PCM System and Code Word Length

PCM stands for Pulse Code Modulation, which is a digital representation of an analog signal. In PCM, the analog signal is converted into a digital signal by sampling the signal and quantizing the sampled values into a finite number of levels. The quantized samples are then represented by a series of binary digits called code words.

The code word length is the number of bits used to represent each sample. For example, in a 6-bit PCM system, each sample is represented by a 6-bit code word. Increasing the code word length from 6 to 8 bits means that each sample is now represented by an 8-bit code word.

Signal to Quantization Noise Ratio (SQNR)

SQNR is a measure of the quality of the digitized signal. It is the ratio of the signal power to the quantization noise power. The quantization noise is the error introduced by the quantization process, which results in a loss of information.

Improvement in SQNR

Increasing the code word length from 6 to 8 bits results in an improvement in the SQNR. This is because increasing the number of bits used to represent each sample allows for a greater number of quantization levels, which reduces the quantization error. The improvement in SQNR can be calculated as follows:

Improvement in SQNR = 20log(2^n), where n is the increase in the number of bits.

In this case, n = 8-6 = 2, so the improvement in SQNR is:

Improvement in SQNR = 20log(2^2) = 20log(4) = 20 x 2 = 40 dB

This means that the SQNR improves by a factor of 16 (or 4 bits) when the code word length is increased from 6 to 8 bits. Therefore, the correct answer is option C.