Editing Discrete cosine transform (section)

==Applications==
The DCT is the most widely used transformation technique in [[signal processing]],<ref name="Muchahary">{{cite book |last1=Muchahary |first1=D. |last2=Mondal |first2=A. J. |last3=Parmar |first3=R. S. |last4=Borah |first4=A. D. |last5=Majumder |first5=A. |title=2015 Fifth International Conference on Communication Systems and Network Technologies |chapter=A Simplified Design Approach for Efficient Computation of DCT |date=2015 |pages=483–487 |doi=10.1109/CSNT.2015.134|isbn=978-1-4799-1797-6 |s2cid=16411333 }}</ref> and by far the most widely used linear transform in [[data compression]].<ref>{{cite book |last1=Chen |first1=Wai Kai |title=The Electrical Engineering Handbook |date=2004 |publisher=[[Elsevier]] |isbn=9780080477480 |page=906 |url=https://books.google.com/books?id=qhHsSlazGrQC&pg=PA906}}</ref> Uncompressed [[digital media]] as well as [[lossless compression]] have high [[computer memory|memory]] and [[bandwidth (computing)|bandwidth]] requirements, which is significantly reduced by the DCT [[lossy compression]] technique,<ref name="Barbero">{{cite journal |last1=Barbero |first1=M. |last2=Hofmann |first2=H. |last3=Wells |first3=N. D. |title=DCT source coding and current implementations for HDTV |journal=EBU Technical Review |date=14 November 1991 |issue=251 |pages=22–33 |publisher=[[European Broadcasting Union]] |url=https://tech.ebu.ch/publications/trev_251-barbero |access-date=4 November 2019}}</ref><ref name="Lea"/> capable of achieving [[data compression ratio]]s from 8:1 to 14:1 for near-studio-quality,<ref name="Barbero"/> up to 100:1 for acceptable-quality content.<ref name="Lea"/> DCT compression standards are used in digital media technologies, such as [[digital images]], [[digital photo]]s,<ref name="Atlantic">{{cite web |title=What Is a JPEG? The Invisible Object You See Every Day |url=https://www.theatlantic.com/technology/archive/2013/09/what-is-a-jpeg-the-invisible-object-you-see-every-day/279954/ |access-date=13 September 2019 |website=[[The Atlantic]] |date=24 September 2013}}</ref><ref name="epfl">{{cite news |last1=Pessina |first1=Laure-Anne |title=JPEG changed our world |url=https://actu.epfl.ch/news/jpeg-changed-our-world/ |access-date=13 September 2019 |work=EPFL News |publisher=[[École Polytechnique Fédérale de Lausanne]] |date=12 December 2014}}</ref> [[digital video]],<ref name="Ghanbari">{{cite book |last1=Ghanbari |first1=Mohammed |title=Standard Codecs: Image Compression to Advanced Video Coding |date=2003 |publisher=[[Institution of Engineering and Technology]] |isbn=9780852967102 |pages=1–2 |url=https://books.google.com/books?id=7XuU8T3ooOAC&pg=PA1}}</ref><ref name="Lee1995">{{cite journal|last1=Lee|first1=Ruby Bei-Loh|last2=Beck|first2=John P.|last3=Lamb|first3=Joel|last4=Severson|first4=Kenneth E.|date=April 1995|title=Real-time software MPEG video decoder on multimedia-enhanced PA 7100LC processors|url=https://www.hpl.hp.com/hpjournal/95apr/apr95a7.pdf|journal=[[Hewlett-Packard Journal]]|volume=46|issue=2|issn=0018-1153}}</ref> [[streaming media]],<ref name="Lee">{{cite book |last1=Lee |first1=Jack |title=Scalable Continuous Media Streaming Systems: Architecture, Design, Analysis and Implementation |date=2005 |publisher=[[John Wiley & Sons]] |isbn=9780470857649 |page=25 |url=https://books.google.com/books?id=7fuvu52cyNEC&pg=PA25}}</ref> [[digital television]], [[streaming television]], [[video on demand]] (VOD),<ref name="Lea"/> [[digital cinema]],<ref name="Luo"/> [[high-definition video]] (HD video), and [[high-definition television]] (HDTV).<ref name="Barbero"/><ref name="Shishikui">{{cite book |last1=Shishikui |first1=Yoshiaki |last2=Nakanishi |first2=Hiroshi |last3=Imaizumi |first3=Hiroyuki |title=Signal Processing of HDTV |chapter=An HDTV Coding Scheme using Adaptive-Dimension DCT |date=October 26–28, 1993 |pages=611–618 |doi=10.1016/B978-0-444-81844-7.50072-3 |chapter-url=https://books.google.com/books?id=j9XSBQAAQBAJ&pg=PA611 |publisher=[[Elsevier]] |isbn=9781483298511}}</ref>

The DCT, and in particular the DCT-II, is often used in signal and image processing, especially for lossy compression, because it has a strong ''energy compaction'' property.<ref name="pubDCT"/><ref name="pubRaoYip"/> In typical applications, most of the signal information tends to be concentrated in a few low-frequency components of the DCT. For strongly correlated [[Markov process]]es, the DCT can approach the compaction efficiency of the [[Karhunen-Loève transform]] (which is optimal in the decorrelation sense). As explained below, this stems from the boundary conditions implicit in the cosine functions.

DCTs are widely employed in solving [[partial differential equations]] by [[spectral methods]], where the different variants of the DCT correspond to slightly different even and odd boundary conditions at the two ends of the array.

