Mu-law algorithm
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In telecommunication, a mu-law algorithm (μ-law) is a standard analog signal compression or companding algorithm, used in digital communications systems of the North American and Japanese digital hierarchies, to optimize (in other words, modify) the dynamic range of an audio analog signal prior to digitizing. It is similar to the A-law algorithm used in Europe.
For a given input x, the equation for μ-law encoding is as follows,
- [F(x) = \sgn(x) \frac~~~~-1 \leq x \leq 1],
μ-law expansion is then given by the inverse equation:
- [F^(y) = \sgn(y) (1 / \mu ) [(1 + mu)^
>
- 1]~~~~-1 \leq y \leq 1] This encoding is used because speech has a wide dynamic range that does not lend itself well to efficient linear digital encoding. Moreover, perceived intensity (loudness) is logarithmic. Mu-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 greater than that obtained by linear encoding for a given number of bits. The mu-law algorithm is also used in some rather standard programming language approaches for storing and creating sound (such as the classes in the
sun.audioJava package in Java 1.1, in the .au format, and in some C# methods).Comparison with A-law
A special feature of mu-law encoding is that zero is actually the range of values near zero sound pressure. This means that near silence is encoded as zero, without introducing quantization noise as the value flips between positive and negative values. The inventors at Bell Labs arranged this so that long-distance telephony would have less noise, and therefore be perceived as higher quality. This also reduces the size of run-length encoded speech samples. These are both significant advantages over its main competitor, A-law encoding.The A-law algorithm provides a slightly larger dynamic range than the mu-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.
Source: from Federal Standard 1037C
See also
External links
- [Waveform Coding Techniques] - Has details of implementation
- [A-Law and mu-Law Companding Implementations Using the TMS320C54x] (PDF)
- [A-law and μ-law realisation (on C)]
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