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Audio coding format
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<h2 id="lossless-lossy-and-uncompressed-audio-coding-formats">Lossless, lossy, and uncompressed audio coding formats</h2> <p>A <a href="/facts/Lossless_compression/LS702KsN">lossless</a> audio coding format reduces the total data needed to represent a sound but can be de-coded to its original, uncompressed form. A <a href="/facts/Lossy_compression/jHW7DDv3">lossy</a> audio coding format additionally reduces the <a href="/facts/Audio_bit_depth/24ccTeTT">bit resolution</a> of the sound on top of compression, which results in far less data at the cost of irretrievably lost information. </p><p>Transmitted (streamed) audio is most often compressed using lossy audio codecs as the smaller size is far more convenient for distribution. The most widely used audio coding formats are <a href="/facts/MP3/yrBpxUSD">MP3</a> and <a href="/facts/Advanced_Audio_Coding/VAG9NpI4">Advanced Audio Coding</a> (AAC), both of which are lossy formats based on <a href="/facts/Modified_discrete_cosine_transform/jCaDMSNY">modified discrete cosine transform</a> (MDCT) and <a href="/facts/Perceptual_coding/1GRCBbfQ">perceptual coding</a> algorithms. </p><p>Lossless audio coding formats such as <a href="/facts/FLAC/TbqpHlWy">FLAC</a> and <a href="/facts/Apple_Lossless/a0D0hzbK">Apple Lossless</a> are sometimes available, though at the cost of larger files. </p><p><a href="/facts/Uncompressed_audio/hLgkfATf">Uncompressed audio</a> formats, such as <a href="/facts/Pulse-code_modulation/5gdfjtH3">pulse-code modulation</a> (PCM, or .wav), are also sometimes used. PCM was the standard format for <a href="/facts/Compact_Disc_Digital_Audio/FDMqNLw5">Compact Disc Digital Audio</a> (CDDA). </p> <h2 id="history">History</h2> <p>In 1950, <a href="/facts/Bell_Labs/fKP5Gk0H">Bell Labs</a> filed the patent on <a href="/facts/Differential_pulse-code_modulation/v8H09k06">differential pulse-code modulation</a> (DPCM).<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> <a href="/facts/Adaptive_DPCM/Q6cFrNUb">Adaptive DPCM</a> (ADPCM) was introduced by P. Cummiskey, <a href="/facts/Nikil_Jayant/WqT1a12L">Nikil S. Jayant</a> and <a href="/facts/James_L._Flanagan/SX7EGc37">James L. Flanagan</a> at <a href="/facts/Bell_Labs/fKP5Gk0H">Bell Labs</a> in 1973.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p><p><a href="/facts/Perceptual_coding/1GRCBbfQ">Perceptual coding</a> was first used for <a href="/facts/Speech_coding/xs5gvMXq">speech coding</a> compression, with <a href="/facts/Linear_predictive_coding/2Bl1xdSN">linear predictive coding</a> (LPC).<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> Initial concepts for LPC date back to the work of <a href="/facts/Fumitada_Itakura/RnbyhGNI">Fumitada Itakura</a> (<a href="/facts/Nagoya_University/0MABJXSj">Nagoya University</a>) and Shuzo Saito (<a href="/facts/Nippon_Telegraph_and_Telephone/a3gI457X">Nippon Telegraph and Telephone</a>) in 1966.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> During the 1970s, <a href="/facts/Bishnu_S._Atal/bI2098fu">Bishnu S. Atal</a> and <a href="/facts/Manfred_R._Schroeder/0AQPXT8L">Manfred R. Schroeder</a> at <a href="/facts/Bell_Labs/fKP5Gk0H">Bell Labs</a> developed a form of LPC called <a href="/facts/Adaptive_predictive_coding/7uAwy6mJ">adaptive predictive coding</a> (APC), a perceptual coding algorithm that exploited the masking properties of the human ear, followed in the early 1980s with the <a href="/facts/Code-excited_linear_prediction/Shkm4bjo">code-excited linear prediction</a> (CELP) algorithm which achieved a significant compression ratio for its time.