Explore topic-wise MCQs in Digital Signal Processing.

This section includes 15 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 z-transform of the signal x(n)=[5(3n)-9(7n)]u(n)?

A. ( frac{5}{1-3z^{-1}}- frac{9}{1-7z^{-1}} )
B. ( frac{5}{1+3z^{-1}}- frac{9}{1+7z^{-1}} )
C. ( frac{5}{1-3z}- frac{9}{1-7z} )
D. None of the mentioned
Answer» B. ( frac{5}{1+3z^{-1}}- frac{9}{1+7z^{-1}} )
Discussion
2.

What is the z-transform of the signal defined as x(n)=u(n)-u(n+N)?

A. ( frac{1+z^N}{1+z^{-1}} )
B. ( frac{1-z^N}{1-z^{-1}} )
C. ( frac{1+z^{-N}}{1+z^{-1}} )
D. ( frac{1-z^{-N}}{1-z^{-1}} )
Answer» E.
Discussion
3.

What is the z-transform of the signal x(n)=cos(j 0n)u(n)?

A. ( frac{z^{-1} sin omega_0}{1+2z^{-1} cos _0+z^{-2}} )
B. ( frac{z^{-1} sin omega_0}{1-2z^{-1} cos _0-z^{-2}} )
C. ( frac{1-z^{-1} cos omega_0}{1-2z^{-1} cos _0+z^{-2}} )
D. ( frac{z^{-1} sin omega_0}{1-2z^{-1} cos _0+z^{-2}} )
Answer» D. ( frac{z^{-1} sin omega_0}{1-2z^{-1} cos _0+z^{-2}} )
Discussion
4.

If x1(n)={1,2,3} and x2(n)={1,1,1}, then what is the convolution sequence of the given two signals?

A. {1,2,3,1,1}
B. {1,2,3,4,5}
C. {1,3,5,6,2}
D. {1,2,6,5,3}
Answer» E.
Discussion
5.

What is the z-transform of the signal x(n)= x1(n).x2*(n)?

A. ( frac{1}{2 j} oint X_1(v) X_2 ( frac{z}{v})v^{-1} dv )
B. ( frac{1}{2 j} oint X_1(v) X_2^* ( frac{z^*}{v^*})v^{-1} dv )
C. ( frac{1}{2 j} oint X_1(v) X_2^* ( frac{z}{v})v^{-1} dv )
D. None of the mentioned
Answer» C. ( frac{1}{2 j} oint X_1(v) X_2^* ( frac{z}{v})v^{-1} dv )
Discussion
6.

What is the signal whose z-transform is given as X(z)= ( frac{1}{2 j} oint X_1 (v) X_2 ( frac{z}{v})v^{-1} dv )?

A. x<sub>1</sub>(n)*x<sub>2</sub>(n)
B. x<sub>1</sub>(n)*x<sub>2</sub>(-n)
C. x<sub>1</sub>(n).x<sub>2</sub>(n)
D. x<sub>1</sub>(n)*x<sub>2</sub>*(n)
Answer» D. x<sub>1</sub>(n)*x<sub>2</sub>*(n)
Discussion
7.

If x(n) is an imaginary sequence, then the z-transform of the real part of the sequence is?

A. ( frac{1}{2} )[X(z)+X*(z*)]
B. ( frac{1}{2} )[X(z)-X*(z*)]
C. ( frac{1}{2} )[X(-z)-X*(z*)]
D. ( frac{1}{2} )[X(-z)+X*(z*)]
Answer» B. ( frac{1}{2} )[X(z)-X*(z*)]
Discussion
8.

If X(z) is the z-transform of the signal x(n), then what is the z-transform of x*(n)?

A. X(z*)
B. X*(z)
C. X*(-z)
D. X*(z*)
Answer» E.
Discussion
9.

What is the z-transform of the signal x(n)= (n-n0)?

A. z<sup>n<sub>0</sub></sup>
B. z<sup>-n<sub>0</sub></sup>
C. z<sup>n-n<sub>0</sub></sup>
D. z<sup>n+n<sub>0</sub></sup>
Answer» C. z<sup>n-n<sub>0</sub></sup>
Discussion
10.

If Z{x(n)}=X(z) and the poles of X(z) are all inside the unit circle, then the final value of x(n) as (n rightarrow infty ) is given by i.e., ( lim_{n rightarrow infty} )x(n)=?

A. ( lim_{z rightarrow 1} [(z-1) u2061 X(z)] )
B. ( lim_{z rightarrow 0} [(z-1) u2061 X(z)] )
C. ( lim_{z rightarrow -1} [(z-1) X(z)] )
D. ( lim_{z rightarrow 1} [(z+1) u2061 X(z)] )
Answer» B. ( lim_{z rightarrow 0} [(z-1) u2061 X(z)] )
Discussion
11.

If x(n) is causal, then ( lim_{z rightarrow infty} ) X(z)=?

A. x(-1)
B. x(1)
C. x(0)
D. Cannot be determined
Answer» D. Cannot be determined
Discussion
12.

If Z{x1(n)}=X1(z) and Z{x2(n)}=X2(z) then what is the z-transform of correlation between the two signals?

A. X<sub>1</sub>(z).X<sub>2</sub>(z<sup>-1</sup>)
B. X<sub>1</sub>(z).X<sub>2</sub>(z<sup>-1</sup>)
C. X<sub>1</sub>(z).X<sub>2</sub>(z)
D. X<sub>1</sub>(z).X<sub>2</sub>(-z)
Answer» C. X<sub>1</sub>(z).X<sub>2</sub>(z)
Discussion
13.

What is the convolution x(n) of the signals x1(n)={1,-2,1} and x2(n)={1,1,1,1,1,1}?

A. {1,1,0,0,0,0,1,1}
B. {-1,-1,0,0,0,0,-1,-1}
C. {-1,1,0,0,0,0,1,-1}
D. {1,-1,0,0,0,0,-1,1}
Answer» E.
Discussion
14.

If Z{x1(n)}=X1(z) and Z{x2(n)}=X2(z) then Z{x1(n)*x2(n)}=?

A. X<sub>1</sub>(z).X<sub>2</sub>(z)
B. X<sub>1</sub>(z)+X<sub>2</sub>(z)
C. X<sub>1</sub>(z)*X<sub>2</sub>(z)
D. None of the mentioned
Answer» B. X<sub>1</sub>(z)+X<sub>2</sub>(z)
Discussion
15.

What is the signal x(n) whose z-transform X(z)=log(1+az-1);|z|&gt;|a|?

A. ((-1)^n. frac{a^n}{n}.u(n-1) )
B. ((-1)^n. frac{a^n}{n}.u(n+1) )
C. ((-1)^{n-1}. frac{a^n}{n}.u(n-1) )
D. ((-1)^{n-1}. frac{a^n}{n}.u(n+1) )
Answer» D. ((-1)^{n-1}. frac{a^n}{n}.u(n+1) )
Discussion