DCTs are closely related to [[Chebyshev polynomials]], and fast DCT algorithms (below) are used in [[Chebyshev approximation]] of arbitrary functions by series of Chebyshev polynomials, for example in [[Clenshaw–Curtis quadrature]].

===General applications===
The DCT is widely used in many applications, which include the following.

{{columns-list|colwidth=50em|
*[[Audio signal processing]] — [[audio coding]], [[audio data compression]] (lossy and lossless),<ref name="Ochoa129">{{cite book |last1=Ochoa-Dominguez |first1=Humberto |last2=Rao |first2=K. R. |author2-link=K. R. Rao |title=Discrete Cosine Transform, Second Edition |date=2019 |publisher=[[CRC Press]] |isbn=9781351396486 |pages=1–3, 129 |url=https://books.google.com/books?id=dVOWDwAAQBAJ}}</ref> [[surround sound]],<ref name="Luo"/> [[Acoustic echo cancellation|acoustic echo]] and [[adaptive feedback cancellation|feedback cancellation]], [[phoneme]] recognition, [[time-domain aliasing cancellation]] (TDAC)<ref name="Ochoa"/>
**[[Digital audio]]<ref name="Stankovic"/>
**[[Digital radio]] — [[Digital Audio Broadcasting]] (DAB+),<ref name="Britanak"/> [[HD Radio]]<ref name="Jones">{{cite book |last1=Jones |first1=Graham A. |last2=Layer |first2=David H. |last3=Osenkowsky |first3=Thomas G. |title=National Association of Broadcasters Engineering Handbook: NAB Engineering Handbook |date=2013 |publisher=[[Taylor & Francis]] |isbn=978-1-136-03410-7 |pages=558–9 |url=https://books.google.com/books?id=K9N1TVhf82YC&pg=PA558}}</ref>
**[[Speech processing]] — [[speech coding]]<ref name="Hersent"/><ref name="AppleInsider standards 1"/> [[speech recognition]], [[voice activity detection]] (VAD)<ref name="Ochoa"/>
**[[Digital telephony]] — [[voice over IP]] (VoIP),<ref name="Hersent"/> [[mobile telephony]], [[video telephony]],<ref name="AppleInsider standards 1"/> [[teleconferencing]], [[videoconferencing]]<ref name="Stankovic"/>
*[[Biometrics]] — [[fingerprint]] orientation, [[facial recognition systems]], biometric [[digital watermarking|watermarking]], fingerprint-based biometric watermarking, [[palm print]] identification/recognition<ref name="Ochoa"/>
**[[Face detection]] — [[facial recognition system|facial recognition]]<ref name="Ochoa"/>
*[[Computers]] and the [[Internet]] — the [[World Wide Web]], [[social media]],<ref name="Atlantic"/><ref name="epfl"/> [[Internet video]]<ref name="Encodes"/>
**[[Network bandwidth]] usage reducation<ref name="Stankovic"/>
*[[Consumer electronics]]<ref name="Ochoa"/> — [[multimedia]] systems,<ref name="Stankovic"/> multimedia [[telecommunication]] devices,<ref name="Stankovic"/> consumer devices<ref name="Encodes"/>
*[[Cryptography]] — [[encryption]], [[steganography]], [[copyright]] protection<ref name="Ochoa"/>
*[[Data compression]] — [[transform coding]], [[lossy compression]], [[lossless compression]]<ref name="Ochoa129"/>
**[[Encoding]] operations — [[Quantization (signal processing)|quantization]], perceptual weighting, [[entropy encoding]], [[variable bitrate encoding]]<ref name="Stankovic"/>
*[[Digital media]]<ref name="Lee"/> — [[digital distribution]]<ref name="Bitmovin"/>
**[[Streaming media]]<ref name="Lee"/> — [[streaming audio]], [[streaming video]], [[streaming television]], [[video-on-demand]] (VOD)<ref name="Lea"/>
*[[Forgery detection]]<ref name="Ochoa"/>
*[[Geophysical]] [[transient electromagnetics]] (transient EM)<ref name="Ochoa"/>
*[[Image]]s — [[artist]] identification,<ref name="Ochoa">{{cite book |last1=Ochoa-Dominguez |first1=Humberto |last2=Rao |first2=K. R. |author2-link=K. R. Rao |title=Discrete Cosine Transform, Second Edition |date=2019 |publisher=[[CRC Press]] |isbn=9781351396486 |pages=1–3 |url=https://books.google.com/books?id=dVOWDwAAQBAJ&pg=PA1}}</ref> [[Focus (optics)|focus]] and [[Bokeh|blurriness]] measure,<ref name="Ochoa"/> [[feature extraction]]<ref name="Ochoa"/>
**[[Color]] formatting — formatting [[luminance]] and color differences, color formats (such as [[YUV444]] and [[YUV411]]), [[Encoding|decoding]] operations such as the inverse operation between display color formats ([[YIQ]], [[YUV]], [[RGB]])<ref name="Stankovic"/>
**[[Digital imaging]] — [[digital image]]s, [[digital camera]]s, [[digital photography]],<ref name="Atlantic"/><ref name="epfl"/> [[high-dynamic-range imaging]] (HDR imaging)<ref>{{cite book |last1=Ochoa-Dominguez |first1=Humberto |last2=Rao |first2=K. R. |title=Discrete Cosine Transform, Second Edition |date=2019 |publisher=CRC Press |isbn=9781351396486 |page=186 |url=https://books.google.com/books?id=dVOWDwAAQBAJ&pg=PA186}}</ref>
**[[Image compression]]<ref name="Ochoa"/><ref name="McKernan58"/> — [[image file format]]s,<ref name="Baraniuk"/> [[2D-plus-depth|multiview image]] compression, [[Progressive JPEG|progressive image]] transmission<ref name="Ochoa"/>
**[[Image processing]] — [[digital image processing]],<ref name="Stankovic"/> [[image analysis]], [[content-based image retrieval]], [[corner detection]], directional block-wise [[Sparse approximation|image representation]], [[edge detection]], [[image enhancement]], [[image fusion]], [[image segmentation]], [[interpolation]], [[image noise]] level estimation, mirroring, rotation, [[Just-noticeable difference|just-noticeable distortion]] (JND) profile, [[spatiotemporal]] masking effects, [[foveated imaging]]<ref name="Ochoa"/>
**[[Image quality]] assessment — DCT-based quality degradation metric (DCT QM)<ref name="Ochoa"/>
**[[Image reconstruction]] — directional [[image texture|textures]] auto inspection, image restoration, [[inpainting]], [[photo recovery|visual recovery]]<ref name="Ochoa"/>
*[[Medical technology]]
