Mu-law compresses audio signals for telecommunications systems to improve dynamic range ratio and reduce distortion. It is used in both analog and digital systems, with the formula F(x) = sign(x)*ln(1 + μ׀x׀)). Mu-law is used in North America and Japan to convert data into 8-bit format.
Mu-law is an algorithm used to compress the dynamic range of an audio signal transmitted over a telecommunications system. An algorithm is a series of calculations processed in a predefined order within a computer or processor. The dynamic range of an audio signal is the ratio of the loudest, undistorted sound to the level of background noise picked up by the microphone.
Human speech has a dynamic range of 40dB and human hearing has a dynamic range of approximately 140dB. When transmitting human voice over a telecommunication system, the mu-law algorithm is applied to compress the data or audio signal. The purpose of this calculation is to improve the dynamic range ratio to ensure that the sound of the human voice is carried with as little distortion as possible.
This formula is in use with both older analog-based systems and newer digital systems. With the analog system, the mu-law algorithm was used to reduce the impact of background noise or static electricity. In the digital system, this formula compresses the digital signal to 8 bits, while maintaining the same approximate noise level.
The mathematical formula for mu-law is:
F(x) = sign(x)*ln(1 + μ׀x׀))
ln(1 + micro)
where μ = 255 (8 bits) and for a given input x.
Mu-law is used for digital telecommunications networks in North America and Japan to change data into the supported 8-bit format. This is done after the signal or sound has been received and processed by the digital computer system. In an analog system, this change is complete with the use of a non-linear gain amplifier. When working with an analog network, signal compression and adjustments should be completed within the analog system wherever possible.
To convert an analog signal to digital, a conversion with set quantization levels is required for an analog to digital conversion. Quantization refers to the conversion of an analog signal into a digital one. The level must be of unequal space according to the mu-law algorithm.
If the signal is already digital, nothing needs to be converted and the mu-law formula can be applied directly. The 8-bit data file size is ideal for a digital file and matches the symbol size of most computers. This coincidence removed a major potential barrier to the digitization of the telecommunications system and was instrumental in the transition and acceptance of digital telecommunications.
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