companding

Companding is a signal processing technique that improves the dynamic range of a signal as it passes through a system with limited dynamic range, such as an analog-to-digital converter or a communication channel. The process involves compressing the signal's dynamic range before transmission or quantization and then expanding it back to its original form at the receiver.

In telephony and related applications, two standard companding laws are widely used: mu-law (mu-law) and A-law. Mu-law is favored in North America and Japan, while A-law is standardized in Europe and many other regions. Both implement a nonlinear mapping that emphasizes finer resolution for smaller amplitudes and larger amplitudes, though they differ in their exact piecewise or logarithmic formulations. The encoder maps input amplitudes to a smaller dynamic range, and the decoder applies the inverse function to recover the signal at the destination.

The primary purpose of companding is to improve the effective signal-to-quantization-noise ratio. By reallocating quantization steps toward smaller signals, low-level components are preserved more accurately, while higher-amplitude parts are compressed. This is particularly advantageous in systems with limited bit depth or bandwidth, such as PCM voice channels, radio transmitters, and certain data links.

Companding is distinct from data compression, as it is a nonlinear, lossy transformation applied in the analog or early digital domain to facilitate subsequent quantization and transmission. It requires matched encoder and decoder implementations to avoid distortion. Limitations include introduced nonlinearity and the need for compatible circuitry; it is less suitable for signals with high crest factors or in systems with significant nonlinearities elsewhere in the chain.