Signal to Quantization Noise Ratio in PCM System

Signal to Quantization Noise Ratio (SQNR) is a measure of the quality of a PCM system. It represents the ratio of the power of the input signal to the power of the quantization noise. In a PCM system, the analog signal is sampled, quantized, and then encoded into binary code words. The length of the code word determines the number of quantization levels and hence affects the quantization noise.

Effect of Increasing Code Word Length

Increasing the code word length in a PCM system has a significant impact on the SQNR. When the code word length is increased from 6 to 8 bits, the SQNR improves by a factor of 16.

Explanation:

1. Code Word Length: The code word length represents the number of bits used to encode each sample in the PCM system. A longer code word length allows for more quantization levels and hence reduces the quantization noise.

2. Quantization Noise: Quantization noise is the error introduced during the quantization process. It is caused by the difference between the actual analog signal and its quantized representation. A higher code word length reduces the quantization noise and improves the signal quality.

3. Number of Quantization Levels: The number of quantization levels in a PCM system is given by 2^n, where n is the code word length. For example, with a 6-bit code word length, there are 2^6 = 64 quantization levels. Similarly, with an 8-bit code word length, there are 2^8 = 256 quantization levels.

4. SQNR Calculation: The SQNR can be calculated using the formula:
SQNR = (Power of Signal) / (Power of Quantization Noise)

5. Power of Signal: The power of the signal is directly proportional to the square of the amplitude of the signal. Increasing the code word length does not affect the power of the signal.

6. Power of Quantization Noise: The power of the quantization noise is inversely proportional to the number of quantization levels. As the code word length increases, the number of quantization levels also increases, leading to a decrease in the power of the quantization noise.

7. Improvement in SQNR: Since the power of the signal remains the same and the power of the quantization noise decreases, the SQNR improves. In this case, the improvement is by a factor of 16, which is equal to (2^8) / (2^6).

Conclusion:

Increasing the code word length in a PCM system improves the SQNR by increasing the number of quantization levels and reducing the quantization noise. In this specific case, increasing the code word length from 6 to 8 bits improves the SQNR by a factor of 16.