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<title>Μ-law algorithm</title>

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<span id="openzim-page-title" class="mw-page-title-main">μ-law algorithm</span>

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<p>The <b>μ-law algorithm</b> (sometimes written <b><a href="Mu_(letter)" title="Mu (letter)">mu</a>-law</b>, often abbreviated as <b>u-law</b>) is a <a href="Companding" title="Companding">companding</a> algorithm, primarily used in 8-bit <a href="PCM" class="mw-redirect" title="PCM">PCM</a> <a href="Digital_data" title="Digital data">digital</a> <a href="Telecommunications_system" class="mw-redirect" title="Telecommunications system">telecommunications systems</a> in <a href="North_America" title="North America">North America</a> and <a href="Japan" title="Japan">Japan</a>. It is one of the two companding algorithms in the <a href="G.711" title="G.711">G.711</a> standard from <a href="ITU-T" title="ITU-T">ITU-T</a>, the other being the similar <a href="A-law" class="mw-redirect" title="A-law">A-law</a>. A-law is used in regions where digital telecommunication signals are carried on E-1 circuits, e.g. Europe.

</p><p>The terms <b>PCMU</b>, G711u or G711MU are used for G711 μ-law.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Companding algorithms reduce the <a href="Dynamic_range" title="Dynamic range">dynamic range</a> of an audio <a href="Signal" title="Signal">signal</a>. In analog systems, this can increase the <a href="Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a> (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 <a href="Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a> for equivalent SNR.

</p><p>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 dB or <style data-mw-deduplicate="TemplateStyles:r1154941027">

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</style><span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> 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.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Algorithm_types">Algorithm types</h2></div>

<p>The μ-law algorithm may be described in an analog form and in a quantized digital form.

</p>

<div class="mw-heading mw-heading3"><h3 id="Continuous">Continuous</h3></div>

<p>For a given input <span class="texhtml mvar" style="font-style:italic;">x</span>, the equation for μ-law encoding is<sup id="cite_ref-mulaw-equation_3-0" class="reference"><a href="#cite_note-mulaw-equation-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle F(x)=\operatorname {sgn}(x){\dfrac {\ln(1+\mu |x|)}{\ln(1+\mu )}},\quad -1\leq x\leq 1,}</annotation>

</semantics>

</math></span></span>

</p><p>where <span class="texhtml"><i>μ</i> = 255</span> in the North American and Japanese standards, and <span class="texhtml">sgn(<i>x</i>)</span> is the <a href="Sign_function" title="Sign function">sign function</a>. The <a href="Range_of_a_function" title="Range of a function">range</a> of this function is −1 to 1.

</p><p>μ-law expansion is then given by the inverse equation:<sup id="cite_ref-mulaw-equation_3-1" class="reference"><a href="#cite_note-mulaw-equation-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

<msup>

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</msup>

<mfrac>

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<msup>

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<annotation encoding="application/x-tex">{\displaystyle F^{-1}(y)=\operatorname {sgn}(y){\dfrac {(1+\mu )^{|y|}-1}{\mu }},\quad -1\leq y\leq 1.}</annotation>

</semantics>

</math></span></span>

</p>

<div class="mw-heading mw-heading3"><h3 id="Discrete">Discrete</h3></div>

<p>The discrete form is defined in ITU-T Recommendation <a href="G.711" title="G.711">G.711</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

</p><p>G.711 is unclear about how to code the values at the limit of a range (e.g. whether +31 codes to 0xEF or 0xF0).

However, G.191 provides example code in the <a href="C_language" class="mw-redirect" title="C language">C language</a> for a μ-law encoder.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The difference between the positive and negative ranges, e.g. the negative range corresponding to +30 to +1 is −31 to −2. This is accounted for by the use of <a href="1's_complement" class="mw-redirect" title="1's complement">1's complement</a> (simple bit inversion) rather than <a href="2's_complement" class="mw-redirect" title="2's complement">2's complement</a> to convert a negative value to a positive value during encoding.

