companded

Companding is a signal processing technique that combines compression of a signal's dynamic range before quantization with expansion on reconstruction. The goal is to improve the effective resolution of an analog-to-digital conversion for signals with a wide dynamic range, most commonly speech, and to reduce quantization noise for low-amplitude parts of the signal.

During encoding, the input signal is passed through a nonlinear transfer function that compresses large amplitudes more than small ones. After transmission or storage, the inverse function expands the signal back to its original dynamic range. Because the compression and expansion are matched, the overall system is designed to be approximately lossless apart from quantization noise, but it is inherently nonlinear.

Two widely used companding schemes in telecommunications are the mu-law and A-law. In ITU-T standards, μ-law is defined for North American and Japanese telephony, while A-law is used in European systems. Both reduce the effective bit depth of the signal prior to quantization (commonly 8-bit PCM) and then recover the dynamic range on playback. The standard implementations are μ-law and A-law with specific characteristic curves and parameters (μ ≈ 255, A ≈ 87.6). Sampling rates are typically 8 kHz for speech codecs in telephony.

Applications include landline telephone networks, wireless voice codecs, and some audio processing pipelines. Benefits include improved signal-to-noise ratio for small signals and reduced data rate for a given perceived quality. Limitations include the nonlinearity of the process, which can complicate processing and requires accurate compensation; distortion for signals with fast dynamics; and reduced fidelity for high-quality music compared with linear processing.