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For 10 bit PCM system, the signal to quantization noise ratio is 62 dB. If the number of bits is increased by 2, then the signal to quantization noise ratio will
- a)increased by 6 dB
- b)increased by 12 dB
- c)decreased by 6 dB
- d)decreased by 12 dB
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
For 10 bit PCM system, the signal to quantization noise ratio is 62 dB...
= (SNR)Q + 6.02 x 2 
(SNE)Q + 12 dB.
(SNE)Q + 12 dB.Most Upvoted Answer
For 10 bit PCM system, the signal to quantization noise ratio is 62 dB...
Signal to Quantization Noise Ratio (SQNR)
The Signal to Quantization Noise Ratio (SQNR) is a measure of the quality of a digital signal. It represents the ratio of the power of the signal to the power of the quantization noise introduced during the quantization process.
Given Information
- 10 bit PCM system
- SQNR = 62 dB
Solution
To determine the effect of increasing the number of bits by 2 on the SQNR, we need to calculate the new SQNR after the increase.
Calculating the Initial SQNR
The SQNR can be calculated using the formula:
SQNR = 6.02 * N + 1.76 dB
where N is the number of bits.
In our case, for a 10-bit PCM system, the initial SQNR is given as 62 dB. So, we can substitute the value of N as 10 in the formula:
62 = 6.02 * 10 + 1.76
62 = 60.2 + 1.76
62 = 61.96 dB (approximately)
Calculating the New SQNR
Now, let's calculate the new SQNR after increasing the number of bits by 2.
For a new N, the formula becomes:
SQNR = 6.02 * (N+2) + 1.76 dB
Substituting the value of N as 10, we get:
SQNR = 6.02 * (10+2) + 1.76
SQNR = 6.02 * 12 + 1.76
SQNR = 72.24 + 1.76
SQNR = 74 dB (approximately)
Comparison and Conclusion
By comparing the initial SQNR (61.96 dB) with the new SQNR (74 dB), we can see that the new SQNR is higher. Therefore, the signal to quantization noise ratio has increased by 12 dB when the number of bits is increased by 2.
Answer
The correct answer is option B: increased by 12 dB.
The Signal to Quantization Noise Ratio (SQNR) is a measure of the quality of a digital signal. It represents the ratio of the power of the signal to the power of the quantization noise introduced during the quantization process.
Given Information
- 10 bit PCM system
- SQNR = 62 dB
Solution
To determine the effect of increasing the number of bits by 2 on the SQNR, we need to calculate the new SQNR after the increase.
Calculating the Initial SQNR
The SQNR can be calculated using the formula:
SQNR = 6.02 * N + 1.76 dB
where N is the number of bits.
In our case, for a 10-bit PCM system, the initial SQNR is given as 62 dB. So, we can substitute the value of N as 10 in the formula:
62 = 6.02 * 10 + 1.76
62 = 60.2 + 1.76
62 = 61.96 dB (approximately)
Calculating the New SQNR
Now, let's calculate the new SQNR after increasing the number of bits by 2.
For a new N, the formula becomes:
SQNR = 6.02 * (N+2) + 1.76 dB
Substituting the value of N as 10, we get:
SQNR = 6.02 * (10+2) + 1.76
SQNR = 6.02 * 12 + 1.76
SQNR = 72.24 + 1.76
SQNR = 74 dB (approximately)
Comparison and Conclusion
By comparing the initial SQNR (61.96 dB) with the new SQNR (74 dB), we can see that the new SQNR is higher. Therefore, the signal to quantization noise ratio has increased by 12 dB when the number of bits is increased by 2.
Answer
The correct answer is option B: increased by 12 dB.
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For 10 bit PCM system, the signal to quantization noise ratio is 62 dB...
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For 10 bit PCM system, the signal to quantization noise ratio is 62 dB. If the number of bits is increased by 2, then the signal to quantization noise ratio willa)increased by 6 dBb)increased by 12 dBc)decreased by 6 dBd)decreased by 12 dBCorrect answer is option 'B'. Can you explain this answer?
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