How it works
A compressor applies a logarithmic input–output characteristic before the ADC. For μ-law (μ = 255, used in North America and Japan), the compressed output is y = ln(1+μ|x|)/ln(1+μ) · sgn(x). A-law (A = 87.6, ITU-T G.711 Europe) uses a piecewise linear approximation with 13 segments for implementation ease in digital hardware. Both laws allocate more quantisation levels to small-amplitude signals, improving SNR for low-level speech. The expander at the receiver applies the exact inverse characteristic. Quantisation noise power becomes approximately proportional to signal power, making SNR nearly constant across the dynamic range.
Key points to remember
Companding improves dynamic range by approximately 40 dB compared with uniform PCM at the same number of bits. μ = 255 and A = 87.6 are the standard constants you must memorise for ITU-T G.711. A-law has better small-signal SNR, while μ-law handles overload more gracefully. Both laws approximate logarithmic compression with 8-bit, 256-level quantisation, giving 13-segment (A-law) or 15-segment (μ-law) piecewise linear digital implementations. The term "instantaneous companding" means compression is applied sample by sample, as opposed to syllabic companding used in analog voice processors.
Exam tip
The examiner always asks you to state the values of μ and A, sketch the compressor characteristic curve, and explain why SNR is more uniform — write all three in your answer even if the question only asks one.