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In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantization noise ratio improves by the factor.
- a)8/6
- b)12
- c)16
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a PCM system, if the code word length is increased from 6 to 8 bits...
Given n1 = 6, n2 = 8,
then (SNR)Q = 22(n2 - n1) 
16.
16.Most Upvoted Answer
In a PCM system, if the code word length is increased from 6 to 8 bits...
Explanation:
Increasing the code word length in a PCM system has a direct impact on the signal to quantization noise ratio.
Signal to Quantization Noise Ratio:
- Signal to Quantization Noise Ratio (SNR) is a measure of the quality of the quantization process in PCM.
- It represents the ratio of the power of the signal to the power of the quantization noise.
Effect of Increasing Code Word Length:
- When the code word length is increased from 6 to 8 bits in a PCM system, the number of quantization levels also increases.
- With more quantization levels, the quantization noise decreases, leading to an improvement in SNR.
Calculation:
- The improvement in SNR can be calculated by the formula: Improvement in SNR = 20 * log10 (2^(n1 - n2)), where n1 and n2 are the initial and final number of bits respectively.
- Substituting n1 = 6 and n2 = 8 into the formula: Improvement in SNR = 20 * log10 (2^(6 - 8)) = 20 * log10 (1/4) = 20 * (-0.6021) ≈ -12 dB.
Therefore, when the code word length is increased from 6 to 8 bits, the SNR improves by a factor of approximately 16 (2^4), which is option 'C'.
Increasing the code word length in a PCM system has a direct impact on the signal to quantization noise ratio.
Signal to Quantization Noise Ratio:
- Signal to Quantization Noise Ratio (SNR) is a measure of the quality of the quantization process in PCM.
- It represents the ratio of the power of the signal to the power of the quantization noise.
Effect of Increasing Code Word Length:
- When the code word length is increased from 6 to 8 bits in a PCM system, the number of quantization levels also increases.
- With more quantization levels, the quantization noise decreases, leading to an improvement in SNR.
Calculation:
- The improvement in SNR can be calculated by the formula: Improvement in SNR = 20 * log10 (2^(n1 - n2)), where n1 and n2 are the initial and final number of bits respectively.
- Substituting n1 = 6 and n2 = 8 into the formula: Improvement in SNR = 20 * log10 (2^(6 - 8)) = 20 * log10 (1/4) = 20 * (-0.6021) ≈ -12 dB.
Therefore, when the code word length is increased from 6 to 8 bits, the SNR improves by a factor of approximately 16 (2^4), which is option 'C'.
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In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantization noise ratio improves by the factor.a)8/6b)12c)16d)8Correct answer is option 'C'. Can you explain this answer?
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