Question

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. 1/16
• B. 16
• C. 3/16
• D. log 16

Hint:

In PCM, every extra bit increases SQNR by a factor of 4 (6 dB), so 2 bits = 4 × 4 = 16× improvement.

Answer 1

The Correct Option is B

In Pulse Code Modulation (PCM), the Signal to Quantization Noise Ratio (SQNR) is proportional to the square of the number of quantization levels: \[ \text{SQNR} \propto 2^{2n} \] Where \( n \) is the number of bits per sample. If the number of bits increases from 6 to 8: \[ \text{Old SQNR} \propto 2^{2 \cdot 6} = 2^{12}
\text{New SQNR} \propto 2^{2 \cdot 8} = 2^{16} \] So, the improvement factor is: \[ \frac{2^{16}}{2^{12}} = 2^4 = 16 \]