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> Perceptual coding is used by modern audio compression formats such as <a href="/facts/MP3/yrBpxUSD">MP3</a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> and <a href="/facts/Advanced_Audio_Codec/VAG9NpI4">AAC</a>. </p><p><a href="/facts/Discrete_cosine_transform/gPpDhPwP">Discrete cosine transform</a> (DCT), developed by <a href="/facts/Nasir_Ahmed_(engineer)/LImldyWe">Nasir Ahmed</a>, T. Natarajan and <a href="/facts/K._R._Rao/DwrVrQ6u">K. R. Rao</a> in 1974,<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> provided the basis for the <a href="/facts/Modified_discrete_cosine_transform/jCaDMSNY">modified discrete cosine transform</a> (MDCT) used by modern audio compression formats such as MP3<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> and AAC. MDCT was proposed by J. P. Princen, A. W. Johnson and A. B. Bradley in 1987,<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> following earlier work by Princen and Bradley in 1986.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> The MDCT is used by modern audio compression formats such as <a href="/facts/Dolby_Digital/58JfURnU">Dolby Digital</a>,<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a><a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> <a href="/facts/MP3/yrBpxUSD">MP3</a>,<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> and <a href="/facts/Advanced_Audio_Coding/VAG9NpI4">Advanced Audio Coding</a> (AAC).<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> </p> <h2 id="list-of-lossy-formats">List of lossy formats</h2> <h3>General</h3> <table><tbody><tr><th rowspan="2">Basic compression algorithm</th><th rowspan="2">Audio coding standard</th><th rowspan="2">Abbreviation</th><th rowspan="2">Introduction</th><th colspan="2">Market share (2023)<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a></th><th>Ref</th></tr><tr><th>Production</th><th>Streaming</th><th></th></tr><tr><td rowspan="11"><a href="/facts/Modified_discrete_cosine_transform/jCaDMSNY">Modified discrete cosine transform</a> (MDCT)</td><td><a href="/facts/Dolby_Digital/58JfURnU">Dolby Digital</a> (AC-3)</td><td>AC3</td><td>1991</td><td rowspan="2">36–54%<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></td><td rowspan="2">37–61%<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a></td><td><a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a><a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></td></tr><tr><td><a href="/facts/Dolby_Digital/58JfURnU">Dolby Digital Plus</a> (E-AC-3)</td><td>EAC3</td><td>2004</td><td><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></td></tr><tr><td><a href="/facts/ATRAC/kD9psz23">Adaptive Transform Acoustic Coding</a></td><td>ATRAC</td><td>1992</td><td>Unknown</td><td>Unknown</td><td><a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></td></tr><tr><td><a href="/facts/MPEG_Layer_III/yrBpxUSD">MPEG Layer III</a></td><td>MP3</td><td>1993</td><td>15%</td><td>19%</td><td><a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a><a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a></td></tr><tr><td><a href="/facts/Advanced_Audio_Coding/VAG9NpI4">Advanced Audio Coding</a> (<a href="/facts/MPEG-2/SpuH5FJu">MPEG-2</a> / <a href="/facts/MPEG-4/6svV1w2H">MPEG-4</a>)</td><td>AAC</td><td>1997</td><td>83%</td><td>87%</td><td><a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a><a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a></td></tr><tr><td><a href="/facts/Windows_Media_Audio/s5zePro7">Windows Media Audio</a></td><td>WMA</td><td>1999</td><td>Unknown</td><td>Unknown</td><td><a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a></td></tr><tr><td><a href="/facts/Ogg/KF4j68N7">Ogg</a> <a