Mu-law algorithm - Definition and Overview

In telecommunication, a mu-law algorithm (μ-law) is a standard analog signal compression or companding algorithm, used in digital communications systems of the North American and Japanese digital hierarchies, to optimize, i.e., modify, the dynamic range of an audio analog signal prior to digitizing. It is similar to the A-law algorithm used in Europe.

For a given input x, the equation for μ-law encoding is as follows,

<math>F(x) = \sgn(x) \frac{\ln(1+ \mu |x|)}{\ln(1+\mu)}~~~~-1 \leq x \leq 1<math>,

where μ = 255 (8 bits) in the North American and Japanese standards.

This encoding is used because speech has a wide dynamic range that does not lend itself well to efficient linear digital encoding. Moreover, perceived intensity (loudness) is logarithmic. Mu-law encoding effectively reduces the dynamic range of the signal, thereby increasing the coding efficiency and resulting in a signal-to-distortion ratio that is greater than that obtained by linear encoding for a given number of bits.

Source: from Federal Standard 1037C

See also

• Audio level compression
• Signal compression
• Companding
• G.711