**[[Electrocardiography]] (ECG) — [[vectorcardiography]] (VCG)<ref name="Ochoa"/>
**[[Medical imaging]] — medical image compression, image fusion, watermarking, [[brain tumor]] [[brain compression|compression]] classification<ref name="Ochoa"/>
*[[Pattern recognition]]<ref name="Ochoa"/>
*[[Region of interest]] (ROI) extraction<ref name="Ochoa"/>
*[[Signal processing]] — [[digital signal processing]], [[digital signal processor]]s (DSP), DSP [[software]], [[multiplexing]], [[signaling]], control signals, [[analog-to-digital conversion]] (ADC),<ref name="Stankovic"/> [[compressive sampling]], DCT pyramid [[error concealment]], [[downsampling]], [[upsampling]], [[signal-to-noise ratio]] (SNR) estimation, [[transmux]], [[Wiener filter]]<ref name="Ochoa"/>
**[[Complex cepstrum]] feature analysis<ref name="Ochoa"/>
**DCT [[Filter (signal processing)|filtering]]<ref name="Ochoa"/>
*[[Surveillance]]<ref name="Ochoa"/>
*Vehicular [[event data recorder]] camera<ref name="Ochoa"/>
*[[Video]]
**[[Digital cinema]]<ref name="McKernan58">{{cite book |last1=McKernan |first1=Brian |title=Digital cinema: the revolution in cinematography, postproduction, distribution |date=2005 |publisher=[[McGraw-Hill]] |isbn=978-0-07-142963-4 |page=58 |url=https://books.google.com/books?id=5vBTAAAAMAAJ |quote=DCT is used in most of the compression systems standardized by the Moving Picture Experts Group (MPEG), is the dominant technology for image compression. In particular, it is the core technology of MPEG-2, the system used for DVDs, digital television broadcasting, that has been used for many of the trials of digital cinema.}}</ref> — [[digital cinematography]], [[digital movie camera]]s, [[video editing]], [[film editing]],<ref>{{cite book |last1=Ascher |first1=Steven |last2=Pincus |first2=Edward |title=The Filmmaker's Handbook: A Comprehensive Guide for the Digital Age: Fifth Edition |date=2012 |publisher=Penguin |isbn=978-1-101-61380-1 |pages=246–7 |url=https://books.google.com/books?id=zp4KMKwnYVoC&pg=PA246}}</ref><ref>{{cite book |last1=Bertalmio |first1=Marcelo |title=Image Processing for Cinema |date=2014 |publisher=[[CRC Press]] |isbn=978-1-4398-9928-1 |page=95 |url=https://books.google.com/books?id=6mnNBQAAQBAJ&pg=PA95}}</ref> [[Dolby Digital]] audio<ref name="Stankovic"/><ref name="Luo"/>
**[[Digital television]] (DTV)<ref name="Barbero"/> — [[digital television broadcasting]],<ref name="McKernan58"/> [[standard-definition television]] (SDTV), [[high-definition TV]] (HDTV),<ref name="Barbero"/><ref name="Shishikui"/> HDTV [[Video decoder|encoder/decoder chips]], [[ultra HDTV]] (UHDTV)<ref name="Stankovic"/>
**[[Digital video]]<ref name="Ghanbari"/><ref name="Lee1995"/> — [[digital versatile disc]] (DVD),<ref name="McKernan58"/> [[high-definition video|high-definition]] (HD) video<ref name="Barbero"/><ref name="Shishikui"/> 
**[[Video coding]] — [[video compression]],<ref name="Stankovic"/> [[video coding standards]],<ref name="Ochoa"/> [[motion estimation]], [[motion compensation]], [[inter-frame]] prediction, [[motion vector]]s,<ref name="Stankovic"/> [[Stereoscopic video coding|3D video coding]], local distortion detection probability (LDDP) model, [[moving object detection]], [[Multiview Video Coding]] (MVC)<ref name="Ochoa"/>
**[[Video processing]] — [[motion analysis]], 3D-DCT motion analysis, [[video content analysis]], [[data extraction]],<ref name="Ochoa"/> [[video browsing]],<ref>{{cite book |last1=Zhang |first1=HongJiang |chapter=Content-Based Video Browsing And Retrieval |editor-last1=Furht |editor-first1=Borko |title=Handbook of Internet and Multimedia Systems and Applications |date=1998 |publisher=[[CRC Press]] |isbn=9780849318580 |pages=[https://archive.org/details/handbookofintern0000unse_a3l0/page/83 83–108 (89)] |chapter-url=https://books.google.com/books?id=5zfC1wI0wzUC&pg=PA89 |url=https://archive.org/details/handbookofintern0000unse_a3l0/page/83 }}</ref> professional [[video production]]<ref name="loc"/>
*[[Watermark]]ing — [[digital watermarking]], [[image watermarking]], video watermarking, [[3D video]] watermarking, [[Digital watermarking#Reversible data hiding|reversible data hiding]], watermarking detection<ref name="Ochoa"/>
*[[Wireless]] technology
**[[Mobile devices]]<ref name="Encodes"/> — [[mobile phones]], [[smartphones]],<ref name="AppleInsider standards 1"/> [[videophones]]<ref name="Stankovic"/>
**[[Radio frequency]] (RF) technology — [[RF engineering]], [[Aperture synthesis|aperture]] [[Sensor array|arrays]],<ref name="Ochoa"/> [[beamforming]], [[digital electronics|digital]] [[arithmetic circuit]]s, directional [[Sensor|sensing]], [[astronomical image processing|space imaging]]<ref>{{cite journal |last1=Potluri |first1=U. S. |last2=Madanayake |first2=A. |last3=Cintra |first3=R. J. |last4=Bayer |first4=F. M. |last5=Rajapaksha |first5=N. |title=Multiplier-free DCT approximations for RF multi-beam digital aperture-array space imaging and directional sensing |journal=Measurement Science and Technology |date=17 October 2012 |volume=23 |issue=11 |pages=114003 |doi=10.1088/0957-0233/23/11/114003 |s2cid=119888170 |issn=0957-0233}}</ref>
*[[Wireless sensor network]] (WSN) — wireless [[Surface acoustic wave sensor|acoustic sensor]] networks<ref name="Ochoa"/>
}}

