Quantization Errors Analysis

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Analysis of Quantization Errors”.

1. If the input analog signal is within the range of the quantizer, the quantization error eq (n) is bounded in magnitude i.e., |eq (n)| < Δ/2 and the resulting error is called?
a) Granular noise
b) Overload noise
c) Particulate noise
d) Heavy noise

2. If the input analog signal falls outside the range of the quantizer (clipping), eq (n) becomes unbounded and results in _____________
a) Granular noise
b) Overload noise
c) Particulate noise
d) Heavy noise

3. In the mathematical model for the quantization error eq (n), to carry out the analysis, what are the assumptions made about the statistical properties of eq (n)?
i. The error eq (n) is uniformly distributed over the range — Δ/2 < eq (n) < Δ/2.
ii. The error sequence is a stationary white noise sequence. In other words, the error eq (m) and the error eq (n) for m≠n are uncorrelated.
iii. The error sequence {eq (n)} is uncorrelated with the signal sequence x(n).
iv. The signal sequence x(n) is zero mean and stationary.
a) i, ii & iii
b) i, ii, iii, iv
c) i, iii
d) ii, iii, iv

4. What is the abbreviation of SQNR?
a) Signal-to-Quantization Net Ratio
b) Signal-to-Quantization Noise Ratio
c) Signal-to-Quantization Noise Region
d) Signal-to-Quantization Net Region

5. What is the scale used for the measurement of SQNR?
a) DB
b) db
c) dB
d) All of the mentioned

6. What is the expression for SQNR which can be expressed in a logarithmic scale?
a) 10 log10PxPn
b) 10 log10PnPx
c) 10 log2PxPn
d) 2 log2PxPn

7. In the equation SQNR = 10 log10PxPn. what are the terms Px and Pn are called ___ respectively.
a) Power of the Quantization noise and Signal power
b) Signal power and power of the quantization noise
c) None of the mentioned
d) All of the mentioned

8. In the equation SQNR = 10 ⁡log10PxPn, what are the expressions of Px and Pn?
a) Px=σ2=E[x2(n)]andPn=σ2e=E[e2q(n)]
b) Px=σ2=E[x2(n)]andPn=σ2e=E[e3q(n)]
c) Px=σ2=E[x3(n)]andPn=σ2e=E[e2q(n)]
d) None of the mentioned

9. If the quantization error is uniformly distributed in the range (-Δ/2, Δ/2), the mean value of the error is zero then the variance Pn is?
a) Pn=σ2e=Δ2/12
b) Pn=σ2e=Δ2/6
c) Pn=σ2e=Δ2/4
d) Pn=σ2e=Δ2/2

10. By combining Δ=R2b+1 with Pn=σ2e=Δ2/12 and substituting the result into SQNR = 10 log10PxPn, what is the final expression for SQNR = ?
a) 6.02b + 16.81 + 20log10Rσx
b) 6.02b + 16.81 – 20log10Rσx
c) 6.02b – 16.81 – 20log10Rσx
d) 6.02b – 16.81 – 20log10Rσx

11. In the equation SQNR = 6.02b + 16.81 – 20log10Rσx, for R = 6σx the equation becomes?
a) SQNR = 6.02b-1.25 dB
b) SQNR = 6.87b-1.55 dB
c) SQNR = 6.02b+1.25 dB
d) SQNR = 6.87b+1.25 dB

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