Editing Μ-law algorithm (section)

{{Short description|Audio companding algorithm}}
{{more footnotes needed|date=May 2018}}
{{lowercase title}}
[[File:Comparison of A-law and μ-law compression on an input signal.svg|thumb|Comparison of [[A-law]] (blue) and [[μ-law]] (red) [[Dynamic range compression|compression]] on an input signal (green). Both axes use [[logarithmic scale]]s in [[decibel]]s.|350x350px]]
{{Listen
| type         = speech
| header       = Audio quality comparison
| filename     = Speech 12dB s16.flac
| title        = 16-bit linear PCM (reference/original)
| filename2    = Speech 12dB mulaw8.flac
| title2       = 8-bit µ-law PCM
| filename3    = Speech 12dB u8.flac
| title3       = 8-bit linear PCM
}}

The '''μ-law algorithm''' (sometimes written '''[[Mu (letter)|mu]]-law''', often abbreviated as '''u-law''') is a [[companding]] algorithm, primarily used in 8-bit [[PCM]] [[Digital data|digital]] [[telecommunications system]]s in [[North America]] and [[Japan]]. It is one of the two companding algorithms in the [[G.711]] standard from [[ITU-T]], the other being the similar [[A-law]]. A-law is used in regions where digital telecommunication signals are carried on E-1 circuits, e.g. Europe.

The terms '''PCMU''', G711u or G711MU are used for G711 μ-law.<ref>{{cite web |url=http://www.grandstream.com/support/faq/common-questions/video/voice/speech-codecs |title=Video/Voice/Speech Codecs |website=Grandstream| access-date= 19 July 2020}}</ref>

Companding algorithms reduce the [[dynamic range]] of an audio [[signal]]. In analog systems, this can increase the [[signal-to-noise ratio]] (SNR) achieved during transmission; in the digital domain, it can reduce the quantization error (hence increasing the signal-to-quantization-noise ratio). These SNR increases can be traded instead for reduced [[Bandwidth (signal processing)|bandwidth]] for equivalent SNR.

At the cost of a reduced peak SNR, it can be mathematically shown that μ-law's non-linear quantization effectively increases dynamic range by 33&nbsp;dB or {{Fraction|5|1|2}} bits over a linearly-quantized signal, hence 13.5 bits (which rounds up to 14 bits) is the most resolution required for an input digital signal to be compressed for 8-bit μ-law.<ref>{{Cite web |last=Ess |first=David Van |date=2014-12-29 |orig-date=2007-10-09 |title=Cypress Semiconductor AN2095: Algorithm - Logarithmic Signal Companding - Not Just a Good Idea - It Is μ-Law |url=https://www.infineon.com/dgdl/Infineon-AN2095_Algorithm_Logarithmic_Signal_Companding_Not_Just_a_Good_Idea_It_Is_-Law-ApplicationNotes-v05_00-EN.pdf?fileId=8ac78c8c7cdc391c017d073725525a59 |url-status=live |archive-url=https://web.archive.org/web/20221006014433/https://www.infineon.com/dgdl/Infineon-AN2095_Algorithm_Logarithmic_Signal_Companding_Not_Just_a_Good_Idea_It_Is_-Law-ApplicationNotes-v05_00-EN.pdf?fileId=8ac78c8c7cdc391c017d073725525a59 |archive-date=2022-10-06 |access-date=2023-06-28 |website=[[Infineon Technologies]]}}</ref>