===Visual media standards===
The DCT-II is an important image compression technique. It is used in image compression standards such as [[JPEG]], and [[video compression]] standards such as {{nowrap|[[H.26x]]}}, [[MJPEG]], [[MPEG]], [[DV (video format)|DV]], [[Theora]] and [[Daala]]. There, the two-dimensional DCT-II of <math>N \times N</math> blocks are computed and the results are [[Quantization (signal processing)|quantized]] and [[Entropy encoding|entropy coded]]. In this case, <math>N</math> is typically 8 and the DCT-II formula is applied to each row and column of the block. The result is an 8&nbsp;× 8 transform coefficient array in which the <math>(0,0)</math> element (top-left) is the DC (zero-frequency) component and entries with increasing vertical and horizontal index values represent higher vertical and horizontal spatial frequencies.

The integer DCT, an integer approximation of the DCT,<ref name="Britanak2010"/><ref name="Stankovic"/> is used in [[Advanced Video Coding]] (AVC),<ref name="Wang">{{cite journal |last1=Wang |first1=Hanli |last2=Kwong |first2=S. |last3=Kok |first3=C. |title=Efficient prediction algorithm of integer DCT coefficients for {{nowrap|H.264}}/AVC optimization |journal=IEEE Transactions on Circuits and Systems for Video Technology |date=2006 |volume=16 |issue=4 |pages=547–552 |doi=10.1109/TCSVT.2006.871390|s2cid=2060937 }}</ref><ref name="Stankovic"/> introduced in 2003, and [[High Efficiency Video Coding]] (HEVC),<ref name="apple"/><ref name="Stankovic"/> introduced in 2013. The integer DCT is also used in the [[High Efficiency Image Format]] (HEIF), which uses a subset of the [[HEVC]] video coding format for coding still images.<ref name="apple"/> AVC uses 4&nbsp;x 4 and 8&nbsp;x 8 blocks. HEVC and HEIF use varied block sizes between 4&nbsp;x 4 and 32&nbsp;x 32 [[pixels]].<ref name="apple"/><ref name="Stankovic"/> {{As of|2019}}, AVC is by far the most commonly used format for the recording, compression and distribution of video content, used by 91% of video developers, followed by HEVC which is used by 43% of developers.<ref name="Bitmovin">{{cite web |url=https://cdn2.hubspot.net/hubfs/3411032/Bitmovin%20Magazine/Video%20Developer%20Report%202019/bitmovin-video-developer-report-2019.pdf |title=Video Developer Report 2019 |website=[[Bitmovin]] |year=2019 |access-date=5 November 2019}}</ref>

