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AnA-law algorithm is a standardcompanding algorithm, used inEuropean 8-bitPCMdigital communications systems to optimize, i.e. modify, thedynamic range of ananalog signal for digitizing. It is one of the two companding algorithms in theG.711 standard fromITU-T, the other being the similarμ-law, used in North America and Japan.
For a given input, the equation for A-law encoding is as follows:
where is the compression parameter. In Europe,.
A-law expansion is given by the inverse function:
The reason for this encoding is that the widedynamic range ofspeech does not lend itself well to efficient linear digital encoding. A-law encoding effectively reduces the dynamic range of the signal, thereby increasing thecoding efficiency and resulting in a signal-to-distortion ratio that is superior to that obtained by linear encoding for a given number of bits.
Theμ-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.