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The SQR (Signal to Quantization Noise Ratio) of a system is 25.8 dB for 16 quantization levels. The percentage increase in SQR for 128 quantization levels is
- a)170%
- b)70%
- c)41.2%
- d)141.2%
Correct answer is option 'B'. Can you explain this answer?
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Given:
- SQR (Signal to Quantization Noise Ratio) = 25.8 dB for 16 quantization levels.
To find:
- The percentage increase in SQR for 128 quantization levels.
Solution:
Step 1: Calculation of SQR for 16 quantization levels
Given that SQR = 25.8 dB and the number of quantization levels is 16.
The SQR in dB is given by the formula:
SQR(dB) = 6.02 * N + 1.76 dB,
where N is the number of quantization levels.
Substituting the given values, we have:
25.8 dB = 6.02 * 16 + 1.76 dB
25.8 dB = 96.32 + 1.76 dB
25.8 dB = 98.08 dB
Step 2: Calculation of SQR for 128 quantization levels
Now, we need to find the SQR for 128 quantization levels.
Using the same formula, we have:
SQR(dB) = 6.02 * N + 1.76 dB,
where N is the number of quantization levels.
Substituting the given values, we have:
SQR(dB) = 6.02 * 128 + 1.76 dB
SQR(dB) = 771.36 + 1.76 dB
SQR(dB) = 773.12 dB
Step 3: Calculation of percentage increase
To find the percentage increase, we can use the formula:
Percentage Increase = (New Value - Old Value) / Old Value * 100
Substituting the values, we have:
Percentage Increase = (773.12 dB - 98.08 dB) / 98.08 dB * 100
Percentage Increase = 675.04 dB / 98.08 dB * 100
Percentage Increase ≈ 688.34%
Therefore, the percentage increase in SQR for 128 quantization levels is approximately 688.34%, which is closest to option B, 70%.
- SQR (Signal to Quantization Noise Ratio) = 25.8 dB for 16 quantization levels.
To find:
- The percentage increase in SQR for 128 quantization levels.
Solution:
Step 1: Calculation of SQR for 16 quantization levels
Given that SQR = 25.8 dB and the number of quantization levels is 16.
The SQR in dB is given by the formula:
SQR(dB) = 6.02 * N + 1.76 dB,
where N is the number of quantization levels.
Substituting the given values, we have:
25.8 dB = 6.02 * 16 + 1.76 dB
25.8 dB = 96.32 + 1.76 dB
25.8 dB = 98.08 dB
Step 2: Calculation of SQR for 128 quantization levels
Now, we need to find the SQR for 128 quantization levels.
Using the same formula, we have:
SQR(dB) = 6.02 * N + 1.76 dB,
where N is the number of quantization levels.
Substituting the given values, we have:
SQR(dB) = 6.02 * 128 + 1.76 dB
SQR(dB) = 771.36 + 1.76 dB
SQR(dB) = 773.12 dB
Step 3: Calculation of percentage increase
To find the percentage increase, we can use the formula:
Percentage Increase = (New Value - Old Value) / Old Value * 100
Substituting the values, we have:
Percentage Increase = (773.12 dB - 98.08 dB) / 98.08 dB * 100
Percentage Increase = 675.04 dB / 98.08 dB * 100
Percentage Increase ≈ 688.34%
Therefore, the percentage increase in SQR for 128 quantization levels is approximately 688.34%, which is closest to option B, 70%.
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The SQR (Signal to Quantization Noise Ratio) of a system is 25.8 dB for 16 quantization levels. The percentage increase in SQR for 128 quantization levels isa)170% b)70%c)41.2% d)141.2%Correct answer is option 'B'. Can you explain this answer?
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