A-law

The A-law method is a companding method used primarily in Europe for analog audio signals in the telecommunications sector , which is standardized in Recommendation G.711 of the International Telecommunication Union (ITU-T). In this case, the signal at the digitization with a nonlinear characteristic curve , the so-called A-characteristic curve , quantized . The aim is to achieve a higher dynamic range or a higher signal-to-noise ratio with the same resolution by resolving large signal deflections more coarse and small signal deflections more finely.

In North America and Japan, the similar µ-law method is used, which is similar to A-law, but is not compatible. For communication, e.g. B. in a telephone conversation between Europe and the USA, the digital data must be converted by appropriate converters.

The A curve

A-law and µ-law characteristics and linear quantization in comparison

The companding of the analog signals takes place with a logarithmic quantization characteristic, the A characteristic. It is defined as a continuous function :

{\ displaystyle C (x) = {\ begin {cases} {\ frac {A} {1+ \ ln A}} | x | & {\ mbox {if}} 0 \ leq | x | \ leq {\ frac {1} {A}} \\ {\ frac {1} {1+ \ ln A}} + {\ frac {\ ln (A | x |)} {1+ \ ln A}}, & {\ mbox {if}} {\ frac {1} {A}} <| x | \ leq 1 \ end {cases}} {\ mbox {with}} A = 87 {,} 56}

The inverse function is:

{\ displaystyle C ^ {- 1} (y) = \ operatorname {sgn} (y) {\ begin {cases} {| y | (1+ \ ln A) \ over A}, & {\ mbox {if} } | y | <{1 \ over 1+ \ ln (A)} \\ {\ exp (| y | (1+ \ ln A) -1) \ over A}, & {\ mbox {if}} { 1 \ over 1+ \ ln A} \ leq | y | <1. \ end {cases}} {\ mbox {with}} A = 87 {,} 56}

The following applies: ${\ displaystyle C (\ pm 1) = \ pm 1}$

The A characteristic has a high dynamic at low signal levels and low dynamic at high levels.

The 13-segment characteristic

Recommendation G.711 also describes a linear approximation of the A characteristic curve in sections, which is much more suitable for use in digitally operating systems, the so-called 13-segment characteristic curve .

The intended PCM coding ( pulse code modulation ) with 8-bit words would lead to a level-independent resolution of 1/128 of the maximum amplitude if a linear characteristic curve was used. According to the 13-segment characteristic, small signal levels are now quantized to 1/2048 of the maximum amplitude, while large signal levels are only quantized with a resolution of 1/32. The signals are first digitized with 12-bit accuracy. The division into the segments was done in such a way that compression and expansion can be done very easily by a 12-bit to 8-bit conversion or an 8-bit to 12-bit conversion.

The audio signal is first linear 13-bit value in the form of an integer with sign digitized. This 13-bit value is represented as an 8-bit value according to the following table:

Linear input	output
s0000000wxyza ...	n000wxyz
s0000001wxyza ...	n001wxyz
s000001wxyzab ...	n010wxyz
s00001wxyzabc ...	n011wxyz
s0001wxyzabcd ...	n100wxyz
s001wxyzabcde ...	n101wxyz
s01wxyzabcdef ...	n110wxyz
s1wxyzabcdefg ...	n111wxyz

This coding can be viewed as a 1.3.4 floating point number with 8 bits (so-called minifloat ) and an integer value (1 bit sign, 3 bit exponent, 4 bit mantissa). The sign bit in the result is used inversely (n = not s).

In order to avoid the continuous transmission of zeros in the case of silence, the 8-bit words in the data stream are marked with 0x 55, i.e. H. 01010101 _b exclusive-OR linked so that bits 2, 4, 6 and 8 (from the point of view of the ITU standard) or 6, 4, 2, 0 (from the point of view of the binary position system ) are inverted.

Web links

Commons : A-law - collection of pictures, videos and audio files

ITU