</p>

<caption>Quantized μ-law algorithm

</caption>

<th>14-bit binary linear input code</th>

<th>8-bit compressed code

</th></tr>

<tr>

<td>+8158 to +4063 in 16 intervals of 256</td>

<td>0x80 + interval number

</td></tr>

<tr>

<td>+4062 to +2015 in 16 intervals of 128</td>

<td>0x90 + interval number

</td></tr>

<tr>

<td>+2014 to +991 in 16 intervals of 64</td>

<td>0xA0 + interval number

</td></tr>

<tr>

<td>+990 to +479 in 16 intervals of 32</td>

<td>0xB0 + interval number

</td></tr>

<tr>

<td>+478 to +223 in 16 intervals of 16</td>

<td>0xC0 + interval number

</td></tr>

<tr>

<td>+222 to +95 in 16 intervals of 8</td>

<td>0xD0 + interval number

</td></tr>

<tr>

<td>+94 to +31 in 16 intervals of 4</td>

<td>0xE0 + interval number

</td></tr>

<tr>

<td>+30 to +1 in 15 intervals of 2</td>

<td>0xF0 + interval number

</td></tr>

<tr>

<td>0xFF

</td></tr>

<tr>

<td>0x7F

</td></tr>

<tr>

<td>−31 to −2 in 15 intervals of 2</td>

<td>0x70 + interval number

</td></tr>

<tr>

<td>−95 to −32 in 16 intervals of 4</td>

<td>0x60 + interval number

</td></tr>

<tr>

<td>−223 to −96 in 16 intervals of 8</td>

<td>0x50 + interval number

</td></tr>

<tr>

<td>−479 to −224 in 16 intervals of 16</td>

<td>0x40 + interval number

</td></tr>

<tr>

<td>−991 to −480 in 16 intervals of 32</td>

<td>0x30 + interval number

</td></tr>

<tr>

<td>−2015 to −992 in 16 intervals of 64</td>

<td>0x20 + interval number

</td></tr>

<tr>

<td>−4063 to −2016 in 16 intervals of 128</td>

<td>0x10 + interval number

</td></tr>

<tr>

<td>−8159 to −4064 in 16 intervals of 256</td>

<td>0x00 + interval number

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2></div>

<p>The μ-law algorithm may be implemented in several ways:

</p>

<dl><dt>Analog</dt>

<dd>Use an amplifier with non-linear gain to achieve companding entirely in the analog domain.</dd>

<dt>Non-linear ADC</dt>

<dd>Use an <a href="Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital converter</a> with quantization levels which are unequally spaced to match the μ-law algorithm.</dd>

<dt>Digital</dt>

<dd>Use the quantized digital version of the μ-law algorithm to convert data once it is in the digital domain.</dd></dl>

<dl><dt>Software/DSP</dt>

<dd>Use the continuous version of the μ-law algorithm to calculate the companded values.</dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Usage_justification">Usage justification</h2></div>

<p>μ-law encoding is used because <a href="Speech" title="Speech">speech</a> has a wide <a href="Dynamic_range" title="Dynamic range">dynamic range</a>. In analog signal transmission, in the presence of relatively constant background noise, the finer detail is lost. Given that the precision of the detail is compromised anyway, and assuming that the signal is to be perceived as audio by a human, one can take advantage of the fact that the perceived <a href="Acoustic_intensity_level" class="mw-redirect" title="Acoustic intensity level">acoustic intensity level</a> or <a href="Loudness" title="Loudness">loudness</a> is logarithmic by compressing the signal using a logarithmic-response operational amplifier (<a href="Weber%E2%80%93Fechner_law" title="Weber–Fechner law">Weber–Fechner law</a>). In telecommunications circuits, most of the noise is injected on the lines, thus after the compressor, the intended signal is perceived as significantly louder than the static, compared to an uncompressed source. This became a common solution, and thus, prior to common digital usage, the μ-law specification was developed to define an interoperable standard.

