Editing Discrete cosine transform (section)

===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
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| [[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>
|}