MCQOPTIONS
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MCQOPTIONS
This section includes 25 Mcqs, each offering curated multiple-choice questions to sharpen your Digital Signal Processing knowledge and support exam preparation. Choose a topic below to get started.
| 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 | |
| 2. |
Given the z-transform pair\(X[n] \leftrightarrow \frac{32}{z^2-16}\), |z|<4The z-transform of the signal y[n] = x[n+1] + x[n-1] is _________ |
| 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. \(\frac{a^{n+1} + b^{n+1}}{a-b}\) | |
| 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<0. If x (n) = δ(n), then y (z) will be? |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» D. -1 | |
| 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] | |
| 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]) | |
| 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] | |
| 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. \(\frac{1}{n^2} 3^{\frac{1}{n}} u[n]\) | |
| 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. | |
| 10. |
What is the inverse z-transform of X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is 0.5<|z|<1? |
| 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) | |
| 11. |
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. | [-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) | |
| 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. | |
| 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+\(\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\) | |
| 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 | |
| 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…..} | |
| 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,….} | |
| 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) | |
| 18. |
What_is_the_inverse_z-transform_of_X(z)=_1/(1-1.5z-1+0.5z-2_)_if_ROC_is_|z|<0.5? a)_[-2-0.5n]u(n)$ |
| 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. | |
| 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. | |
| 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„Äñ(z+1)„Äó<sup>2</sup> ) |
| B. | z/(4(z+1)) + 3z/(4(z-1)) – z/(2〖(z+1)〗<sup>2</sup> ) |
| C. | z/(4(z+1)) + 3z/(4(z-1)) + z/(2„Äñ(z-1)„Äó<sup>2</sup> ) |
| D. | z/(4(z+1)) + z/(4(z-1)) + z/(2„Äñ(z+1)„Äó<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> ) | |
| 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) – (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) |
| 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) | |
| 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. | |
| 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> ) | |
| 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,….} |
| 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,‚Äö√Ñ√∂‚àö√묨‚àÇ.} | |
| 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. | |