</p><p>This pre-existing algorithm had the effect of significantly lowering the amount of bits required to encode a recognizable human voice in digital systems. A sample could be effectively encoded using μ-law in as little as 8 bits, which conveniently matched the symbol size of the majority of common computers.

</p><p>μ-law encoding effectively reduced the dynamic range of the signal, thereby increasing the <a href="Channel_coding" class="mw-redirect" title="Channel coding">coding</a> efficiency while biasing the signal in a way that results in a signal-to-<a href="Distortion" title="Distortion">distortion</a> ratio that is greater than that obtained by linear encoding for a given number of bits.

</p>

<p>The μ-law algorithm is also used in the <a href="Au_file_format" title="Au file format">.au format</a>, which dates back at least to the <a href="SPARCstation_1" title="SPARCstation 1">SPARCstation 1</a> by Sun Microsystems as the native method used by the /dev/audio interface, widely used as a de facto standard for sound on Unix systems. The au format is also used in various common audio <a href="API" title="API">APIs</a> such as the classes in the sun.audio <a href="Java_package" title="Java package">Java package</a> in <a href="Java_platform" class="mw-redirect" title="Java platform">Java</a> 1.1 and in some <a href="C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a> methods.

</p><p>This plot illustrates how μ-law concentrates sampling in the smaller (softer) values. The horizontal axis represents the byte values 0-255 and the vertical axis is the 16-bit linear decoded value of μ-law encoding.

</p>

<div class="mw-heading mw-heading2"><h2 id="Comparison_with_A-law">Comparison with A-law</h2></div>

<p>The μ-law algorithm provides a slightly larger dynamic range than the A-law at the cost of worse proportional distortions for small signals. By convention, A-law is used for an international connection if at least one country uses it.

</p>

<ul><li><a href="Dynamic_range_compression" title="Dynamic range compression">Dynamic range compression</a></li>

<li><a href="Signal_compression_(disambiguation)" class="mw-redirect" title="Signal compression (disambiguation)">Signal compression (disambiguation)</a></li>

<li><a href="G.711" title="G.711">G.711</a>, a waveform speech coder using either A-law or μ-law encoding</li>

<li><a href="Tapered_floating_point" title="Tapered floating point">Tapered floating point</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.grandstream.com/support/faq/common-questions/video/voice/speech-codecs">"Video/Voice/Speech Codecs"</a>. <i>Grandstream</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 July</span> 2020</span>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFEss2014" class="citation web cs1">Ess, David Van (29 December 2014) [2007-10-09]. <a rel="nofollow" class="external text" href="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">"Cypress Semiconductor AN2095: Algorithm - Logarithmic Signal Companding - Not Just a Good Idea - It Is μ-Law"</a> <span class="cs1-format">(PDF)</span>. <i><a href="Infineon_Technologies" title="Infineon Technologies">Infineon Technologies</a></i>. <a rel="nofollow" class="external text" href="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">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 6 October 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2023</span>.</cite></span>

</li>

<li id="cite_note-mulaw-equation-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-mulaw-equation_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-mulaw-equation_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.cisco.com/c/en/us/support/docs/voice/h323/8123-waveform-coding.html">"Waveform Coding Techniques - Cisco"</a>. 2 February 2006<span class="reference-accessdate">. Retrieved <span class="nowrap">7 December</span> 2020</span>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.711-198811-I!!PDF-E&type=items">"ITU-T Recommendation G.711"</a>.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.itu.int/rec/T-REC-G.191/en">"G.191 : Software tools for speech and audio coding standardization"</a>. <i>www.itu.int</i>.</cite></span>

</li>

</ol></div>

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</style><span class="citation 1037C"><span class="noviewer" typeof="mw:File"><span></span></span> This article incorporates <a href="Copyright_status_of_works_by_the_federal_government_of_the_United_States" title="Copyright status of works by the federal government of the United States">public domain material</a> from <cite class="citation cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm"><i>Federal Standard 1037C</i></a>. <a href="General_Services_Administration" title="General Services Administration">General Services Administration</a>. Archived from <a rel="nofollow" class="external text" href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 22 January 2022.</cite></span>

