Explore topic-wise MCQs in Digital Signal Processing.

This section includes 10 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.

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)<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
2.

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

A. -2u(-n-1)+(0.5)<sup>n</sup>u(n)
B. -2u(-n-1)-(0.5)<sup>n</sup>u(n)
C. -2u(-n-1)+(0.5)<sup>n</sup>u(-n-1)
D. 2u(n)+(0.5)<sup>n</sup>u(-n-1)
Answer» C. -2u(-n-1)+(0.5)<sup>n</sup>u(-n-1)
Discussion
3.

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

A. [-2-0.5<sup>n</sup>]u(n)
B. [-2+0.5<sup>n</sup>]u(n)
C. [-2+0.5<sup>n</sup>]u(-n-1)
D. [-2-0.5<sup>n</sup>]u(-n-1)
Answer» D. [-2-0.5<sup>n</sup>]u(-n-1)
Discussion
4.

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

A. ( frac{z}{4(z+1)} + frac{3z}{4(z-1)} + frac{z}{2(z+1)^2} )
B. ( frac{z}{4(z+1)} + frac{3z}{4(z-1)} frac{z}{2(z+1)^2} )
C. ( frac{z}{4(z+1)} + frac{3z}{4(z-1)} + frac{z}{2(z-1)^2} )
D. ( frac{z}{4(z+1)} + frac{z}{4(z-1)} + frac{z}{2(z+1)^2} )
Answer» D. ( frac{z}{4(z+1)} + frac{z}{4(z-1)} + frac{z}{2(z+1)^2} )
Discussion
5.

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

A. ( frac{z(0.5-1.5j)}{z-0.5-0.5j} frac{z(0.5+1.5j)}{z-0.5+0.5j} )
B. ( frac{z(0.5-1.5j)}{z-0.5-0.5j} + frac{z(0.5+1.5j)}{z-0.5+0.5j} )
C. ( frac{z(0.5+1.5j)}{z-0.5-0.5j} frac{z(0.5-1.5j)}{z-0.5+0.5j} )
D. ( frac{z(0.5+1.5j)}{z-0.5-0.5j} + frac{z(0.5-1.5j)}{z-0.5+0.5j} )
Answer» C. ( frac{z(0.5+1.5j)}{z-0.5-0.5j} frac{z(0.5-1.5j)}{z-0.5+0.5j} )
Discussion
6.

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
7.

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<sup>-1</sup>+ ( frac{ frac{1}{6}z^{-1}}{1+ frac{5}{6} z^{-1}+ frac{1}{6} z^{-2}} )
B. 1-2z<sup>-1</sup>+ ( frac{ frac{1}{6} z^{-1}}{1+ frac{5}{6} z^{-1}+ frac{1}{6} z^{-2}} )
C. 1+2z<sup>-1</sup>+ ( frac{ frac{1}{3} z^{-1}}{1+ frac{5}{6} z^{-1}+ frac{1}{6} z^{-2}} )
D. 1+2z<sup>-1</sup> ( frac{ frac{1}{6} z^{-1}}{1+ frac{5}{6} z^{-1}+ frac{1}{6} z^{-2}} )
Answer» B. 1-2z<sup>-1</sup>+ ( frac{ frac{1}{6} z^{-1}}{1+ frac{5}{6} z^{-1}+ frac{1}{6} z^{-2}} )
Discussion
8.

What is the inverse z-transform of X(z)=log(1+az-1) |z|&gt;|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
9.

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

A. { .62,30,14,6,<strong>2</strong>}
B. { ..62,30,14,6,2,0,<strong>0</strong>}
C. {0,0,2,6,14,30,62 ..}
D. {2,6,14,30,62 ..}
Answer» C. {0,0,2,6,14,30,62 ..}
Discussion
10.

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