Number of bits in a binary PCM system is increased from n to n + 2. What is the improvement in SNR?

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  1. (n+2) / n
  2. 2(n+2) / n
  3. 2(n+2) / n
  4. independent of n

Answer (Detailed Solution Below)

Option 4 : independent of n
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Detailed Solution

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Explanation:

The SNR in a binary PCM system can be expressed as:

SNR = (6 × n) dB

where n is the number of bits used for quantization. This indicates that the SNR increases linearly with the number of bits used in the PCM system.

Effect of Increasing Number of Bits:

When the number of bits in the PCM system is increased from n to n + 2, the SNR also increases. The improvement in SNR can be calculated using the difference in SNR values before and after increasing the number of bits:

Improvement in SNR = SNR (n + 2) - SNR (n)

Substituting the values:

Improvement in SNR = (6 × (n + 2)) - (6 × n)

Improvement in SNR = 6 × n + 12 - 6 × n

Improvement in SNR = 12 dB

Hence the correct answer is 12 dB

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