20 + Mcqs in Quantization Effects Computation Dft Page 1 McqOptions

1.	How many number of bits are required to compute the DFT of a 1024 point sequence with a SNR of 30db?
A.	15
B.	10
C.	5
D.	20
Answer» B. 10

Discussion

2.	What is the signal-to-noise ratio?
A.	σX2.σq2
B.	σX2/σq2
C.	σX2+σq2
D.	σX2-σq2
Answer» C. σX2+σq2

Discussion

3.	What is the variance of the output DFT coefficients \|X(k)\|?
A.	$\frac{1}{N}$
B.	$\frac{1}{2N}$
C.	$\frac{1}{3N}$
D.	$\frac{1}{4N}$
Answer» D. $\frac{1}{4N}$

Discussion

4.	Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.
A.	True
B.	False
Answer» B. False

Discussion

5.	What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2-b?
A.	(0,Δ)
B.	(-Δ,0)
C.	(-Δ/2,Δ/2)
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

6.	EVERY_FOURFOLD_INCREASE_IN_THE_SIZE_N_OF_THE_DFT_REQUIRES_AN_ADDITIONAL_BIT_IN_COMPUTATIONAL_PRECISION_TO_OFFSET_THE_ADDITIONAL_QUANTIZATION_ERRORS.?$
A.	True
B.	False
Answer» B. False

Discussion

7.	What is the signal-to-noise ratio?$
A.	‚âà√¨‚àö√¢<sub>X</sub><sup>2</sup>. ‚âà√¨‚àö√¢<sub>q</sub><sup>2</sup>
B.	‚âà√¨‚àö√¢<sub>X</sub><sup>2</sup>/ ‚âà√¨‚àö√¢<sub>q</sub><sup>2</sup>
C.	‚âà√¨‚àö√¢<sub>X</sub><sup>2</sup>+ ‚âà√¨‚àö√¢<sub>q</sub><sup>2</sup>
D.	‚âà√¨‚àö√¢<sub>X</sub><sup>2</sup>-‚âà√¨‚àö√¢<sub>q</sub><sup>2</sup>
Answer» C. ‚âà√¨‚àö√¢<sub>X</sub><sup>2</sup>+ ‚âà√¨‚àö√¢<sub>q</sub><sup>2</sup>

Discussion

8.	What_is_the_variance_of_the_output_DFT_coefficients_\|X(k)\|?$
A.	1/N
B.	1/2N
C.	1/3N
D.	1/4N
Answer» D. 1/4N

Discussion

9.	How many number of bits are required to compute the FFT of a 1024 point sequence with a SNR of 30db?
A.	11
B.	10
C.	5
D.	20
Answer» B. 10

Discussion

10.	What is the value of the variance of quantization error in FFT algorithm, compared to that of direct computation?
A.	Greater
B.	Less
C.	Equal
D.	Cannot be compared
Answer» D. Cannot be compared

Discussion

11.	How many number of butterflies are required per output point in FFT algorithm?
A.	N
B.	N+1
C.	2N
D.	N-1
Answer» E.

Discussion

12.	How_many_number_of_bits_are_required_to_compute_the_DFT_of_a_1024_point_sequence_with_a_SNR_of_30db?
A.	15
B.	10
C.	5
D.	20
Answer» B. 10

Discussion

13.	How is the variance of the quantization error related to the size of the DFT?
A.	Equal
B.	Inversely proportional
C.	Square proportional
D.	Proportional
Answer» E.

Discussion

14.	The 4N quantization errors are correlated with the sequence {x(n)}.
A.	True
B.	False
Answer» C.

Discussion

15.	The 4N quantization errors are mutually uncorrelated.
A.	True
B.	False
Answer» B. False

Discussion

16.	What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if ‚âà√≠‚àö√Ü=2-b?$
A.	(0,‚âà√≠‚àö√Ü)
B.	(-‚âà√≠‚àö√Ü,0)
C.	(-‚âà√≠‚àö√Ü/2,‚âà√≠‚àö√Ü/2)
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

17.	What is the total number of quantization errors in the computation of single point DFT of a sequence of length N?
A.	2N
B.	4N
C.	8N
D.	12N
Answer» C. 8N

Discussion

18.	How many quantization errors are present in one complex valued multiplication?
A.	One
B.	Two
C.	Three
D.	Four
Answer» E.

Discussion

19.	What is the model that has been adopt for characterizing round of errors in multiplication?
A.	Multiplicative white noise model
B.	Subtractive white noise model
C.	Additive white noise model
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

20.	The effect of round off errors due to the multiplications performed in the DFT with fixed point arithmetic is known as Quantization error.
A.	True
B.	False
Answer» B. False

Discussion

3.	What is the variance of the output DFT coefficients \|X(k)\|?
A.	\(\frac{1}{N}\)
B.	\(\frac{1}{2N}\)
C.	\(\frac{1}{3N}\)
D.	\(\frac{1}{4N}\)
Answer» D. \(\frac{1}{4N}\)

Explore topic-wise MCQs in Digital Signal Processing.

How many number of bits are required to compute the DFT of a 1024 point sequence with a SNR of 30db?

What is the signal-to-noise ratio?

What is the variance of the output DFT coefficients |X(k)|?

Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.

What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2-b?

EVERY_FOURFOLD_INCREASE_IN_THE_SIZE_N_OF_THE_DFT_REQUIRES_AN_ADDITIONAL_BIT_IN_COMPUTATIONAL_PRECISION_TO_OFFSET_THE_ADDITIONAL_QUANTIZATION_ERRORS.?$

What is the signal-to-noise ratio?$

What_is_the_variance_of_the_output_DFT_coefficients_|X(k)|?$

How many number of bits are required to compute the FFT of a 1024 point sequence with a SNR of 30db?

What is the value of the variance of quantization error in FFT algorithm, compared to that of direct computation?

How many number of butterflies are required per output point in FFT algorithm?

How_many_number_of_bits_are_required_to_compute_the_DFT_of_a_1024_point_sequence_with_a_SNR_of_30db?

How is the variance of the quantization error related to the size of the DFT?

The 4N quantization errors are correlated with the sequence {x(n)}.

The 4N quantization errors are mutually uncorrelated.

What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if ‚âà√≠‚àö√Ü=2-b?$

What is the total number of quantization errors in the computation of single point DFT of a sequence of length N?

How many quantization errors are present in one complex valued multiplication?

What is the model that has been adopt for characterizing round of errors in multiplication?

The effect of round off errors due to the multiplications performed in the DFT with fixed point arithmetic is known as Quantization error.