Explore topic-wise MCQs in Digital Signal Processing.

This section includes 13 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(jω0n)u(n)?

A. \(\frac{z^{-1} sin\omega_0}{1+2z^{-1} cosω_0+z^{-2}}\)
B. \(\frac{z^{-1} sin\omega_0}{1-2z^{-1} cosω_0-z^{-2}}\)
C. \(\frac{1-z^{-1} cos\omega_0}{1-2z^{-1} cosω_0+z^{-2}}\)
D. \(\frac{z^{-1} sin\omega_0}{1-2z^{-1} cosω_0+z^{-2}}\)
Answer» D. \(\frac{z^{-1} sin\omega_0}{1-2z^{-1} cosω_0+z^{-2}}\)
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 signal whose z-transform is given as X(z)=\(\frac{1}{2πj} \oint X_1 (v) X_2 (\frac{z}{v})v^{-1} dv\)?

A. x1(n)*x2(n)
B. x1(n)*x2(-n)
C. x1(n).x2(n)
D. x1(n)*x2*(n)
Answer» D. x1(n)*x2*(n)
Discussion
6.

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
7.

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
8.

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. \(\lim_{z \rightarrow 1} [(z-1) ⁡ X(z)] \)
B. \(\lim_{z \rightarrow 0} [(z-1) ⁡ X(z)] \)
C. \(\lim_{z \rightarrow -1} [(z-1) X(z)] \)
D. \(\lim_{z \rightarrow 1} [(z+1) ⁡ X(z)] \)
Answer» B. \(\lim_{z \rightarrow 0} [(z-1) ⁡ X(z)] \)
Discussion
9.

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
10.

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. X1(z).X2(z-1)
B. X1(z).X2(z-1)
C. X1(z).X2(z)
D. X1(z).X2(-z)
Answer» C. X1(z).X2(z)
Discussion
11.

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
12.

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

A. X1(z).X2(z)
B. X1(z)+X2(z)
C. X1(z)*X2(z)
D. None of the mentioned
Answer» B. X1(z)+X2(z)
Discussion
13.

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