</p>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.cisco.com/en/US/tech/tk1077/technologies_tech_note09186a00801149b3.shtml">Waveform Coding Techniques</a> – details of implementation</li>

<li><a rel="nofollow" class="external text" href="http://focus.ti.com/lit/an/spra163a/spra163a.pdf">A-Law and mu-Law Companding Implementations Using the TMS320C54x</a> (<a href="PDF" title="PDF">PDF</a>)</li>

<li><a rel="nofollow" class="external text" href="http://focus.ti.com/lit/an/spra634/spra634.pdf">TMS320C6000 μ-Law and A-Law Companding with Software or the McBSP</a> (<a href="PDF" title="PDF">PDF</a>)</li>

<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110719132013/http://hazelware.luggle.com/tutorials/mulawcompression.html">A-law and μ-law realisation (in C)</a></li>

<li><a rel="nofollow" class="external text" href="https://github.com/deftio/companders">u-law implementation in C-language with example code</a></li></ul>

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</style><div id="Data_compression_methods241" style="font-size:114%;margin:0 4em"><a href="Data_compression" title="Data compression">Data compression</a> methods</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Lossless_compression" title="Lossless compression">Lossless</a><br>type</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Entropy_coding" title="Entropy coding">Entropy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Adaptive_coding" title="Adaptive coding">Adaptive coding</a></li>

<li><a href="Arithmetic_coding" title="Arithmetic coding">Arithmetic</a></li>

<li><a href="Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric numeral systems</a></li>

<li><a href="Golomb_coding" title="Golomb coding">Golomb</a></li>

<li><a href="Huffman_coding" title="Huffman coding">Huffman</a>

<ul><li><a href="Adaptive_Huffman_coding" title="Adaptive Huffman coding">Adaptive</a></li>

<li><a href="Canonical_Huffman_code" title="Canonical Huffman code">Canonical</a></li>

<li><a href="Modified_Huffman_coding" title="Modified Huffman coding">Modified</a></li></ul></li>

<li><a href="Range_coding" title="Range coding">Range</a></li>

<li><a href="Shannon_coding" title="Shannon coding">Shannon</a></li>

<li><a href="Shannon%E2%80%93Fano_coding" title="Shannon–Fano coding">Shannon–Fano</a></li>

<li><a href="Shannon%E2%80%93Fano%E2%80%93Elias_coding" title="Shannon–Fano–Elias coding">Shannon–Fano–Elias</a></li>

<li><a href="Tunstall_coding" title="Tunstall coding">Tunstall</a></li>

<li><a href="Unary_coding" title="Unary coding">Unary</a></li>

<li><a href="Universal_code_(data_compression)" title="Universal code (data compression)">Universal</a>

<ul><li><a href="Exponential-Golomb_coding" title="Exponential-Golomb coding">Exp-Golomb</a></li>

<li><a href="Fibonacci_coding" title="Fibonacci coding">Fibonacci</a></li>

<li><a href="Elias_gamma_coding" title="Elias gamma coding">Gamma</a></li>

<li><a href="Levenshtein_coding" title="Levenshtein coding">Levenshtein</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Dictionary_coder" title="Dictionary coder">Dictionary</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Byte-pair_encoding" title="Byte-pair encoding">Byte-pair encoding</a></li>

<li><a href="LZ77_and_LZ78" title="LZ77 and LZ78">Lempel–Ziv</a>

<li><a href="Snappy_(compression)" title="Snappy (compression)">Snappy</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Delta_encoding" title="Delta encoding">Delta</a>

<ul><li><a href="Incremental_encoding" title="Incremental encoding">Incremental</a></li></ul></li>

<li><a href="Grammar-based_code" title="Grammar-based code">Grammar</a>

<li><a href="Sequitur_algorithm" title="Sequitur algorithm">Sequitur</a></li></ul></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hybrid</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>LZ77 + Huffman

