While the compression used in audio recording and the like depends on a variable gain amplifier, and so is a locally linear process (linear for short regions, but not globally), companding is non-linear and takes place in the same way at all points in time. The dynamic range of a signal is compressed before transmission and is expanded to the original value at the receiver.
The use of companding allows signals with a large dynamic range to be transmitted over facilities that have a smaller dynamic range capability. Companding reduces the noise and crosstalk levels at the receiver.
This is sometimes used in digital systems, compressing before input to a analog-to-digital converter, and then expanding after a digital-to-analog converter. This is equivalent to using a non-linear ADC. This is also used in digital file formats for better signal-to-noise ratio at lower bit rates. For example, a linearly encoded 16-bit PCM signal can be converted to an 8-bit WAV or AU file while maintaining a decent signal-to-noise ratio by compressing before the transition to 8-bit and expanding after a conversion back to 16-bit. This is effectively a form of lossy audio data compression.
Companding can also refer to the use of compression, where gain is decreased when levels rise above a certain threshold, and its complement, expansion, where gain is also decreased when levels drop below a certain threshold.
Companding is used in professional wireless microphones to improve the dynamic range of the microphone (the dynamic range of the microphone itself is higher than the dynamic range of the radio transmission).
Companding is sometimes used in digital systems, compressing before input to an analog-to-digital converter, and then expanding after a digital-to-analog converter.