A-law algorithm

AnA-law algorithmis a standardcompandingalgorithm, used inEuropean8-bitPCMdigital communicationssystems to optimize, i.e. modify, thedynamic rangeof ananalog signalfor digitizing. It is one of the two companding algorithms in theG.711standard fromITU-T,the other being the similarμ-law,used in North America and Japan.

Comparison ofA-law(blue) andμ-law(red)compressionon an input signal (green). Both axis uselogarithmic scaleindecibels.

Plot ofF(x) for A-Law forA= 87.6

For a given input$x$,the equation for A-law encoding is as follows: $$F(x)=\operatorname {sgn}(x){\begin{cases}{\dfrac {A|x|}{1+\ln(A)}},&|x|<{\dfrac {1}{A}},\\[1ex]{\dfrac {1+\ln(A|x|)}{1+\ln(A)}},&{\dfrac {1}{A}}\leq |x|\leq 1,\end{cases}}$$

where$A$is the compression parameter. In Europe,$A=87.6$.

A-law expansion is given by the inverse function: $$F^{-1}(y)=\operatorname {sgn}(y){\begin{cases}{\dfrac {|y|(1+\ln(A))}{A}},&|y|<{\dfrac {1}{1+\ln(A)}},\\{\dfrac {e^{-1+|y|(1+\ln(A))}}{A}},&{\dfrac {1}{1+\ln(A)}}\leq |y|<1.\end{cases}}$$

The reason for this encoding is that the widedynamic rangeofspeechdoes not lend itself well to efficient linear digital encoding. A-law encoding effectively reduces the dynamic range of the signal, thereby increasing thecodingefficiency and resulting in a signal-to-distortionratio that is superior to that obtained by linear encoding for a given number of bits.

Comparison to μ-law

Theμ-law algorithmprovides 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
• Dynamic range compression
• Signal compression
• Companding
• G.711
• DS0
• Tapered floating point

External links

• Waveform Coding Techniques- Has details of implementation (but note that the A-law equation is incorrect)
• A-law implementation in C-language with example code