<ul><li><a href="Deflate" title="Deflate">Deflate</a></li>

<li>LZ77 + ANS

<ul><li><a href="LZFSE" title="LZFSE">LZFSE</a></li></ul></li>

<li>LZ77 + Huffman + ANS

<ul><li><a href="Zstd" title="Zstd">Zstandard</a></li></ul></li>

<li>LZ77 + Huffman + context

<ul><li><a href="Brotli" title="Brotli">Brotli</a></li></ul></li>

<li>LZSS + Huffman

<li>LZ77 + Range

<li>LZHAM</li></ul></li>

<li>RLE + BWT + MTF + Huffman

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Lossy_compression" title="Lossy compression">Lossy</a><br>type</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Transform_coding" title="Transform coding">Transform</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a>

<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

<li><a href="Set_partitioning_in_hierarchical_trees" title="Set partitioning in hierarchical trees">SPIHT</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Predictive</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li></ul></li>

<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>

<li>Motion

<ul><li><a href="Motion_compensation" title="Motion compensation">Compensation</a></li>

<li><a href="Motion_estimation" title="Motion estimation">Estimation</a></li>

<li><a href="Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li>

<li><a href="Psychoacoustics" title="Psychoacoustics">Psychoacoustic</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Data_compression#Audio" title="Data compression">Audio</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Companding" title="Companding">Companding</a></li>

<li><a href="Convolution" title="Convolution">Convolution</a></li>

<li><a href="Dynamic_range" title="Dynamic range">Dynamic range</a></li>

<li><a href="Latency_(audio)" title="Latency (audio)">Latency</a></li>

<li><a href="Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon theorem</a></li>

<li><a href="Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></li>

<li><a href="Silence_compression" title="Silence compression">Silence compression</a></li>

<li><a href="Sound_quality" title="Sound quality">Sound quality</a></li>

<li><a href="Speech_coding" title="Speech coding">Speech coding</a></li>

<li><a href="Sub-band_coding" title="Sub-band coding">Sub-band coding</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Audio_codec" title="Audio codec">Codec</a><br>parts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li>

<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>

<li><a href="Psychoacoustics" title="Psychoacoustics">Psychoacoustic model</a></li></ul>

<ul><li><a href="Chroma_subsampling" title="Chroma subsampling">Chroma subsampling</a></li>

<li><a href="Coding_tree_unit" title="Coding tree unit">Coding tree unit</a></li>

<li><a href="Color_space" title="Color space">Color space</a></li>

<li><a href="Compression_artifact" title="Compression artifact">Compression artifact</a></li>

<li><a href="Image_resolution" title="Image resolution">Image resolution</a></li>

<li><a href="Macroblock" title="Macroblock">Macroblock</a></li>

<li><a href="Pixel" title="Pixel">Pixel</a></li>

<li><a href="Quantization_(image_processing)" title="Quantization (image processing)">Quantization</a></li>

<li><a href="Standard_test_image" title="Standard test image">Standard test image</a></li>

<li><a href="Texture_compression" title="Texture compression">Texture compression</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Methods</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Chain_code" title="Chain code">Chain code</a></li>

<li><a href="Deflate" title="Deflate">Deflate</a></li>

<li><a href="Fractal_compression" title="Fractal compression">Fractal</a></li>

<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

<li><a href="Set_partitioning_in_hierarchical_trees" title="Set partitioning in hierarchical trees">SPIHT</a></li></ul></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Data_compression#Video" title="Data compression">Video</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Display_resolution" title="Display resolution">Display resolution</a></li>

<li><a href="Film_frame" title="Film frame">Frame</a></li>

<li><a href="Frame_rate" title="Frame rate">Frame rate</a></li>

<li><a href="Video_compression_picture_types" title="Video compression picture types">Frame types</a></li>

<li><a href="Interlaced_video" title="Interlaced video">Interlace</a></li>

<li><a href="Video#Characteristics_of_video_streams" title="Video">Video characteristics</a></li>

