A-law algorithm
Audio companding in communications
An A-law algorithm is a standard companding algorithm, used in European eight-bit PCM digital communications systems to optimize, i.e. modify, the dynamic range of an analog signal for digitizing. It is one of the two companding algorithms in the G.711 standard from ITU-T, the other being the similar μ-law, used in North America and Japan.
For a given input 
![F(x)=\operatorname {sgn} (x){\begin{cases}{\dfrac {A|x|}{1+\ln(A)}},&|x|<{\dfrac {1}{A}},\\[1ex]{\dfrac {1+\ln(A|x|)}{1+\ln(A)}},&{\dfrac {1}{A}}\leq |x|\leq 1,\end{cases}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbf1f46065c88a4f95d80217488dee2786e69fb5)
where 
A-law expansion is given by the inverse function:
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.
01Comparison 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.
Sources and credits
This article is adapted from the Wikipedia article “A-law algorithm”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Comparison of A-law and μ-law compression on an input signal.svg by User:Ozhiker / User:Em3rgent0rdr, CC BY-SA 3.0
- Plot of F(x) for A-Law for A = 87.6.svg by Masterxilo1992, CC BY-SA 4.0
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