What is the difference between linear quantization and nonlinear quantization?

Question

What is the difference between linear quantization and nonlinear quantization? I am talking about PCM samples. http://www.blurtit.com/q927781.html contains an article about this, but I'm looking for a more detailed answer.

Answer 1

It is pretty simple. With linear quantization, each increment in the sample corresponds to an analog increment of a fixed size. For instance. 8 bits of AD or DA with an analog range of 0 - 1 V have 1/256 = 3.9 mV per bit, regardless of the actual signal amplitude.

With nonlinear quantization, you usually have some kind of logarithmic coding (e.g. μ-Law or A-law ), so the increment for small sample values ​​is much smaller than the increment for large sample values. Ideally, the step size should be approximately proportional to the sample size. This means a fixed S / N ratio (due to quantization noise), regardless of the amplitude of the signal. Another way to look 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 for each sample, except when the sample size exactly matches the middle of the decision level. If smaller steps are taken, the quantization error will be less. However, increasing the steps will complicate the coding process and increase the bandwidth requirements. The quantization of noise depends on the step size, and not on the signal amplitude

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

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

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

At the receiving end, 101 converted to a pulse of +1.5V (the average value of the decision level in the encoder) This causes a 0.2V error between the original input and output signals.

Nonlinear quantization In linear quantization, the signal-to-noise ratio is large for high levels, but small for low-level signals.

Therefore, nonlinear quantization is used.

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