A-LAW ALGORITHM

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,
:$$
F(x) = sgn(x) egin{cases} {A |x| over 1 + ln(A)}, & |x| < {1 over A} \
rac{1+ ln(A |x|)}{1 + ln(A)}, & {1 over A} leq |x| leq 1 end{cases}
,
where ''A'' is the compression parameter. In Europe, $A\; =\; 87.7$; the value 87.6 is also used.
A-law expansion is given by the inverse function,
:$$
F^{-1}(y) = sgn(y) egin{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.

Contents

Comparison to μ-law

See also

External links

Comparison to μ-law

The A-law algorithm provides a slightly larger dynamic range than the μ-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

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 (on C)