Question

4.1. To explain how the signal dynamic range is related with the number of bits in codewords.

4.2. Analyse the linear quantization characteristic, parameters, features.

4.3. Analyse the nonlinear quantization characteristic, parameters features.

Answer 1

(4.1) Signal dynamic range is the ratio of the largest signal that exists to the noise present when no signal exists. They describe the ratio between the largest representable number to the quantization error.

Some of the comparison of codewords in bits with signal dynamic range is given below.

16-bit Audio Converters	90 to 95 dB
18-bit Audio Converters	104 dB
20-bit Audio Converters	110 dB
24-bit Audio Converters	110 to 120 dB

Dynamic Range = Peak Level - Noise Floor in dB

An n bit data word yields 2n quantization levels.

Further, dynamic range(dB)=6.02n+1.76 dB=6n(nearly).

(4.2 and 4.3) Quantization is the process of mapping input values from a large continuous set to output values in a smaller finite set. Eg:- Rounding and truncation.

With linear quantization, every increment in the sampled value corresponds to a fixed size increment, independent of the actual signal amplitude. Here, the signal to noise ratio is large for high levels but small for low level signals. The quantizing intervals are of equal size.

With non-linear quantization, there is generally some sort of logarithmic encoding, so that the increment for small sample values is much smaller than the increment for large sample values. The step size should be almost proportional to the sample size. Thus, S/N ratio due to quantization noise, is regardless of the signal amplitude. We can use fewer bits to get a given S/N ratio over the signal amplitude range of interest.