====Image formats====
{| class="wikitable"
|-
! Image compression standard !! Year !! Common applications
|-
| [[JPEG]]<ref name="Stankovic"/> ||1992|| The most widely used image compression standard<ref name="Hudson">{{cite journal |last1=Hudson |first1=Graham |last2=Léger |first2=Alain |last3=Niss |first3=Birger |last4=Sebestyén |first4=István |last5=Vaaben |first5=Jørgen |title=JPEG-1 standard 25 years: past, present, and future reasons for a success |journal=[[Journal of Electronic Imaging]] |date=31 August 2018 |volume=27 |issue=4 |pages=1 |doi=10.1117/1.JEI.27.4.040901|doi-access=free }}</ref><ref>{{cite web |title=The JPEG image format explained |url=https://home.bt.com/tech-gadgets/photography/what-is-a-jpeg-11364206889349 |website=[[BT.com]] |publisher=[[BT Group]] |access-date=5 August 2019 |date=31 May 2018}}</ref> and digital [[image format]].<ref name="Baraniuk">{{cite news |last1=Baraniuk |first1=Chris |title=Copy protections could come to JPegs |url=https://www.bbc.co.uk/news/technology-34538705 |access-date=13 September 2019 |work=[[BBC News]] |agency=[[BBC]] |date=15 October 2015}}</ref>
|-
| [[JPEG XR]] ||2009|| [[Open XML Paper Specification]]
|-
| [[WebP]] ||2010|| A graphic format that supports the lossy compression of digital images. Developed by [[Google]].
|-
| [[High Efficiency Image Format]] (HEIF) ||2013|| [[Image file format]] based on HEVC compression. It improves compression over JPEG,<ref name="apple">{{cite web |last1=Thomson |first1=Gavin |last2=Shah |first2=Athar |title=Introducing HEIF and HEVC |url=https://devstreaming-cdn.apple.com/videos/wwdc/2017/503i6plfvfi7o3222/503/503_introducing_heif_and_hevc.pdf |publisher=[[Apple Inc.]] |year=2017 |access-date=5 August 2019}}</ref> and supports [[animation]] with much more efficient compression than the [[animated GIF]] format.<ref>{{cite web |title=HEIF Comparison - High Efficiency Image File Format |url=https://nokiatech.github.io/heif/comparison.html |publisher=[[Nokia Technologies]] |access-date=5 August 2019}}</ref>
|-
| [[Better Portable Graphics|BPG]] ||2014||Based on HEVC compression
|-
| [[JPEG XL]]<ref name="jxl">{{Cite web |url=http://ds.jpeg.org/whitepapers/jpeg-xl-whitepaper.pdf |title=JPEG XL White Paper |last1=Alakuijala | first1=Jyrki |last2=Sneyers |first2=Jon |last3=Versari |first3=Luca |last4=Wassenberg |first4=Jan |access-date=14 Jan 2022 |date=22 January 2021 |website=JPEG Org. |archive-date=2 May 2021 |archive-url=https://web.archive.org/web/20210502025653/http://ds.jpeg.org/whitepapers/jpeg-xl-whitepaper.pdf |url-status=live |quote=Variable-sized DCT (square or rectangular from 2x2 to 256x256) serves as a fast approximation of the optimal decorrelating transform.}}</ref> ||2020|| A royalty-free raster-graphics file format that supports both lossy and lossless compression. 
|}

