Explore topic-wise MCQs in Digital Signal Processing.

This section includes 9 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-j2 kl/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 u2061 frac{2 kn}{N} )
B. ( frac{1}{N} sum_{k=0}^{N-1} x(k) cos u2061 frac{2 kn}{N} )
C. (-j frac{1}{N} sum_{k=0}^{N-1} x(k) sin u2061 frac{2 kn}{N} )
D. None of the mentioned
Answer» B. ( frac{1}{N} sum_{k=0}^{N-1} x(k) cos u2061 frac{2 kn}{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 u2061 frac{2 kn}{N} )
B. ( sum_{n=0}^{N-1} x(n) cos u2061 frac{2 kn}{N} )
C. -j ( sum_{n=0}^{N-1} x(n) sin u2061 frac{2 kn}{N} )
D. None of the mentioned
Answer» C. -j ( sum_{n=0}^{N-1} x(n) sin u2061 frac{2 kn}{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 u2061 frac{2 kn}{N}+x_I (n) sin u2061 frac{2 kn}{N} )
B. ( sum_{n=0}^N x_R (n) cos u2061 frac{2 kn}{N}-x_I (n) sin u2061 frac{2 kn}{N} )
C. ( sum_{n=0}^{N-1} x_R (n) cos u2061 frac{2 kn}{N}-x_I (n) sin u2061 frac{2 kn}{N} )
D. ( sum_{n=0}^{N-1} x_R (n) cos u2061 frac{2 kn}{N}+x_I (n) sin u2061 frac{2 kn}{N} )
Answer» E.
Discussion
9.

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. X<sub>1</sub>(ak)+X<sub>2</sub>(bk)
B. aX<sub>1</sub>(k)+bX<sub>2</sub>(k)
C. e<sup>ak</sup>X<sub>1</sub>(k)+e<sup>bk</sup>X<sub>2</sub>(k)
D. None of the mentioned
Answer» C. e<sup>ak</sup>X<sub>1</sub>(k)+e<sup>bk</sup>X<sub>2</sub>(k)
Discussion