Linear quantization and Non Linear quantization

Linear quantization : Here quantization step size is uniform. So signals with small amplitude and large amplitude are quantized with the same step size. So in linear method,  quantization error can be higher. Because quantizatied results will not be good for very small amplitude signals.

In the below figure uniform quantization  occurs at 8 different  input signal levels 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5 and 4.0

So here uniform quantization step size is 0.5.

Non Linear quantization :  Here the quantization step size is different.  Eg) logarithmic quantization ( A-law speech codec  and U-law speech codec are good examples of logarithmic quantization).

When considering speech signals, majority of signals will be of lower amplitude only. So we need to concentrate more on these low amplitude signals. So signals with small amplitude are quantized with smaller quantization steps and signals with  large amplitude are quantized with larger step size. As a result quantization errors with lower amplitude signals will decrease, but errors with higher amplitude will increase. But in effect, the total quantization errors will decrease, because higher amplitude speech signals occur only very rarely. 

In the below figure non uniform quantization  occurs at 8 different  input signal levels 0.1, 0.3, 0.6, 1.0, 1,5, 2.2, 3.0 and 4.

So the non-uniform quantization step size is 0.1, 0.2, 0.3, 0.4. 0.5, 0.7, 0.8 and 1.0

Logarithamic quantization is an example of non-linear quantization. Here the quantaization step size will be non-uniform. Step size will be very small at start and then keeps increasing.

In audio codecs, non-linear quantization techniques are used. So for small amplitude signals they will have small step size and for large amplitude signals they will have larger step size. In doing so, the quantization errors which occurs for lower amplitude signals can be decreased. Non-linear quantization is selected because a small error/noise in lower amplitude signals is easily detected by ear.