====Video formats====
{| class="wikitable"
|-
! [[Video coding standard]] !! Year !! Common applications
|-
| {{nowrap|[[H.261]]}}<ref name="video-standards">{{cite web|first=Yao|last=Wang|archive-url=https://web.archive.org/web/20130123211453/http://eeweb.poly.edu/~yao/EL6123/coding_standards_pt1.pdf|archive-date=2013-01-23|url=http://eeweb.poly.edu/~yao/EL6123/coding_standards_pt1.pdf|title=Video Coding Standards: Part I|year=2006}}</ref><ref>{{cite web|first=Yao|last=Wang|archive-url=https://web.archive.org/web/20130123211453/http://eeweb.poly.edu/~yao/EL6123/coding_standards_pt2.pdf|archive-date=2013-01-23|url=http://eeweb.poly.edu/~yao/EL6123/coding_standards_pt2.pdf|title=Video Coding Standards: Part II|year=2006}}</ref> ||1988|| First of a family of [[video coding standards]]. Used primarily in older [[video conferencing]] and [[video telephone]] products.
|-
| [[Motion JPEG]] (MJPEG)<ref>{{cite book |last1=Hoffman |first1=Roy |title=Data Compression in Digital Systems |date=2012 |publisher=[[Springer Science & Business Media]] |isbn=9781461560319 |page=255 |url=https://books.google.com/books?id=FOfTBwAAQBAJ}}</ref> ||1992|| [[QuickTime]], [[video editing]], [[non-linear editing]], [[digital cameras]]
|-
| [[MPEG-1]] Video<ref name="Rao">{{cite book | last1 = Rao | first1 = K.R. | author-link1 = K. R. Rao | last2 = Hwang | first2 = J. J. | date = 1996-07-18 | title = Techniques and Standards for Image, Video, and Audio Coding | language = en | publisher = Prentice Hall | at = JPEG: Chapter 8; {{nowrap|H.261}}: Chapter 9; MPEG-1: Chapter 10; MPEG-2: Chapter 11 | isbn = 978-0133099072 | lccn = 96015550 | oclc = 34617596 | ol = OL978319M | s2cid = 56983045 | df = dmy-all}}</ref> ||1993|| [[Digital video]] distribution on [[CD]] or [[Internet video]]
|-
| [[MPEG-2 Video]] ({{nowrap|H.262}})<ref name="Rao"/> ||1995|| Storage and handling of digital images in broadcast applications, [[digital television]], [[HDTV]], cable, satellite, high-speed [[Internet]], [[DVD]] video distribution
|-
| [[DV (video format)|DV]] ||1995|| [[Camcorders]], [[digital cassettes]]
|-
| [[H.263]] ([[MPEG-4 Part 2]])<ref name="video-standards"/> ||1996|| [[Video telephony]] over [[public switched telephone network]] (PSTN), {{nowrap|[[H.320]]}}, [[Integrated Services Digital Network]] (ISDN)<ref>{{cite news |last1=Davis |first1=Andrew |title=The H.320 Recommendation Overview |url=https://www.eetimes.com/document.asp?doc_id=1275886 |access-date=7 November 2019 |work=[[EE Times]] |date=13 June 1997}}</ref><ref>{{cite book |title=IEEE WESCANEX 97: communications, power, and computing : conference proceedings |date=May 22–23, 1997 |publisher=[[Institute of Electrical and Electronics Engineers]] |location=University of Manitoba, Winnipeg, Manitoba, Canada |isbn=9780780341470 |page=30 |url=https://books.google.com/books?id=8vhEAQAAIAAJ |quote={{nowrap|H.263}} is similar to, but more complex than {{nowrap|H.261}}. It is currently the most widely used international video compression standard for video telephony on ISDN (Integrated Services Digital Network) telephone lines.}}</ref>
|-
| [[Advanced Video Coding]] (AVC, {{nowrap|H.264}}, [[MPEG-4]])<ref name="Stankovic"/><ref name="Wang"/> ||2003|| Popular [[HD video]] recording, compression and distribution format, [[Internet video]], [[YouTube]], [[Blu-ray Discs]], [[HDTV]] broadcasts, [[web browsers]], [[streaming television]], [[mobile devices]], consumer devices, [[Netflix]],<ref name="Encodes">{{cite news |author=Netflix Technology Blog |title=More Efficient Mobile Encodes for Netflix Downloads |url=https://medium.com/netflix-techblog/more-efficient-mobile-encodes-for-netflix-downloads-625d7b082909 |access-date=20 October 2019 |work=[[Medium.com]] |publisher=[[Netflix]] |date=19 April 2017}}</ref> [[video telephony]], [[FaceTime]]<ref name="AppleInsider standards 1">{{cite web|url=http://www.appleinsider.com/articles/10/06/08/inside_iphone_4_facetime_video_calling.html|date=June 8, 2010|access-date=June 9, 2010|title=Inside iPhone 4: FaceTime video calling|publisher=[[Apple community#AppleInsider|AppleInsider]]|author=Daniel Eran Dilger}}</ref>
|-
| [[Theora]] ||2004|| Internet video, web browsers
|-
| [[VC-1]] ||2006|| [[Windows]] media, [[Blu-ray Disc]]s
|-
| [[Apple ProRes]] ||2007|| Professional video production.<ref name="loc">{{cite web |title=Apple ProRes 422 Codec Family |url=http://www.loc.gov/preservation/digital/formats/fdd/fdd000389.shtml |website=[[Library of Congress]] |access-date=13 October 2019 |date=17 November 2014}}</ref>
|-
| [[VP9]]||2010|| A video codec developed by [[Google]] used in the [[WebM]] container format with [[HTML5]].
|-
| [[High Efficiency Video Coding]] (HEVC, {{nowrap|H.265}})<ref name="Stankovic"/><ref name="apple"/> ||2013|| Successor to the {{nowrap|H.264}} standard, having substantially improved compression capability
|-
| [[Daala]] ||2013|| Research video format by [[Xiph.org]]
|-
| [[AV1]]<ref name="AV1">{{cite web |url=https://aomediacodec.github.io/av1-spec/av1-spec.pdf |title=AV1 Bitstream & Decoding Process Specification |author=Peter de Rivaz |author2=Jack Haughton |date=2018 |publisher=[[Alliance for Open Media]] |access-date=2022-01-14}}</ref> ||2018|| An open source format based on VP10 ([[VP9]]'s internal successor), [[Daala]] and [[Thor (video codec)|Thor]]; used by content providers such as [[YouTube]]<ref name="YT AV1 Beta Playlist">{{cite web |url=https://www.youtube.com/playlist?list=PLyqf6gJt7KuHBmeVzZteZUlNUQAVLwrZS |title=AV1 Beta Launch Playlist |author=YouTube Developers |website=[[YouTube]] |date=15 September 2018 |access-date=14 January 2022 |quote=The first videos to receive YouTube's AV1 transcodes.}}</ref><ref name="YT AV1">{{cite web |url=https://www.ghacks.net/2018/09/13/how-to-enable-av1-support-on-youtube/ |title=How to enable AV1 support on YouTube |last=Brinkmann |first=Martin |date=13 September 2018 |access-date=14 January 2022}}</ref> and [[Netflix]].<ref name="Netflix AV1 Android">{{cite web |url=https://netflixtechblog.com/netflix-now-streaming-av1-on-android-d5264a515202 |title=Netflix Now Streaming AV1 on Android |author=Netflix Technology Blog |date=5 February 2020 |access-date=14 January 2022}}</ref><ref name="Netflix AV1 TV">{{cite web |url=https://netflixtechblog.com/bringing-av1-streaming-to-netflix-members-tvs-b7fc88e42320 |title=Bringing AV1 Streaming to Netflix Members' TVs |author=Netflix Technology Blog |date=9 November 2021 |access-date=14 January 2022}}</ref>
|}

