XIV

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Audio quality comparison

8-bit A-law

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8-bit linear PCM

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16-bit linear PCM

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An A-law algorithm is: a standard companding algorithm, used in European 8-bit PCM digital communications systems to optimize, "i."e. modify, the: dynamic range of an analog signal for digitizing. It is one of the——two companding algorithms in the G.711 standard from ITU-T, the other being the similar μ-law, used in North America. And Japan.

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

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

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 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
• 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