What is the difference between Linear Quantization and Non-linear Quantization?

Question

What is the difference between Linear Quantization and Non-linear Quantization ? I'm talking with regard to PCM samples. http://www.blurtit.com/q927781.html has an article about it but I'm looking for a more elaborate answer.

Answer 1

It's pretty simple really. With linear quantization every increment in the sampled value corresponds to a fixed size analogue increment. E.g. an 8 bit A-D or D-A with a 0 - 1 V analogue range has 1 / 256 = 3.9 mV per bit, regardless of the actual signal amplitude.

With non-linear quantization you normally have some sort of logarithmic encoding (e.g. µ-Law or A-law), so that the increment for small sample values is much smaller than the increment for large sample values. Ideally the step size should be roughly proportional to the sample size. This translates to a fixed S/N ratio (due to quantization noise), regardless of the signal amplitude. Another way of looking at this is that you can use fewer bits to get a given S/N ratio over the signal amplitude range of interest.

Answer 2

Errors occur on every sample except where the sample size exactly coincides the mid-point of the decision level. If smaller steps are taken the quantization error will be less. However, increasing the steps will complicate the coding operation and increase bandwidth requirements. Quantizing noise depends on step size and not on signal amplitude

The quantizing intervals are of equal size. Quantization noise: the difference between the input signal and the quantized output signal Signal-to-quantized-noise ratio S/N= 6n+1.76 dB n=8, S/N=49.76 dB In other words, every added binary digit increases the ratio by 6dBs Example

Consider sample 2, the actual amplitude of the signal is +1.7V.

This is assigned level 2 (same for any voltage between 1 & 2), which is transmitted as line code 101.

At the receiving end 101 is converted to a pulse of +1.5V (the middle value of the decision level at the encoder) This produces an error of 0.2V between original input and output signals.

Non-Linear Quantization With linear quantization, the signal to noise ratio is large for high levels but small for low level signals.

Therefore, non-linear quantization is used.

The quantizing intervals are not of equal size. Small quantizing intervals are allocated to small signal values (samples) and large quantization intervals to large samples so that the signal-to-quantization distortion ratio is nearly independent of the signal level. S/N ratios for weak signals are much better but are slightly less for the stronger signals. Commanding: a process in which compression is followed by expansion. Two separate laws are used A-Law adopted by ITU-T for 30 channel PCM. µ-law used mainly in USA,Canada and Japan.