If the number bits per sample in a PCM system is increased from 16 to 17, the improvement in signal to quantization noise ratio will be : 

Explanation:

Improvement in Signal to Quantization Noise Ratio in PCM System

Definition: In a Pulse Code Modulation (PCM) system, the signal to quantization noise ratio (SQNR) is a measure of the quality of the digitized signal. It compares the power of the original signal to the power of the quantization noise, which is introduced during the digitization process.

Quantization Noise: Quantization noise is the error introduced when an analog signal is quantized to a finite number of levels. This noise is inherent in the process of converting an analog signal to a digital signal and is a function of the number of bits used in the quantization process.

Key Formula: The SQNR in a PCM system can be approximated using the following formula:

SQNR (dB) ≈ 6.02N + 1.76

where N is the number of bits per sample.

Analysis:

Given the initial number of bits per sample (N₁) is 16, the initial SQNR (SQNR₁) can be calculated as follows:

SQNR₁ (dB) ≈ 6.02 × 16 + 1.76 = 96.32 dB

When the number of bits per sample is increased to 17 (N₂), the new SQNR (SQNR₂) can be calculated as:

SQNR₂ (dB) ≈ 6.02 × 17 + 1.76 = 102.34 dB

The improvement in SQNR is the difference between the new SQNR and the initial SQNR:

Improvement in SQNR (dB) = SQNR₂ - SQNR₁

Improvement in SQNR (dB) = 102.34 dB - 96.32 dB = 6.02 dB

However, since we are looking for an approximate improvement, we can round this value to the nearest whole number, which gives us:

Improvement in SQNR ≈ 6 dB

Correct Option:

The correct option is:

Option 3: 6 dB

This option reflects the fact that increasing the number of bits per sample by 1 in a PCM system results in an improvement of approximately 6 dB in the signal to quantization noise ratio.