Explore topic-wise MCQs in Digital Signal Processing.

This section includes 16 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.

If X(k) is the N-point DFT of a sequence x(n), then what is the DFT of x*(n)?

A. X(N-k)
B. X*(k)
C. X*(N-k)
D. None of the mentioned
Answer» D. None of the mentioned
Discussion
2.

If X(k) is the N-point DFT of a sequence x(n), then circular time shift property is that N-point DFT of x((n-l))N is X(k)e-j2πkl/N.

A. True
B. False
Answer» B. False
Discussion
3.

What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}, find using the DFT and IDFT concepts?

A. {16,16,14,14}
B. {14,16,14,16}
C. {14,14,16,16}
D. None of the mentioned
Answer» C. {14,14,16,16}
Discussion
4.

What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}?

A. {14,14,16,16}
B. {16,16,14,14}
C. {2,3,6,4}
D. {14,16,14,16}
Answer» E.
Discussion
5.

If X1(n), x2(n) and x3(m) are three sequences each of length N whose DFTs are given as X1(k), X2(k) and X3(k) respectively and X3(k)=X1(k).X2(k), then what is the expression for x3(m)?

A. \(\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)\)
B. \(\sum_{n=0}^{N-1}x_1 (n) x_2 (m-n)\)
C. \(\sum_{n=0}^{N-1}x_1 (n) x_2 (m-n)_N \)
D. \(\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)_N \)
Answer» D. \(\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)_N \)
Discussion
6.

If x(n) is real and odd, then what is the IDFT of the given sequence?

A. \(j \frac{1}{N} \sum_{k=0}^{N-1} x(k) sin⁡\frac{2πkn}{N}\)
B. \(\frac{1}{N} \sum_{k=0}^{N-1} x(k) cos⁡\frac{2πkn}{N}\)
C. \(-j \frac{1}{N} \sum_{k=0}^{N-1} x(k) sin⁡\frac{2πkn}{N}\)
D. None of the mentioned
Answer» B. \(\frac{1}{N} \sum_{k=0}^{N-1} x(k) cos⁡\frac{2πkn}{N}\)
Discussion
7.

If x(n) is real and even, then what is the DFT of x(n)?

A. \(\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}\)
B. \(\sum_{n=0}^{N-1} x(n) cos⁡\frac{2πkn}{N}\)
C. -j\(\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}\)
D. None of the mentioned
Answer» C. -j\(\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}\)
Discussion
8.

If x(n) is a complex valued sequence given by x(n)=xR(n)+jxI(n), then what is the DFT of xR(n)?

A. \(\sum_{n=0}^N x_R (n) cos⁡\frac{2πkn}{N}+x_I (n) sin⁡\frac{2πkn}{N}\)
B. \(\sum_{n=0}^N x_R (n) cos⁡\frac{2πkn}{N}-x_I (n) sin⁡\frac{2πkn}{N}\)
C. \(\sum_{n=0}^{N-1} x_R (n) cos⁡\frac{2πkn}{N}-x_I (n) sin⁡\frac{2πkn}{N}\)
D. \(\sum_{n=0}^{N-1} x_R (n) cos⁡\frac{2πkn}{N}+x_I (n) sin⁡\frac{2πkn}{N}\)
Answer» E.
Discussion
9.

WHAT_IS_THE_CIRCULAR_CONVOLUTION_OF_THE_SEQUENCES_X1(N)={2,1,2,1}_AND_X2(N)={1,2,3,4}??$

A. {14,14,16,16}
B. {16,16,14,14}
C. {2,3,6,4}
D. {14,16,14,16}
Answer» E.
Discussion
10.

If X(k) is the N-point DFT of a sequence x(n), then circular time shift property is that N-point DFT of x((n-l))N is X(k)e-j2πkl/N.$#

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

What_is_the_circular_convolution_of_the_sequences_x1(n)={2,1,2,1}_and_x2(n)={1,2,3,4},_find_using_the_DFT_and_IDFT_concepts?$

A. {16,16,14,14}
B. {14,16,14,16}
C. {14,14,16,16}
D. None of the mentioned
Answer» C. {14,14,16,16}
Discussion
12.

If_X(k)_is_the_N-point_DFT_of_a_sequence_x(n),_then_what_is_the_DFT_of_x*(n)?

A. X(N-k)
B. X*(k)
C. X*(N-k)
D. None of the mentioned
Answer» B. X*(k)
Discussion
13.

If x(n) is a real sequence and X(k) is its N-point DFT, then which of the following is true?

A. X(N-k)=X(-k)
B. X(N-k)=X*(k)
C. X(-k)=X*(k)
D. All of the mentioned
Answer» E.
Discussion
14.

If X1(k) and X2(k) are the N-point DFTs of x1(n) and x2(n) respectively, then what is the N-point DFT of x(n)=ax1(n)+bx2(n)?

A. X1(ak)+X2(bk)
B. aX1(k)+bX2(k)
C. e<sup>ak</sup>X1(k)+e<sup>bk</sup>X2(k)
D. None of the mentioned
Answer» C. e<sup>ak</sup>X1(k)+e<sup>bk</sup>X2(k)
Discussion
15.

If x(n) and X(k) are an N-point DFT pair, then X(k+N)=?

A. X(-k)
B. -X(k)
C. X(k)
D. None of the mentioned
Answer» D. None of the mentioned
Discussion
16.

If x(n) and X(k) are an N-point DFT pair, then x(n+N)=x(n).

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