Nonlinear Filter Example:
Dynamic Range Compression

A simple practical example of a nonlinear filtering operation is dynamic range compression, such as occurs in Dolby or DBX noise reduction when recording to magnetic tape. The purpose of dynamic range compression is to map the natural dynamic range of a signal to a smaller range. For example, audio can easily span a range of 100 dB or more, while magnetic tape has a linear range on the order of only 55 dB. It is therefore important to compress the dynamic range when making analog recordings to magnetic tape.

Another type of dynamic range compressor is called a limiter, which is used in recording studios to ``soft limit'' a signal when it begins to exceed the available dynamic range. This replaces ``hard clipping'' by ``soft limiting,'' which sounds less harsh and may even go unnoticed if there were no indicator light.

Another variation is the compander (compressor/expander) which intentionally ``flattens'' audio dynamic range for musical purposes.

The preceding examples can all be modeled as a slowly varying gain which automatically turns up the ``volume'' (increases the gain) when the signal level (average magnitude) is low and turns it down when it is high. The gain does not react instantly to the signal, since that would cause too much distortion. Instead, the signal level is measured over a short time which is at least one period of the lowest frequency allowed, and typically several periods of any pitched signal present.

A different kind of dynamic range compressor is the CODEC (coder/decoder chip). CODECs were originally the 8-bit digital audio converters found in telephone transmission equipment, but now they are found in cell phones and on computer motherboards. Most current CODECs use a nonlinear quantization scheme known as mu-law encoding [66]. Mu-law quantization states are distributed almost linearly when the input signal amplitude is low, and they approach an exponential distribution at high amplitudes. Thus, mu-law approaches a log-magnitude encoding at large amplitude.