===MDCT audio standards===
{{Further|Modified discrete cosine transform}}

====General audio====
{| class="wikitable"
|-
! Audio compression standard 
! Year
! Common applications
|-
| [[Dolby Digital]] (AC-3)<ref name="Luo" /><ref name="Britanak2011" />
| 1991
| [[Film|Cinema]], [[digital cinema]], [[DVD]], [[Blu-ray]], [[streaming media]], [[video games]]
|-
| [[Adaptive Transform Acoustic Coding]] (ATRAC)<ref name="Luo"/>
| 1992
| [[MiniDisc]]
|-
| [[MP3]]<ref name="Guckert"/><ref name="Stankovic"/>
| 1993
| [[Digital audio]] distribution, [[MP3 players]], [[portable media players]], [[streaming media]]
|-
| [[Perceptual Audio Coder]] (PAC)<ref name="Luo"/>
| 1996
| [[Digital audio radio service]] (DARS)
|-
| [[Advanced Audio Coding]] (AAC / [[MP4]] Audio)<ref name=brandenburg/><ref name="Luo"/>
| 1997
| [[Digital audio]] distribution, [[portable media players]], [[streaming media]], [[game consoles]], [[mobile devices]], [[iOS]], [[iTunes]], [[Android (operating system)|Android]], [[BlackBerry]]
|-
| [[High-Efficiency Advanced Audio Coding]] (AAC+)<ref name="Herre" /><ref name="Britanak" />{{rp|page = [https://books.google.com/books?id=cZ4vDwAAQBAJ&pg=PA478 478]}}
| 1997
| [[Digital radio]], [[digital audio broadcasting]] (DAB+),<ref name="Britanak" /> [[Digital Radio Mondiale]] (DRM)
|-
| [[Cook Codec]]
| 1998
| [[RealAudio]]
|-
| [[Windows Media Audio]] (WMA)<ref name="Luo"/>
| 1999
| [[Windows Media]]
|-
| [[Vorbis]]<ref name="vorbis-mdct" /><ref name="Luo" />
| 2000
| [[Digital audio]] distribution, [[radio station]]s, [[streaming media]], [[video game]]s, [[Spotify]], [[Wikipedia]]
|-
| [[High-Definition Coding]] (HDC)<ref name="Jones"/>
| 2002
| Digital radio, [[HD Radio]]
|-
| [[Dynamic Resolution Adaptation]] (DRA)<ref name="Luo"/>
| 2008
| China national audio standard, [[China Multimedia Mobile Broadcasting]], [[DVB-H]]
|-
| [[Opus (audio format)|Opus]]<ref name="Valin" />
| 2012
| VoIP,<ref name="homepage" /> mobile telephony, [[WhatsApp]],<ref name="Register" /><ref name="Hazra" /><ref name="Srivastava" /> [[PlayStation 4]]<ref name="PlayStation" />
|-
| [[Dolby AC-4]]<ref name="Dolby AC-4" />
| rowspan="2" | 2015
| rowspan="2" | [[ATSC 3.0]], [[ultra-high-definition television]] (UHD TV)
|-
| [[MPEG-H 3D Audio]]<ref name="Bleidt" />
|}

====Speech coding====
{| class="wikitable"
|-
![[Speech coding]] standard !! Year
!Common applications
|-
|[[AAC-LD]] (LD-MDCT)<ref name="Schnell" />
|1999
|[[Mobile telephony]], [[voice-over-IP]] (VoIP), [[iOS]], [[FaceTime]]<ref name="AppleInsider standards 1"/>
|-
|[[Siren (codec)|Siren]]<ref name="Hersent" />
|1999
|[[VoIP]], [[wideband audio]], [[G.722.1]]
|-
|[[G.722.1]]<ref name="Lutzky" />
|1999
|VoIP, wideband audio, [[G.722]]
|-
|[[G.729.1]]<ref name="Nagireddi" />
|2006
|[[G.729]], VoIP, wideband audio,<ref name="Nagireddi" /> [[mobile telephony]]
|-
|[[Enhanced Variable Rate Codec B|EVRC-WB]]<ref name="Britanak"/>{{rp|page=[https://books.google.com/books?id=cZ4vDwAAQBAJ&pg=PA31 31], 478]}}
|2007
|[[Wideband audio]]
|-
|[[G.718]]<ref name="ITU-T" />
|2008
|VoIP, wideband audio, mobile telephony
|-
|[[G.719]]<ref name="Britanak"/>
|2008
|[[Teleconferencing]], [[videoconferencing]], [[voice mail]]
|-
|[[CELT]]<ref name="Terriberry" />
|2011
|VoIP,<ref name="ekiga" /><ref name="FreeSWITCH" /> mobile telephony
|-
|[[Enhanced Voice Services]] (EVS)<ref name="EVS" />
|2014
|Mobile telephony, VoIP, wideband audio
|}