href="/facts/Vorbis/rqJDTF0T">Vorbis</a></td><td>Ogg</td><td>2000</td><td>6%</td><td>4%</td><td><a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a><a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a></td></tr><tr><td><a href="/facts/CELT/52Wt9cbu">Constrained Energy Lapped Transform</a></td><td>CELT</td><td>2011</td><td>—</td><td>—</td><td><a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a></td></tr><tr><td><a href="/facts/Opus_(audio_format)/VP4KuGre">Opus</a></td><td>Opus</td><td>2012</td><td>12%</td><td>9%</td><td><a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a></td></tr><tr><td><a href="/facts/Dolby_AC-4/FXj0MW2d">Dolby AC-4</a></td><td>AC4</td><td>2014</td><td>Unknown</td><td>Unknown</td><td><a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a></td></tr><tr><td><a href="/facts/LDAC_(codec)/IMFHz8ux">LDAC</a></td><td>LDAC</td><td>2015</td><td>Unknown</td><td>Unknown</td><td><a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a><a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a></td></tr><tr><td rowspan="3"><a href="/facts/Adaptive_differential_pulse-code_modulation/Q6cFrNUb">Adaptive differential pulse-code modulation</a> (ADPCM)</td><td><a href="/facts/AptX/cSevMczh">aptX / aptX-HD</a></td><td>aptX</td><td>1989</td><td>Unknown</td><td>Unknown</td><td><a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a></td></tr><tr><td><a href="/facts/DTS_(company)/wbQwqtdQ">Digital Theater Systems</a></td><td>DTS</td><td>1990</td><td>8%</td><td>6%</td><td><a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a><a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a></td></tr><tr><td><a href="/facts/Master_Quality_Authenticated/alxKG7Se">Master Quality Authenticated</a></td><td>MQA</td><td>2014</td><td>Unknown</td><td>Unknown</td><td></td></tr><tr><td rowspan="3"><a href="/facts/Sub-band_coding/HWMqu3DR">Sub-band coding</a> (SBC)</td><td><a href="/facts/MPEG-1_Audio_Layer_II/eBSjFASu">MPEG-1 Audio Layer II</a></td><td>MP2</td><td>1993</td><td rowspan="2">Unknown</td><td rowspan="2">Unknown</td><td><a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a></td></tr><tr><td><a href="/facts/Musepack/GX6WMwkl">Musepack</a></td><td>MPC</td><td>1997</td><td></td></tr><tr><td><a href="/facts/SBC_(codec)/SQCUG3JY">SBC</a></td><td>SBC</td><td>2003</td><td>Unknown</td><td>Unknown</td><td><a class="footnote-ref" id="fnref:42" href="#fn:42"><sup>42</sup></a></td></tr></tbody></table> <h3>Speech</h3> <p class="note">Further information: <a href="/facts/Speech_coding/xs5gvMXq">Speech coding</a></p> <ul><li><a href="/facts/Linear_predictive_coding/2Bl1xdSN">Linear predictive coding</a> (LPC) <ul><li><a href="/facts/Adaptive_predictive_coding/7uAwy6mJ">Adaptive predictive coding</a> (APC)</li> <li><a href="/facts/Code-excited_linear_prediction/Shkm4bjo">Code-excited linear prediction</a> (CELP)</li> <li><a href="/facts/Algebraic_code-excited_linear_prediction/zGb0XLT2">Algebraic code-excited linear prediction</a> (ACELP)</li> <li><a href="/facts/Relaxed_code-excited_linear_prediction/oMh2HQH9">Relaxed code-excited linear prediction</a> (RCELP)</li> <li><a href="/facts/Low-delay_CELP/x3aq2vED">Low-delay CELP</a> (LD-CELP)</li> <li><a href="/facts/Adaptive_Multi-Rate_audio_codec/lE2gNqNr">Adaptive Multi-Rate</a> (used in <a href="/facts/GSM/Sw8QYaLE">GSM</a> and <a href="/facts/3GPP/TBrQYKFF">3GPP</a>)</li> <li><a href="/facts/Codec_2/c1v01HdD">Codec 2</a> (noted for its lack of patent restrictions)</li> <li><a href="/facts/Speex/M7xqnPxN">Speex</a> (noted for its lack of patent restrictions)</li></ul></li> <li><a href="/facts/Modified_discrete_cosine_transform/jCaDMSNY">Modified discrete cosine transform</a> (MDCT) <ul><li><a href="/facts/AAC-LD/VndVLu7F">AAC-LD</a></li> <li><a