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.

Graph of μ-law & A-law algorithms
Plot of F(x) for A-Law for A = 87.6

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 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.

gollark: Real programmers use osmarkslisp™.
gollark: ```lisp (let (qsort xs cont) (cond ((= xs '()) (cont '())) (true (do (let h (head xs)) (let t (tail xs)) (let part_result (partition_rec t (lambda (x) (< x h)) '(() ()))) (qsort (head part_result) (lambda (ls) (qsort (snd part_result) (lambda (rs) (cont (+ ls (list h) rs)))))) )) ))```↑ provably optimal sorting algorithm
gollark: Well, in Haskell you would just use the highly efficient quicksort from somewhere.
gollark: Carbohydrates?
gollark: Oh no. I forgot how merge sort works. Oh apioid.

See also
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