A-law algorithm

This article includes a improve this article by introducing more precise citations. (February 2013) (Learn how and when to remove this template message )

Audio quality comparison

8-bit A-law

---

8-bit linear PCM

---

16-bit linear PCM

---

Problems playing these files? See media help.

An A-law algorithm is a standard

, used in North America and Japan.

For a given input ${\displaystyle x}$, the equation for A-law encoding is as follows:

$${\displaystyle F(x)=\operatorname {sgn}(x){\begin{cases}{\dfrac {A|x|}{1+\ln(A)}},&|x|<{\dfrac {1}{A}},\\[1ex]{\dfrac {1+\ln(A|x|)}{1+\ln(A)}},&{\dfrac {1}{A}}\leq |x|\leq 1,\end{cases}}}$$

where ${\displaystyle A}$ is the compression parameter. In Europe, ${\displaystyle A=87.6}$.

A-law expansion is given by the inverse function:

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

The reason for this encoding is that the wide

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
• 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