<li><a href="Video_quality" title="Video quality">Video quality</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Video_codec" title="Video codec">Codec</a><br>parts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Deblocking_filter" title="Deblocking filter">Deblocking filter</a></li>

<li><a href="Lapped_transform" title="Lapped transform">Lapped transform</a></li>

<li>Motion

<ul><li><a href="Motion_compensation" title="Motion compensation">Compensation</a></li>

<li><a href="Motion_estimation" title="Motion estimation">Estimation</a></li>

<li><a href="Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li>

<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Information_theory" title="Information theory">Theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Compressed_data_structure" title="Compressed data structure">Compressed data structures</a>

<ul><li><a href="Compressed_suffix_array" title="Compressed suffix array">Compressed suffix array</a></li>

<li><a href="FM-index" title="FM-index">FM-index</a></li></ul></li>

<li><a href="Entropy_(information_theory)" title="Entropy (information theory)">Entropy</a></li>

<li><a href="Information_theory" title="Information theory">Information theory</a>

<ul><li><a href="Timeline_of_information_theory" title="Timeline of information theory">Timeline</a></li></ul></li>

<li><a href="Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a></li>

<li><a href="Prefix_code" title="Prefix code">Prefix code</a></li>

<li><a href="Quantization_(signal_processing)" title="Quantization (signal processing)">Quantization</a></li>

<li><a href="Rate%E2%80%93distortion_theory" title="Rate–distortion theory">Rate–distortion</a></li>

<li><a href="Redundancy_(information_theory)" title="Redundancy (information theory)">Redundancy</a></li>

<li><a href="Data_compression_symmetry" title="Data compression symmetry">Symmetry</a></li>

<li><a href="Smallest_grammar_problem" title="Smallest grammar problem">Smallest grammar problem</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Community</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Hutter_Prize" title="Hutter Prize">Hutter Prize</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mark_Adler" title="Mark Adler">Mark Adler</a></li>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Multimedia_compression_and_container_formats462" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Multimedia_compression_and_container_formats462" style="font-size:114%;margin:0 4em"><a href="Multimedia" title="Multimedia">Multimedia</a> <a href="Data_compression" title="Data compression">compression</a> and <a href="Container_format_(computing)" class="mw-redirect" title="Container format (computing)">container</a> formats</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Video_coding_format" title="Video coding format">Video<br>compression</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:5em"><a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>, <a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a>, <br><a href="Moving_Picture_Experts_Group" title="Moving Picture Experts Group">MPEG</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<li><a href="Motion_JPEG" title="Motion JPEG">MJPEG</a></li>

<li><a href="Motion_JPEG_2000" title="Motion JPEG 2000">Motion JPEG 2000</a></li>

<li>MPEG-I

<li><a href="LCEVC" title="LCEVC">Part 2 / LCEVC</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="ITU-T" title="ITU-T">ITU-T</a>, <a href="Video_Coding_Experts_Group" title="Video Coding Experts Group">VCEG</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<li>H.267 / Enhanced Compression Model</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="Society_of_Motion_Picture_and_Television_Engineers" title="Society of Motion Picture and Television Engineers">SMPTE</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="On2_Technologies" title="On2 Technologies">TrueMotion</a> and AOMedia</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="On2_Technologies#TrueMotion_S" title="On2 Technologies">TrueMotion S</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Chinese Standard</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<li><a href="Audio_Video_Standard#Second_generation" title="Audio Video Standard">AVS2 P2</a>(GB/T 33475.2,GY/T 299.1)

<ul><li>HDR Vivid(GY/T 358)</li></ul></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Apple_Video" title="Apple Video">Apple Video</a></li>

<li><a href="Cinepak" title="Cinepak">Cinepak</a></li>

<li><a href="Daala" title="Daala">Daala</a></li>

<li><a href="Huffyuv" title="Huffyuv">Huffyuv</a></li>

<li><a href="Indeo" title="Indeo">Indeo</a></li>

<li><a href="Lagarith" title="Lagarith">Lagarith</a></li>

<li><a href="Microsoft_Video_1" title="Microsoft Video 1">Microsoft Video 1</a></li>