href="/facts/CELT/52Wt9cbu">Constrained Energy Lapped Transform</a> (CELT)</li> <li><a href="/facts/Opus_(audio_format)/VP4KuGre">Opus</a> (mostly for real-time applications)</li></ul></li></ul> <h2 id="list-of-lossless-formats">List of lossless formats</h2> <ul><li><a href="/facts/Apple_Lossless_Audio_Codec/a0D0hzbK">Apple Lossless</a> (ALAC – Apple Lossless Audio Codec)</li> <li><a href="/facts/ATRAC/kD9psz23">Adaptive Transform Acoustic Coding</a> (ATRAC)</li> <li><a href="/facts/Audio_Lossless_Coding/ptpbl4hK">Audio Lossless Coding</a> (also known as MPEG-4 ALS)</li> <li><a href="/facts/Super_Audio_CD/f4a7Gu0V">Direct Stream Transfer</a> (DST)</li> <li><a href="/facts/Dolby_TrueHD/ySxj3zIY">Dolby TrueHD</a></li> <li><a href="/facts/DTS-HD_Master_Audio/zprgCEGx">DTS-HD Master Audio</a></li> <li><a href="/facts/FLAC/TbqpHlWy">Free Lossless Audio Codec</a> (FLAC)</li> <li><a href="/facts/Discrete_cosine_transform/gPpDhPwP">Lossless discrete cosine transform</a> (LDCT)</li> <li><a href="/facts/Meridian_Lossless_Packing/uUXCuWSE">Meridian Lossless Packing</a> (MLP)</li> <li><a href="/facts/Monkey%2527s_Audio/UIJz1IQG">Monkey's Audio</a> (Monkey's Audio APE)</li> <li><a href="/facts/MPEG-4_SLS/0hcHB4NH">MPEG-4 SLS</a> (also known as HD-AAC)</li> <li><a href="/facts/OptimFROG/NHF2DoKS">OptimFROG</a></li> <li><a href="/facts/Original_Sound_Quality/WUThq9tU">Original Sound Quality</a> (OSQ)</li> <li><a href="/facts/RealPlayer/IjS4t5h8">RealPlayer</a> (RealAudio Lossless)</li> <li><a href="/facts/Shorten_(codec)/XvWCEsxJ">Shorten</a> (SHN)</li> <li>TTA (True Audio Lossless)</li> <li><a href="/facts/WavPack/MN8nT9Gj">WavPack</a> (WavPack lossless)</li> <li><a href="/facts/Windows_Media_Audio_9_Lossless/s5zePro7">WMA Lossless</a> (Windows Media Lossless)</li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Comparison_of_audio_coding_formats/vn4Ym1dR">Comparison of audio coding formats</a></li> <li><a href="/facts/Data_compression/gMFuY4FT">Data compression#Audio</a></li> <li><a href="/facts/Audio_file_format/hLgkfATf">Audio file format</a></li> <li><a href="/facts/List_of_audio_compression_formats/e5nTCc5X">List of audio compression formats</a></li></ul> <h2 id="notes">Notes</h2> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>The term "audio coding" can be seen in e.g. the name Advanced Audio Coding, and is analogous to the term video coding <a href="/wiki/Advanced_Audio_Coding" target="_blank">/wiki/Advanced_Audio_Coding</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>"Video – Where is synchronization information stored in container formats?". <a href="http://superuser.com/questions/357686/where-is-synchronization-information-stored-in-container-formats" target="_blank">http://superuser.com/questions/357686/where-is-synchronization-information-stored-in-container-formats</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>US patent 2605361, C. Chapin Cutler, "Differential Quantization of Communication Signals", issued 1952-07-29 <a href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US2605361" target="_blank">https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US2605361</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Cummiskey, P.; Jayant, N. S.; Flanagan, J. L. (1973). "Adaptive Quantization in Differential PCM Coding of Speech". Bell System Technical Journal. 52 (7): 1105–1118. doi:10.1002/j.1538-7305.1973.tb02007.x. <a href="https://ieeexplore.ieee.org/document/6770730" target="_blank">https://ieeexplore.ieee.org/document/6770730</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Cummiskey, P.; Jayant, Nikil S.; Flanagan, J. L. (1973). "Adaptive quantization in differential PCM coding of speech". The Bell System Technical Journal. 