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 e_q (n) is bounded in magnitude i.e.,

| e_q (n) | < ∆/2

and the resulting error is called?

a) Granular noise

b) Overload noise

c) Particulate noise

d) Heavy noise

View Answer

Explanation: In the statistical approach, we assume that the quantization error is random in nature. We model this error as noise that is added to the original (unquantized) signal. If the input analog signal is within the range of the quantizer, the quantization error e_q (n) is bounded in magnitude

i.e.,

| e_q (n) | < ∆/2

and the resulting error is called Granular noise.

a) Granular noise

b) Overload noise

c) Particulate noise

d) Heavy noise

View Answer

Explanation: In the statistical approach, we assume that the quantization error is random in nature. We model this error as noise that is added to the original (unquantized) signal. If the input analog signal falls outside the range of the quantizer (clipping), e_q (n) becomes unbounded and results in overload noise.

3. In the mathematical model for the quantization error e_q (n), to carry out the analysis, what are the assumptions made about the statistical properties of e_q (n)?

1. The error e_q (n) is uniformly distributed over the range — ∆ /2 < e_q (n) < ∆ /2.

2. The error sequence is a stationary white noise sequence. In other words, the error e_q (m) and the error e_q (n) for m≠n are uncorrelated.

3. The error sequence {e_q (n)} is uncorrelated with the signal sequence x(n).

4. The signal sequence x(n) is zero mean and stationary.

a) 1, 2 & 3

b) 1,2,3,4

c) 1, 3

d) 2, 3, 4

View Answer

Explanation: In the mathematical model for the quantization error e_q (n). To carry out the analysis, the following are the assumptions made about the statistical properties of e_q (n).

1. The error e_q (n) is uniformly distributed over the range — ∆ /2 < e_q (n) < ∆ /2.

2. The error sequence is a stationary white noise sequence. In other words, the error e_q (m)and the error e_q (n) for m≠n are uncorrelated.

3. The error sequence {e_q (n)} is uncorrelated with the signal sequence x(n).

4. The signal sequence x(n) is zero mean and stationary.

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

View Answer

Explanation: The effect of the additive noise e_q (n) on the desired signal can be quantified by evaluating the signal-to-quantization noise (power) ratio (SQNR).

5. What is the scale used for the measurement of SQNR?

a) DB

b) db

c) dB

d) All of the mentioned

View Answer

Explanation: The effect of the additive noise e_q (n) on the desired signal can be quantified by evaluating the signal-to-quantization noise (power) ratio (SQNR), which can be expressed on a logarithmic scale (in decibels or dB)

6. What is the expression for SQNR which can be expressed in a logarithmic scale?

View Answer

Explanation: The signal-to-quantization noise (power) ratio (SQNR), which can be expressed on a logarithmic scale (in decibels or dB) :

SQNR =

7. In the equation SQNR = what are the terms P_x and P_n 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

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Explanation: In the equation SQNR = then the terms P_x is the signal power and P_n is the power of the quantization noise

d) None of the mentioned

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9. If the quantization error is uniformly distributed in the range (-∆ /2, ∆ /2) ,the mean value of the error is zero then the variance P_n is?

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10. By combining with P_n=σ_(e )^2= ∆^2/12 and substituting the result into SQNR = what is the final expression for SQNR = ?

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11. In the equation SQNR = for R = 6σ_x 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

View Answer

Explanation: For example, if we assume that x(n) is Gaussian distributed and the range o f the quantizer extends from -3σ_x to 3σ_x (i.e., R = 6σ_x ), then less than 3 out o f every 1000 input signal amplitudes would result in an overload on the average. For R = 6σ_x , then the equation becomes

SQNR = 6.02b+1.25 dB.

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