Mulaw

Mu-law, often written as μ-law, is a companding algorithm used in digital telephony to optimize the dynamic range of audio signals encoded with 8-bit PCM. It is standardized in ITU-T G.711 and is widely used in North America and Japan. The goal is to compress the wide dynamic range of human speech into a format that can be efficiently quantized with 8 bits, improving the signal-to-noise ratio for low-amplitude signals.

Mu-law applies a nonlinear logarithmic compression to the amplitude before quantization. The typical parameter for 8-bit mu-law is μ = 255. The forward transform maps a linear PCM amplitude to an 8-bit code word; the receiver performs the inverse companding to reconstruct a linear waveform. The net effect is reduced quantization noise for quieter passages while preserving larger amplitudes.

Mu-law is often contrasted with A-law, the European alternative. Both laws implement the same general purpose but have slightly different companding curves; G.711 defines both to support interoperation across regions.

Implementation notes: in software and hardware, mu-law encoding follows a piecewise-law function with sign-preserving compression, then quantization to 8 bits; decoding applies the inverse function. In practice, μ-law is commonly used for 8-bit PCM in telephone systems and is supported in many audio APIs and codecs, including VoIP.

History: Mu-law originated in the Bell System as a method to improve voice quality over telephone channels, and it remains a foundational component of PCM telephony today.