A-law algorithm

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,

$F(x)=\operatorname {sgn}(x){\begin{cases}{A|x| \over 1+\ln(A)},&|x|<{1 \over A}\\{\frac {1+\ln(A|x|)}{1+\ln(A)}},&{1 \over A}\leq |x|\leq 1,\end{cases}}$

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,

$F^{-1}(y)=\operatorname {sgn}(y){\begin{cases}{|y|(1+\ln(A)) \over A},&|y|<{1 \over 1+\ln(A)}\\{\exp(|y|(1+\ln(A))-1) \over A},&{1 \over 1+\ln(A)}\leq |y|<1.\end{cases}}$

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 and μ-law realisation (in C)