A-law algorithm

An A-law algorithm is a standard companding algorithm, used in European 8-bit PCM digital communications systems to optimize, i.e. modify, the dynamic range of an analog signal for digitizing. It is one of two versions of the G.711 standard from ITU-T, the other version being the similar μ-law, used in North America and Japan.

For a given input $x$, the equation for A-law encoding is as follows:

F(x) = \sgn(x) \begin
\dfrac, & , x, < \dfrac,
\\ ex \dfrac, & \dfrac \leq , x, \leq 1,
\end

where $A$ is the compression parameter. In Europe, $A = 87.6$.

A-law expansion is given by the inverse function:
$F^(y) = \sgn(y) \begin \dfrac, & , y, < \dfrac, \\ \dfrac, & \dfrac \leq , y, < 1. \end$

The reason for this encoding is that the wide dynamic range of speech does not lend itself well to efficient linear digital encoding. A-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 superior to that obtained by linear encoding for a given number of bits.

Comparison to μ-law

The μ-law algorithm provides a slightly larger dynamic range than the A-law at the cost of worse proportional distortion for small signals. By convention, A-law is used for an international connection if at least one country uses it.

See also

* μ-law algorithm
* Audio level compression
* Signal compression
* Companding
* G.711
* DS0
* Tapered floating point

External links

Waveform Coding Techniques
- Has details of implementation (but note that the A-law equation is incorrect)

A-law implementation in C-language with example code
{{Compression Methods

Audio codecs