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,

where A is the compression parameter. In Europe, .

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.

Comparison to μ-law

The μ-law algorithm provides a greater 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.

Alawites

The Alawites, also known as Alawis (ʿAlawīyyah Arabic: علوية‎), are an Islamic sect, centered in Syria, who follow a branch of the Twelver school of Shia Islam but with syncretistic elements. Alawites revere Ali (Ali ibn Abi Talib), and the name "Alawi" means followers of Ali (they are generally considered Ghulat). The sect is believed to have been founded by Ibn Nusayr during the 9th century. For this reason, Alawites are sometimes called "Nusayris" (Nuṣayrīyyah Arabic: نصيرية‎), though this term has come to have derogatory connotations in the modern era; another name, "Ansari" (al-Anṣāriyyah), is believed to be a mistransliteration of "Nusayri". Today, Alawites represent 12 percent of the Syrian population and are a significant minority in Turkey and northern Lebanon. There is also a population living in the village of Ghajar in the occupied Golan Heights. They are often confused with the Alevis of Turkey. Alawites form the dominant religious group on the Syrian coast and towns near the coast which are also inhabited by Sunnis, Christians, and Ismailis.