Analog and Digital Conversion/Non-Uniform Quantization
Consider the situation where we have an analog voice signal. This voice signal tends to stay within certain amplitude limits, although on occasion there are some high-amplitude moments. We can say, for instance, that most of the analog signal is between 0V and 5V, although on occasion the signal can get as high as 20V. It would seem that we want to spend more of our resources in the bottom quarter of our range, and not worry so much about the upper parts of the range.
If our sampler has a resolution of 5 bits (32 levels), then a full 3/4ths, (24) of our levels are essentially a waste of space! Now, what if there was a way to "spend" more of our levels, and use more of our bits, between 0V and 5V, and not spend many levels at all on the upper 15V of our range. There is a way to do this, and it's called Non-Uniform Quantization.
Compression and Expansion
The μ Transform (or "Mu Transform") is a method of non-uniform quantization. This transform takes certain parameters, and can produce a non-uniform quantizer, to meet specific needs.