52 (7): 1105–1118. doi:10.1002/j.1538-7305.1973.tb02007.x. ISSN 0005-8580. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Schroeder, Manfred R. (2014). "Bell Laboratories". Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder. Springer. p. 388. ISBN 9783319056609. <a href="9783319056609" target="_blank">9783319056609</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Gray, Robert M. (2010). "A History of Realtime Digital Speech on Packet Networks: Part II of Linear Predictive Coding and the Internet Protocol" (PDF). Found. Trends Signal Process. 3 (4): 203–303. doi:10.1561/2000000036. ISSN 1932-8346. <a href="https://ee.stanford.edu/~gray/lpcip.pdf" target="_blank">https://ee.stanford.edu/~gray/lpcip.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Schroeder, Manfred R. (2014). "Bell Laboratories". Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder. Springer. p. 388. ISBN 9783319056609. <a href="9783319056609" target="_blank">9783319056609</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Schroeder, Manfred R. (2014). "Bell Laboratories". Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder. Springer. p. 388. ISBN 9783319056609. <a href="9783319056609" target="_blank">9783319056609</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Nasir Ahmed; T. Natarajan; Kamisetty Ramamohan Rao (January 1974). "Discrete Cosine Transform" (PDF). IEEE Transactions on Computers. C-23 (1): 90–93. doi:10.1109/T-C.1974.223784. S2CID 149806273. Archived from the original (PDF) on 2016-12-08. Retrieved 2019-10-20. <a href="/wiki/N._Ahmed" target="_blank">/wiki/N._Ahmed</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Guckert, John (Spring 2012). "The Use of FFT and MDCT in MP3 Audio Compression" (PDF). University of Utah. Retrieved 14 July 2019. <a href="http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf" target="_blank">http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Princen, J.; Johnson, A.; Bradley, A. (1987). "Subband/Transform coding using filter bank designs based on time domain aliasing cancellation". ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing. Vol. 12. pp. 2161–2164. doi:10.1109/ICASSP.1987.1169405. S2CID 58446992. <a href="https://ieeexplore.ieee.org/document/1169405" target="_blank">https://ieeexplore.ieee.org/document/1169405</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Princen, J.; Bradley, A. (1986). "Analysis/Synthesis filter bank design based on time domain aliasing cancellation". IEEE Transactions on Acoustics, Speech, and Signal Processing. 34 (5): 1153–1161. doi:10.1109/TASSP.1986.1164954. <a href="https://ieeexplore.ieee.org/document/1164954" target="_blank">https://ieeexplore.ieee.org/document/1164954</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Luo, Fa-Long (2008). Mobile Multimedia Broadcasting Standards: Technology and Practice. Springer Science & Business Media. p. 590. ISBN 9780387782638. <a href="9780387782638" target="_blank">9780387782638</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Britanak, V. (2011). "On Properties, Relations, and Simplified Implementation of Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards". IEEE Transactions on Audio, Speech, and Language Processing. 19 (5): 1231–1241. doi:10.1109/TASL.2010.2087755. S2CID 897622. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Guckert, John (Spring 2012). "The Use of FFT and MDCT in MP3 Audio Compression" (PDF). University of Utah. Retrieved 14 July 2019. <a href="http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf" target="_blank">http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Brandenburg, Karlheinz (1999). "MP3 and AAC Explained" (PDF). 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