Active laser medium

File:Ulaw alaw db.svg

Graph of μ-law & A-law algorithms

An A-law algorithm is a standard companding algorithm, used in European digital communications systems to optimize, i.e., modify, the dynamic range of an analog signal for digitizing.

It is similar to the μ-law algorithm used in North America and Japan.

For a given input x, the equation for A-law encoding is as follows,

$F(x)=\mathrm{sgn}(x)\{\begin{array}{ll}\frac{A\left|x\right|}{1+\ln (A)},& \left|x\right|<\frac{1}{A}\\ \frac{1+\ln (A|x|)}{1+\ln (A)},& \frac{1}{A}\le \left|x\right|\le 1,\end{array}$

where A is the compression parameter. In Europe, $A=87.7$; the value 87.6 is also used.

A-law expansion is given by the inverse function,

$F^{-1}(y)=\mathrm{sgn}(y)\{\begin{array}{ll}\frac{\left|y\right|(1+\ln (A))}{A},& \left|y\right|<\frac{1}{1+\ln (A)}\\ \frac{\exp (|y|(1+\ln (A))-1)}{A},& \frac{1}{1+\ln (A)}\le \left|y\right|<1.\end{array}$

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.

See also

• μ-law algorithm
• Audio level compression
• Signal compression
• Companding
• G.711
• DS0

External links

• Waveform Coding Techniques - Has details of implementation (but note that the A-law equation is incorrect)
• A-Law and μ-law Companding Implementations Using the TMS320C54x (PDF)
• A-law implementation in C-language with example code