<li><a href="MSU_Lossless_Video_Codec" title="MSU Lossless Video Codec">MSU Lossless</a></li>

<li><a href="OMS_Video" title="OMS Video">OMS Video</a></li>

<li><a href="Pixlet" title="Pixlet">Pixlet</a></li>

<li><a href="Apple_ProRes" title="Apple ProRes">ProRes</a>

<li>QuickTime

<ul><li><a href="QuickTime_Animation" title="QuickTime Animation">Animation</a></li>

<li><a href="QuickTime_Graphics" title="QuickTime Graphics">Graphics</a></li></ul></li>

<li><a href="RealVideo" title="RealVideo">RealVideo</a></li>

<li><a href="RTVideo" title="RTVideo">RTVideo</a></li>

<li><a href="SheerVideo" title="SheerVideo">SheerVideo</a></li>

<li><a href="Smacker_video" title="Smacker video">Smacker</a></li>

<li><a href="Sorenson_Media" title="Sorenson Media">Sorenson Video/Spark</a></li>

<li><a href="Theora" title="Theora">Theora</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Audio_coding_format" title="Audio coding format">Audio<br>compression</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:5em"><a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>, <a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a>,<br> <a href="Moving_Picture_Experts_Group" title="Moving Picture Experts Group">MPEG</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="MPEG-1_Audio_Layer_II" title="MPEG-1 Audio Layer II">MPEG-1 Layer II</a>

<ul><li><a href="MPEG_Multichannel" title="MPEG Multichannel">Multichannel</a></li></ul></li>

<li><a href="MPEG-1_Audio_Layer_I" title="MPEG-1 Audio Layer I">MPEG-1 Layer I</a></li>

<li><a href="MP3" title="MP3">MPEG-1 Layer III (MP3)</a></li>

<li><a href="MPEG_Surround" title="MPEG Surround">MPEG Surround</a></li>

<li><a href="MPEG-H_3D_Audio" title="MPEG-H 3D Audio">MPEG-H 3D Audio</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="ITU-T" title="ITU-T">ITU-T</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

</ul></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="Internet_Engineering_Task_Force" title="Internet Engineering Task Force">IETF</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<li><a href="Speex" title="Speex">Speex</a></li>

<li><a href="Vorbis" title="Vorbis">Vorbis</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="3GPP" title="3GPP">3GPP</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="ETSI" class="mw-redirect" title="ETSI">ETSI</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="Bluetooth_Special_Interest_Group" title="Bluetooth Special Interest Group">Bluetooth SIG</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<li><a href="Audio_Video_Standard#Second_generation" title="Audio Video Standard">AVS2 P3</a>(GB/T 33475.3)

<ul><li>Audio Vivid(GY/T 363)</li></ul></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>

<li><a href="Adaptive_Transform_Acoustic_Coding" class="mw-redirect" title="Adaptive Transform Acoustic Coding">ATRAC</a></li>

<li><a href="Codec_2" title="Codec 2">Codec 2</a></li>

<li><a href="Monkey's_Audio" title="Monkey's Audio">Monkey's Audio</a></li>

<li><a href="Musepack" title="Musepack">Musepack</a></li>

<li><a href="OptimFROG" title="OptimFROG">OptimFROG</a></li>

<li><a href="Qualcomm_code-excited_linear_prediction" title="Qualcomm code-excited linear prediction">QCELP</a></li>

<li><a href="Relaxed_code-excited_linear_prediction" title="Relaxed code-excited linear prediction">RCELP</a></li>