===Multidimensional DCT===
{{See also|ZPEG}}

Multidimensional DCTs (MD DCTs) have several applications, mainly 3-D DCTs such as the 3-D DCT-II, which has several new applications like Hyperspectral Imaging coding systems,<ref name="appDCT">{{Citation |first1=G. P. |last1=Abousleman |first2=M. W. |last2=Marcellin |first3=B. R. |last3=Hunt |title=Compression of hyperspectral imagery using 3-D DCT and hybrid DPCM/DCT |journal=IEEE Trans. Geosci. Remote Sens. |date=January 1995 |volume=33 |issue=1 |pages=26–34 |doi=10.1109/36.368225|bibcode=1995ITGRS..33...26A }}</ref> variable temporal length 3-D DCT coding,<ref name="app2DCT">{{Citation |first1=Y. |last1=Chan |first2=W. |last2=Siu |title= Variable temporal-length 3-D discrete cosine transform coding |journal=IEEE Trans. Image Process. |date=May 1997 |volume=6 |issue=5 |pages=758–763 |doi=10.1109/83.568933|pmid=18282969 |bibcode=1997ITIP....6..758C |hdl=10397/1928 |url=http://www.en.polyu.edu.hk/~wcsiu/paper_store/Journal/1997/1997_J3-IEEE-Chan%26Siu.pdf |citeseerx=10.1.1.516.2824 }}</ref> [[video coding]] algorithms,<ref name="app3DCT">{{Citation |first1=J. |last1=Song |first2=Z. |last2=SXiong |first3=X. |last3=Liu |first4=Y. |last4=Liu |title= An algorithm for layered video coding and transmission| journal= Proc. Fourth Int. Conf./Exh. High Performance Comput. Asia-Pacific Region |volume=2 |pages=700–703}}</ref> adaptive video coding<ref name="app4DCT">{{Citation |first1=S.-C |last1=Tai |first2=Y. |last2=Gi |first3=C.-W. |last3=Lin |title= An adaptive 3-D discrete cosine transform coder for medical image compression |journal= IEEE Trans. Inf. Technol. Biomed. |date=September 2000 |volume=4 |issue=3 |pages=259–263 |doi=10.1109/4233.870036|pmid=11026596 |s2cid=18016215 }}</ref> and 3-D Compression.<ref name="app5DCT">{{Citation |first1=B. |last1=Yeo |first2=B. |last2=Liu |title= Volume rendering of DCT-based compressed 3D scalar data |journal=IEEE Transactions on Visualization and Computer Graphics |date=May 1995 |volume=1 |pages=29–43 |doi=10.1109/2945.468390}}</ref> Due to enhancement in the hardware, software and introduction of several fast algorithms, the necessity of using MD DCTs is rapidly increasing. [[#DCT-IV|DCT-IV]] has gained popularity for its applications in fast implementation of real-valued polyphase filtering banks,<ref>{{cite book| doi=10.1109/ISCAS.2000.856261 | chapter=Perfect reconstruction modulated filter banks with sum of powers-of-two coefficients | title=2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353) | year=2000 | last1=Chan | first1=S.C. | last2=Liu | first2=W. | last3=Ho | first3=K.I. | volume=2 | pages=73–76 | hdl=10722/46174 | isbn=0-7803-5482-6 | s2cid=1757438 }}</ref> lapped orthogonal transform<ref>{{cite journal |last1=Queiroz |first1=R. L. |last2=Nguyen |first2=T. Q. |title=Lapped transforms for efficient transform/subband coding |journal=IEEE Trans. Signal Process. |date=1996 |volume=44 |issue=5 |pages=497–507}}</ref>{{sfn|Malvar|1992}} and cosine-modulated wavelet bases.<ref>{{cite journal |last1=Chan |first1=S. C. |last2=Luo |first2=L. |last3=Ho |first3=K. L. |title=M-Channel compactly supported biorthogonal cosine-modulated wavelet bases |journal=IEEE Trans. Signal Process. |date=1998 |volume=46 |issue=2 |pages=1142–1151|doi=10.1109/78.668566 |bibcode=1998ITSP...46.1142C |hdl=10722/42775 |hdl-access=free }}</ref>

===Digital signal processing===
DCT plays an important role in [[digital signal processing]] specifically [[data compression]]. The DCT is widely implemented in [[digital signal processors]] (DSP), as well as digital signal processing software. Many companies have developed DSPs based on DCT technology. DCTs are widely used for applications such as [[encoding]], decoding, video, audio, [[multiplexing]], control signals, [[signaling]], and [[analog-to-digital conversion]]. DCTs are also commonly used for [[high-definition television]] (HDTV) encoder/decoder [[integrated circuit|chips]].<ref name="Stankovic"/>

===Compression artifacts===
A common issue with DCT compression in [[digital media]] are blocky [[compression artifacts]],<ref name="Katsaggelos">{{cite book |last1=Katsaggelos |first1=Aggelos K. |last2=Babacan |first2=S. Derin |last3=Chun-Jen |first3=Tsai |title=The Essential Guide to Image Processing |date=2009 |publisher=[[Academic Press]] |isbn=9780123744579 |pages=349–383|chapter=Chapter 15 - Iterative Image Restoration}}</ref> caused by DCT blocks.<ref name="Alikhani">{{cite web |last1=Alikhani |first1=Darya |title=Beyond resolution: Rosa Menkman's glitch art |url=http://postmatter.merimedia.com/articles/archive-2012-2016/2015/51-rosa-menkman/ |website=POSTmatter |date=April 1, 2015 |access-date=19 October 2019 |archive-date=19 October 2019 |archive-url=https://web.archive.org/web/20191019082218/http://postmatter.merimedia.com/articles/archive-2012-2016/2015/51-rosa-menkman/ |url-status=dead }}</ref> In a DCT algorithm, an image (or frame in an image sequence) is divided into square blocks which are processed independently from each other, then the DCT blocks is taken within each block and the resulting DCT coefficients are [[Quantization (signal processing)|quantized]]. This process can cause blocking artifacts, primarily at high [[data compression ratio]]s.<ref name="Katsaggelos"/> This can also cause the [[mosquito noise]] effect, commonly found in [[digital video]].<ref>{{cite web |title=Mosquito noise |url=https://www.pcmag.com/encyclopedia/term/55914/mosquito-noise |website=[[PC Magazine]] |access-date=19 October 2019}}</ref>

DCT blocks are often used in [[glitch art]].<ref name="Alikhani"/> The artist [[Rosa Menkman]] makes use of DCT-based compression artifacts in her glitch art,<ref name="Menkman">{{cite book |last1=Menkman |first1=Rosa |title=The Glitch Moment(um) |url=https://networkcultures.org/_uploads/NN%234_RosaMenkman.pdf |publisher=Institute of Network Cultures |isbn=978-90-816021-6-7 |date=October 2011 |access-date=19 October 2019}}</ref> particularly the DCT blocks found in most [[digital media]] formats such as [[JPEG]] digital images and [[MP3]] audio.<ref name="Alikhani"/> Another example is ''Jpegs'' by German photographer [[Thomas Ruff]], which uses intentional [[JPEG]] artifacts as the basis of the picture's style.<ref>{{cite book|chapter=jpegs|first=Thomas|last=Ruff|title=Aperture|date=May 31, 2009|page=132|publisher=Aperture |isbn=9781597110938}}</ref><ref>{{cite web|url=http://jmcolberg.com/weblog/2009/04/review_jpegs_by_thomas_ruff/|title=Review: jpegs by Thomas Ruff|first=Jörg|last=Colberg|date=April 17, 2009}}</ref>