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[[Discrete cosine transform]] (DCT), developed by [[N. Ahmed|Nasir Ahmed]], T. Natarajan and [[K. R. Rao]] in 1974,<ref name="DCT">{{cite journal |author1=Nasir Ahmed |author1-link=N. Ahmed |author2=T. Natarajan |author3=Kamisetty Ramamohan Rao |journal=IEEE Transactions on Computers|title=Discrete Cosine Transform|volume=C-23|issue=1|pages=90–93|date=January 1974 |doi=10.1109/T-C.1974.223784 |url=https://www.ic.tu-berlin.de/fileadmin/fg121/Source-Coding_WS12/selected-readings/Ahmed_et_al.__1974.pdf}}</ref> provided the basis for the [[modified discrete cosine transform]] (MDCT) used by modern audio compression formats such as MP3<ref name="Guckert">{{cite web |last1=Guckert |first1=John |title=The Use of FFT and MDCT in MP3 Audio Compression |url=http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf |website=[[University of Utah]] |date=Spring 2012 |accessdate=14 July 2019}}</ref> and AAC. MDCT was proposed by J. P. Princen, A. W. Johnson and A. B. Bradley in 1987,<ref>J. P. Princen, A. W. Johnson und A. B. Bradley: ''Subband/transform coding using filter bank designs based on time ___domain aliasing cancellation'', IEEE Proc. Intl. Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2161–2164, 1987.</ref> following earlier work by Princen and Bradley in 1986.<ref>John P. Princen, Alan B. Bradley: ''Analysis/synthesis filter bank design based on time ___domain aliasing cancellation'', IEEE Trans. Acoust. Speech Signal Processing, ''ASSP-34'' (5), 1153–1161, 1986.</ref> The MDCT is used by modern audio compression formats such as [[Dolby Digital]],<ref name="Luo">{{cite book |last1=Luo |first1=Fa-Long |title=Mobile Multimedia Broadcasting Standards: Technology and Practice |date=2008 |publisher=[[Springer Science & Business Media]] |isbn=9780387782638 |page=590 |url=https://books.google.com/books?id=l6PovWat8SMC&pg=PA590}}</ref><ref>{{cite journal |last1=Britanak |first1=V. |title=On Properties, Relations, and Simplified Implementation of Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards |journal=IEEE Transactions on Audio, Speech, and Language Processing |date=2011 |volume=19 |issue=5 |pages=1231–1241 |doi=10.1109/TASL.2010.2087755}}</ref> [[MP3]],<ref name="Guckert">{{cite web |last1=Guckert |first1=John |title=The Use of FFT and MDCT in MP3 Audio Compression |url=http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf |website=[[University of Utah]] |date=Spring 2012 |accessdate=14 July 2019}}</ref> and [[Advanced Audio Coding]] (AAC).<ref name=brandenburg>{{cite web|url=http://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf|title=MP3 and AAC Explained|last=Brandenburg|first=Karlheinz|year=1999|url-status=live|archiveurl=https://web.archive.org/web/20170213191747/https://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf|archivedate=2017-02-13}}</ref>
==List of lossy formats==
===General===
*[[Modified discrete cosine transform]] (MDCT)
**[[Dolby Digital]] (AC-3)
**[[Adaptive Transform Acoustic Coding]] (ATRAC)
**[[MPEG Layer III]] (MP3)<ref name="Guckert">{{cite web |last1=Guckert |first1=John |title=The Use of FFT and MDCT in MP3 Audio Compression |url=http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf |website=[[University of Utah]] |date=Spring 2012 |accessdate=14 July 2019}}</ref>
**[[Advanced Audio Coding]] (AAC / [[MP4]] Audio)<ref name=brandenburg>{{cite web|url=http://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf|title=MP3 and AAC Explained|last=Brandenburg|first=Karlheinz|year=1999|url-status=live|archiveurl=https://web.archive.org/web/20170213191747/https://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf|archivedate=2017-02-13}}</ref>
**[[Ogg]] [[Vorbis]] (noted for its lack of patent restrictions)
**[[Windows Media Audio]] (WMA) ([[Lossless compression|lossless]] codec available too)
**[[LDAC (codec)|LDAC]]<ref name="Darko 2017">{{cite web | last=Darko | first=John H. | title=The inconvenient truth about Bluetooth audio | website=DAR__KO | date=2017-03-29 | url=http://www.digitalaudioreview.net/2017/03/the-inconvenient-truth-about-bluetooth-audio/ | access-date=2018-01-13}}</ref><ref name="AVHub 2015">{{cite web|url=http://www.avhub.com.au/news/sound-image/what-is-sony-ldac-and-how-does-it-do-it-408285|title=What is Sony LDAC, and how does it do it?|last=Ford|first=Jez|date=2015-08-24|website=AVHub|url-status=live|archive-url=|archive-date=|access-date=2018-01-13}}</ref>
** [[Constrained Energy Lapped Transform]] (CELT)
** [[Opus (codec)|Opus]] (mostly for real-time applications)
*[[Adaptive differential pulse-code modulation]] (ADPCM)
**[[Master Quality Authenticated]] (MQA)
*[[MPEG-1 Audio Layer II]] (MP2)
*[[Musepack]] (based on Musicam)
*[[AptX|aptX/ aptX-HD]]<ref name="AVHub 2016">{{cite web|url=http://www.avhub.com.au/news/sound-image/aptx-hd---lossless-or-lossy-442124|title=aptX HD - lossless or lossy?|last=Ford|first=Jez|date=2016-11-22|website=AVHub|url-status=live|archive-url=|archive-date=|access-date=2018-01-13}}</ref>
===Speech===
{{further|Speech coding}}
* [[Linear predictive coding]] (LPC)
** [[Adaptive predictive coding]] (APC)
** [[Code-excited linear prediction]] (CELP)
** [[Algebraic code-excited linear prediction]] (ACELP)
** [[Relaxed code-excited linear prediction]] (RCELP)
** [[Low-delay CELP]] (LD-CELP)
** [[Adaptive Multi-Rate audio codec|Adaptive Multi-Rate]] (used in [[GSM]] and [[3GPP]])
** [[Codec2]] (noted for its lack of patent restrictions)
** [[Speex]] (noted for its lack of patent restrictions)
* [[Modified discrete cosine transform]] (MDCT)
** [[AAC-LD]]
** [[Constrained Energy Lapped Transform]] (CELT)
** [[Opus (codec)|Opus]] (mostly for real-time applications)
== List of lossless formats ==
* [[Apple Lossless]] (ALAC – Apple Lossless Audio Codec)
* [[Adaptive Transform Acoustic Coding]] (ATRAC)
* [[Audio Lossless Coding]] (also known as MPEG-4 ALS)
* [[Super Audio CD#DST|Direct Stream Transfer]] (DST)
* [[Dolby TrueHD]]
* [[DTS-HD Master Audio]]
* [[Free Lossless Audio Codec]] (FLAC)
* [[Discrete cosine transform|Lossless discrete cosine transform]] (LDCT)
* [[Meridian Lossless Packing]] (MLP)
* [[Monkey's Audio]] (Monkey's Audio APE)
* [[MPEG-4 SLS]] (also known as HD-AAC)
* [[OptimFROG]]
* [[Original Sound Quality]] (OSQ)
* [[RealPlayer]] (RealAudio Lossless)
* [[Shorten (file format)|Shorten]] (SHN)
* [[TTA (codec)|TTA]] (True Audio Lossless)
* [[WavPack]] (WavPack lossless)
* [[Windows Media Audio 9 Lossless|WMA Lossless]] (Windows Media Lossless)
==See also==
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