______________

Given the z-transform pair\(X[n] \leftrightarrow \frac{32}{z^2-16}\), |z|

The value of \(Z^{-1}\Big\{\frac{z^2}{(z-a)(z-b)}\Big\}\) is ____________

The system described by the difference equation y(n) – 2y(n-1) + y(n-2) = X(n) – X(n-1) has y(n) = 0 and n

Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to {X(z)}2 is ___________

Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to \(\frac{z^2-z^{-2}}{2}\) X(z) is ___________

Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to \(\frac{dX(z)}{dz}\) is ___________

Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to X(z-1) is ___________

What is the causal signal x(n) having the z-transform X(z)=\(\frac{1}{(1+z^{-1})(1-z^{-1})^2}\)?

What is the inverse z-transform of X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is 0.5

What is the inverse z-transform of X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z|

What is the partial fraction expansion of the proper function X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\)?

What is the proper fraction and polynomial form of the improper rational transformX(z)=\(\frac{1+3z^{-1}+\frac{11}{6} z^{-2}+\frac{1}{3} z^{-3}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)?

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

What is the inverse z-transform of X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z| < 0.5?

What is the inverse z-transform of X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z|>1?

WHAT_IS_THE_INVERSE_Z-TRANSFORM_OF_X(Z)=_1/(1-1.5Z-1+0.5Z2-2_)_IF_ROC_IS_|Z|>1??$

What_is_the_inverse_z-transform_of_X(z)=_1/(1-1.5z-1+0.5z-2_)_if_ROC_is_|z|

What_is_the_causal_signal_x(n)_having_the_z-transform_X(z)=_1/((1+z-1_)_[(1-z-1)]2_)?

What is the partial fraction expansion of X(z)=1/((1+z-1 )(1-z-1)2)?

What is the partial fraction expansion of X(z)= (1+z-1)/(1-z-1+0.5z-2 )?

What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2 )?

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

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

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

6.	Given the z-transform pair 3nn2 u[n] ↔ X (z). The time signal corresponding to \(\frac{z^2-z^{-2}}{2}\) X(z) is ___________
A.	\(\frac{1}{2}\)(x[n+2]-x[n-2])
B.	(x[n+2]-x[n-2])
C.	\(\frac{1}{2}\)(x[n-2]-x[n+2])
D.	(x[n-2]-x[n+2])
Answer» B. (x[n+2]-x[n-2])

12.	What is the partial fraction expansion of the proper function X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\)?
A.	\(\frac{2z}{z-1}-\frac{z}{z+0.5}\)
B.	\(\frac{2z}{z-1}+\frac{z}{z-0.5}\)
C.	\(\frac{2z}{z-1}+\frac{z}{z+0.5}\)
D.	\(\frac{2z}{z-1}-\frac{z}{z-0.5}\)
Answer» E.

14.	What is the inverse z-transform of X(z)=log(1+az-1) \|z\|>\|a\|?
A.	x(n)=(-1)n+1 \(\frac{a^{-n}}{n}\), n≥1; x(n)=0, n≤0
B.	x(n)=(-1)n-1 \(\frac{a^{-n}}{n}\), n≥1; x(n)=0, n≤0
C.	x(n)=(-1)n+1 \(\frac{a^{-n}}{n}\), n≥1; x(n)=0, n≤0
D.	None of the mentioned
Answer» D. None of the mentioned