Explore topic-wise MCQs in Digital Signal Processing.

This section includes 24 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 energy density spectrum of the signal x(n)=anu(n), |a|<1?

A. \(\frac{1}{1+2acosω+a^2}\)
B. \(\frac{1}{1-2acosω+a^2}\)
C. \(\frac{1}{1-2acosω-a^2}\)
D. \(\frac{1}{1+2acosω-a^2}\)
Answer» C. \(\frac{1}{1-2acosω-a^2}\)
Discussion
2.

What is the convolution of the sequences of x1(n)=x2(n)={1,1,1}?

A. {1,2,3,2,1}
B. {1,2,3,2,1}
C. {1,1,1,1,1}
D. {1,1,1,1,1}
Answer» B. {1,2,3,2,1}
Discussion
3.

If X(ω) is the Fourier transform of the signal x(n), then what is the Fourier transform of the signal x(n-k)?

A. ejωk. X(-ω)
B. ejωk. X(ω)
C. e-jωk. X(-ω)
D. e-jωk. X(ω)
Answer» E.
Discussion
4.

What is the Fourier transform of the signal x(n)=a|n|, |a|<1?

A. \(\frac{1+a^2}{1-2acosω+a^2}\)
B. \(\frac{1-a^2}{1-2acosω+a^2}\)
C. \(\frac{2a}{1-2acosω+a^2}\)
D. None of the mentioned
Answer» C. \(\frac{2a}{1-2acosω+a^2}\)
Discussion
5.

If x(n)=A, -M

A. A\(\frac{sin⁡(M-\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\)
B. A2\(\frac{sin⁡(M+\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\)
C. A\(\frac{sin⁡(M+\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\)
D. \(\frac{sin⁡(M-\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\)
Answer» D. \(\frac{sin⁡(M-\frac{1}{2})ω}{sin⁡(\frac{ω}{2})}\)
Discussion
6.

What is the value of |X(ω)| given X(ω)=1/(1-ae-jω), |a|<1?

A. \(\frac{1}{\sqrt{1-2acosω+a^2}}\)
B. \(\frac{1}{\sqrt{1+2acosω+a^2}}\)
C. \(\frac{1}{1-2acosω+a^2}\)
D. \(\frac{1}{1+2acosω+a^2}\)
Answer» B. \(\frac{1}{\sqrt{1+2acosω+a^2}}\)
Discussion
7.

What is the value of XI(ω) given \(\frac{1}{1-ae^{-jω}}\), |a|<1?

A. \(\frac{asinω}{1-2acosω+a^2}\)
B. \(\frac{1+acosω}{1-2acosω+a^2}\)
C. \(\frac{1-acosω}{1-2acosω+a^2}\)
D. \(\frac{-asinω}{1-2acosω+a^2}\)
Answer» E.
Discussion
8.

What is the value of XR(ω) given X(ω)=\(\frac{1}{1-ae^{-jω}}\),|a|<1?

A. \(\frac{asinω}{1-2acosω+a^2}\)
B. \(\frac{1+acosω}{1-2acosω+a^2}\)
C. \(\frac{1-acosω}{1-2acosω+a^2}\)
D. \(\frac{-asinω}{1-2acosω+a^2}\)
Answer» D. \(\frac{-asinω}{1-2acosω+a^2}\)
Discussion
9.

If x(n) is a real and odd sequence, then what is the expression for x(n)?

A. \(\frac{1}{π} \int_0^π\)[XI(ω) sinωn] dω
B. –\(\frac{1}{π} \int_0^π\)[XI(ω) sinωn] dω
C. \(\frac{1}{π} \int_0^π\)[XI(ω) cosωn] dω
D. –\(\frac{1}{π} \int_0^π\)[XI(ω) cosωn] dω
Answer» C. \(\frac{1}{π} \int_0^π\)[XI(ω) cosωn] dω
Discussion
10.

If x(n) is a real signal, then x(n)=\(\frac{1}{π}\int_0^π\)[XR(ω) cosωn- XI(ω) sinωn] dω.

A. True
B. False
Answer» B. False
Discussion
11.

If x(n) is a real sequence, then what is the value of XI(ω)?

A. \(\sum_{n=-∞}^∞ x(n)sin⁡(ωn)\)
B. –\(\sum_{n=-∞}^∞ x(n)sin⁡(ωn)\)
C. \(\sum_{n=-∞}^∞ x(n)cos⁡(ωn)\)
D. –\(\sum_{n=-∞}^∞ x(n)cos⁡(ωn)\)
Answer» C. \(\sum_{n=-∞}^∞ x(n)cos⁡(ωn)\)
Discussion
12.

If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X(ω)=XR(ω)+jXI(ω), then what is the value of xI(n)?

A. \(\frac{1}{2π} \int_0^{2π}\)[XR(ω) sinωn+ XI(ω) cosωn] dω
B. \(\int_0^{2π}\)[XR(ω) sinωn+ XI(ω) cosωn] dω
C. \(\frac{1}{2π} \int_0^{2π}\)[XR(ω) sinωn – XI(ω) cosωn] dω
D. None of the mentioned
Answer» B. \(\int_0^{2π}\)[XR(ω) sinωn+ XI(ω) cosωn] dω
Discussion
13.

