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)?

$\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)_N $

$\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)$

$\sum_{n=0}^{N-1}x_1 (n) x_2 (m-n)$

$\sum_{n=0}^{N-1}x_1 (n) x_2 (m-n)_N $

$\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)_N $

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

$\frac{1}{N} \sum_{k=0}^{N-1} x(k) cos⁡\frac{2πkn}{N}$

$j \frac{1}{N} \sum_{k=0}^{N-1} x(k) sin⁡\frac{2πkn}{N}$

$\frac{1}{N} \sum_{k=0}^{N-1} x(k) cos⁡\frac{2πkn}{N}$

$-j \frac{1}{N} \sum_{k=0}^{N-1} x(k) sin⁡\frac{2πkn}{N}$

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

-j$\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}$

$\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}$

$\sum_{n=0}^{N-1} x(n) cos⁡\frac{2πkn}{N}$

-j$\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}$

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

$\sum_{n=0}^N x_R (n) cos⁡\frac{2πkn}{N}+x_I (n) sin⁡\frac{2πkn}{N}$

$\sum_{n=0}^N x_R (n) cos⁡\frac{2πkn}{N}-x_I (n) sin⁡\frac{2πkn}{N}$

$\sum_{n=0}^{N-1} x_R (n) cos⁡\frac{2πkn}{N}-x_I (n) sin⁡\frac{2πkn}{N}$

$\sum_{n=0}^{N-1} x_R (n) cos⁡\frac{2πkn}{N}+x_I (n) sin⁡\frac{2πkn}{N}$

16 + Mcqs in Properties Dft in Digital Signal Processing Page 1 McqOptions

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^{-j2‚âà√¨‚àö√ëkl/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

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. \(\sum_{n=0}^{N-1}x_1 (n) x_2 (m+n)_N \)

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. \(\frac{1}{N} \sum_{k=0}^{N-1} x(k) cos⁡\frac{2πkn}{N}\)

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\(\sum_{n=0}^{N-1} x(n) sin⁡\frac{2πkn}{N}\)

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.

Explore topic-wise MCQs in Digital Signal Processing.

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

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.

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?

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

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)?

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

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

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

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

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‚âà√¨‚àö√ëkl/N.$#

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?$

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

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

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)?

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

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

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‚âà√¨‚àö√ëkl/N}.$#