Quantization Effects

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Quantization Effects in the Computation of DFT”.

1. 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

2. 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

3. How many quantization errors are present in one complex valued multiplication?
a) One
b) Two
c) Three
d) Four

4. 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

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

6. The 4N quantization errors are mutually uncorrelated.
a) True
b) False

7. The 4N quantization errors are correlated with the sequence {x(n)}.
a) True
b) False
.

8. 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

9. 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

10. What is the variance of the output DFT coefficients |X(k)|?
a) 1N
b) 12N
c) 13N
d) 14N

11. What is the signal-to-noise ratio?
a) σX2q2
b) σX2q2
c) σX2q2
d) σX2q2

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

13. How many number of butterflies are required per output point in FFT algorithm?
a) N
b) N+1
c) 2N
d) N-1

14. 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

15. 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

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