If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X(ω)=XR(ω)+jXI(ω), then what is the value of XR(ω)?

A. \(\sum_{n=0}^∞\)xR (n)cosωn-xI (n)sinωn
B. \(\sum_{n=0}^∞\)xR (n)cosωn+xI (n)sinωn
C. \(\sum_{n=-∞}^∞\)xR (n)cosωn+xI (n)sinωn
D. \(\sum_{n=-∞}^∞\)xR (n)cosωn-xI (n)sinωn
Answer» D. \(\sum_{n=-∞}^∞\)xR (n)cosωn-xI (n)sinωn
Discussion
14.

In inverse DTFT, the limits of the integral is defined between -π to π because of the property

A. Time invariance
B. Periodicity
C. Multiplication
D. Implication
Answer» C. Multiplication
Discussion
15.

Consider a complex exponential sequence \({e^{j{\omega _0}n}}\) with frequency ω0. Suppose ω0 = 1, then

A. Such a sequence is periodic
B. Such a sequence is not periodic at all
C. Periodic for some value of period ‘N’
D. Some definite range N0 < n < N exists for a periodic sequence
Answer» C. Periodic for some value of period ‘N’
Discussion
16.

H(ejω) is the frequency response of a discrete time LTI system and H1(ejω) is the frequency response of its inverse function. Then

A. H(ejω)H1(ejω) = 1
B. H(ejω)H1(ejω) = δ(ω)
C. H(ejω) * H1(ejω) = 1
D. H(ejω) * H1 (ejω) = δ(ω)
Answer» B. H(ejω)H1(ejω) = δ(ω)
Discussion
17.

WHAT_IS_THE_VALUE_OF_|X(‚ÂÀ√¨‚ÀÖ¬¢)|_GIVEN_X(‚ÂÀ√¨‚ÀÖ¬¢)=1/(1-AE-J‚ÂÀ√¨‚ÀÖ¬¢_)_,|A|<1??$#

A. 1/√(1-2acosω+a<sup>2</sup> )
B. 1/√(1+2acosω+a<sup>2</sup>)
C. 1/(1-2acosω+a<sup>2</sup> )
D. 1/(1+2acosω+a<sup>2</sup> )
Answer» B. 1/‚Äö√Ñ√∂‚àö‚Ć‚àö‚àÇ(1+2acos‚âà√¨‚àö¬¢+a<sup>2</sup>)
Discussion
18.

What is the Fourier transform of the signal x(n)=a|n|, |a|<1?$

A. (1+a<sup>2</sup>)/(1-2acosω+a<sup>2</sup>)
B. (1-a<sup>2</sup>)/(1-2acosω+a<sup>2</sup>)
C. 2a/(1-2acosω+a<sup>2</sup> )
D. None of the mentioned
Answer» C. 2a/(1-2acos‚âà√¨‚àö¬¢+a<sup>2</sup> )
Discussion
19.

If x(n)=A, -M

A.
B. Asin[(M-1/2)ω]/sin(ω/2)
C. A<sup>2</sup> sin[(M+1/2)ω]/sin(ω/2)
Answer» D.
Discussion
20.

What is the energy density spectrum of the signal x(n)=anu(n), |a|<1?

A. 1/(1+2acosω+a<sup>2</sup> )
B. 1/(1-2acosω+a<sup>2</sup> )
C. 1/(1-2acosω-a<sup>2</sup> )
D. 1/(1+2acosω-a<sup>2</sup> )
Answer» C. 1/(1-2acos‚âà√¨‚àö¬¢-a<sup>2</sup> )
Discussion
21.

What is the convolution of the sequences of x1(n)=x2(n)={1,1,1}?

A. {1,2,<strong>3</strong>,2,1}
B. {1,2,3,2,1}
C. {1,1,1,1,1}
D. {1,1,<strong>1</strong>,1,1}
Answer» B. {1,2,3,2,1}
Discussion
22.

If X(ω) is the Fourier transform of the signal x(n), then what is the Fourier transform of the signal x(n-k)?$

A. e<sup>jωk</sup>. X(-ω)
B. e<sup>jωk</sup>. X(ω)
C. e<sup>-jωk</sup>. X(-ω)
D. e<sup>-jωk</sup>. X(ω)
Answer» E.
Discussion
23.

What is the value of XR(ω) given X(ω)=1/(1-ae-jω ) ,|a|<1?$

A. asinω/(1-2acosω+a<sup>2</sup> )
B. (1+acosω)/(1-2acosω+a<sup>2</sup> )
C. (1-acosω)/(1-2acosω+a<sup>2</sup> )
D. (-asinω)/(1-2acosω+a<sup>2</sup> )
Answer» D. (-asin‚âà√¨‚àö¬¢)/(1-2acos‚âà√¨‚àö¬¢+a<sup>2</sup> )
Discussion
24.

Which of the following relations are true if x(n) is real?

A. X(ω)=X(-ω)
B. X(ω)= -X(-ω)
C. X*(ω)=X(ω)
D. X*(ω)=X(-ω)
Answer» E.
Discussion