<li><a href="RealAudio" title="RealAudio">RealAudio</a></li>

<li><a href="Siren_(codec)" title="Siren (codec)">Siren</a></li>

<li><a href="SVOPC" title="SVOPC">SVOPC</a></li>

<li>TTA

<ul><li>True Audio</li></ul></li>

<li><a href="TwinVQ" title="TwinVQ">TwinVQ</a></li>

<li><a href="Vector_sum_excited_linear_prediction" title="Vector sum excited linear prediction">VSELP</a></li>

<li><a href="WavPack" title="WavPack">WavPack</a></li>

<li><a href="AptX#aptX_Low_Latency" title="AptX">aptX Low Latency</a></li>

<li><a href="AptX#aptX_Adaptive" title="AptX">aptX Adaptive</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Image_compression" title="Image compression">Image<br>compression</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:5em"><a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a>, <a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>, <a href="Internet_Engineering_Task_Force" title="Internet Engineering Task Force">IETF</a>, <br><a href="World_Wide_Web_Consortium" title="World Wide Web Consortium">W3C</a>, <a href="ITU-T" title="ITU-T">ITU-T</a>, <a href="Joint_Photographic_Experts_Group" title="Joint Photographic Experts Group">JPEG</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Group_4_compression" title="Group 4 compression">CCITT Group 4</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Digital_container_format" class="mw-redirect" title="Digital container format">Containers</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:5em"><a href="International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>, <a href="International_Electrotechnical_Commission" title="International Electrotechnical Commission">IEC</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<li><a href="ISO/IEC_base_media_file_format" class="mw-redirect" title="ISO/IEC base media file format">ISO/IEC base media file format</a></li>

<li><a href="Motion_JPEG_2000" title="Motion JPEG 2000">Motion JPEG 2000</a></li>

<li><a href="MPEG_media_transport" title="MPEG media transport">MPEG media transport</a></li></ul>

<li><a href="Matroska" title="Matroska">Matroska</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em"><a href="Society_of_Motion_Picture_and_Television_Engineers" title="Society of Motion Picture and Television Engineers">SMPTE</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Others</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Smacker_video" title="Smacker video">Smacker</a></li></ul></li>

<li><a href="DivX#DivX_Media_Format_(DMF)" title="DivX">DivX Media Format</a></li>

<li><a href="Flash_Video" title="Flash Video">Flash Video</a></li>

<li><a href="Matroska" title="Matroska">Matroska</a>

<li><a href="QuickTime_File_Format" title="QuickTime File Format">QuickTime File Format</a></li>

<li><a href="RatDVD" title="RatDVD">RatDVD</a></li>

<li><a href="RealMedia" title="RealMedia">RealMedia</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Collaborations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="NETVC" title="NETVC">NETVC</a></li>

<li><a href="Alliance_for_Open_Media" title="Alliance for Open Media">Alliance for Open Media</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Data_compression" title="Data compression">Methods</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Entropy_encoding" class="mw-redirect" title="Entropy encoding">Entropy</a>

<ul><li><a href="Arithmetic_coding" title="Arithmetic coding">Arithmetic</a></li>

<li><a href="Huffman_coding" title="Huffman coding">Huffman</a></li>

<li><a href="Modified_Huffman_coding" title="Modified Huffman coding">Modified</a></li></ul></li>

<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>

<li><a href="Lossless_compression" title="Lossless compression">Lossless</a></li>

<li><a href="Lossy_compression" title="Lossy compression">Lossy</a></li>

<ul><li><a href="DEFLATE" class="mw-redirect" title="DEFLATE">DEFLATE</a></li>

<li><a href="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li>

<li><a href="Transform_coding" title="Transform coding">Transforms</a>

<li><a href="Wavelet" title="Wavelet">Wavelet</a>

<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Comparison_of_audio_coding_formats" title="Comparison of audio coding formats">Comparison of audio coding formats</a></li>

<li><a href="Comparison_of_video_codecs" title="Comparison of video codecs">Comparison of video codecs</a></li>

<li><a href="List_of_codecs" title="List of codecs">List of codecs</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>See Compression methods for techniques and Compression software for codecs</div></td></tr></tbody></table></div>

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