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A-law algorithm

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Title: A-law algorithm  
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Subject: Companding, Speech coding, Image compression, Video codec, MPEG-1
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A-law algorithm

Graph of μ-law & A-law algorithms

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 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) \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) = \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

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 implementation in C-language with example code
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