Discrete cosine transform: Difference between revisions

Revision as of 20:49, 20 October 2023

Revision as of 01:02, 3 November 2023

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==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 journalbook |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 |journal=Signal Processing of HDTV: Proceedings of the International Workshop on HDTV '93, Ottawa, Canada |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.

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| [[Opus (audio format)|Opus]]<ref>{{cite conference|last1=Valin|first1=Jean-Marc|last2=Maxwell|first2=Gregory|last3=Terriberry|first3=Timothy B.|last4=Vos|first4=Koen|date=October 2013|title=High-Quality, Low-Delay Music Coding in the Opus Codec|conference=135th AES Convention|publisher=[[Audio Engineering Society]]|arxiv=1602.04845}}</ref>

| 2012

| VoIP,<ref name="homepage">{{cite web|url=http://opus-codec.org/|title=Opus Codec|work=Opus|publisher=Xiph.org Foundation|type=Home page|access-date=July 31, 2012}}</ref> mobile telephony, [[WhatsApp]],<ref name="Register">{{cite news|url=https://www.theregister.co.uk/2015/10/27/whatsapp_forensic_analysis/|title=WhatsApp laid bare: Info-sucking app's innards probed|last1=Leyden|first1=John|date=27 October 2015|work=[[The Register]]|access-date=19 October 2019}}</ref><ref name="Hazra">{{cite book|title=Security in Computing and Communications: 5th International Symposium, SSCC 2017|last1=Hazra|first1=Sudip|last2=Mateti|first2=Prabhaker|date=September 13–16, 2017|publisher=Springer|isbn=9789811068980|editor-last1=Thampi|editor-first1=Sabu M.|pages=286–299 (290)|chapter=Challenges in Android Forensics|doi=10.1007/978-981-10-6898-0_24|editor-last2=Pérez|editor-first2=Gregorio Martínez|editor-last3=Westphall|editor-first3=Carlos Becker|editor-last4=Hu|editor-first4=Jiankun|editor-last5=Fan|editor-first5=Chun I.|editor-last6=Mármol|editor-first6=Félix Gómez|chapter-url=https://books.google.com/books?id=1u09DwAAQBAJ&pg=PA290}}</ref><ref name="Srivastava">{{cite book|title=Cyber Security in Parallel and Distributed Computing: Concepts, Techniques, Applications and Case Studies|last1=Srivastava|first1=Saurabh Ranjan|last2=Dube|first2=Sachin|last3=Shrivastaya|first3=Gulshan|last4=Sharma|first4=Kavita|datechapter=2019|journal=CyberSmartphone Triggered Security inChallenges Parallel‐ Issues, Case Studies and DistributedPrevention Computing|date=2019|publisher=John Wiley & Sons|isbn=9781119488057|editor-last1=Le|editor-first1=Dac-Nhuong|pages=187–206 (200)|chapter=Smartphone Triggered Security Challenges: Issues, Case Studies and Prevention|doi=10.1002/9781119488330.ch12|s2cid=214034702 |editor-last2=Kumar|editor-first2=Raghvendra|editor-last3=Mishra|editor-first3=Brojo Kishore|editor-last4=Chatterjee|editor-first4=Jyotir Moy|editor-last5=Khari|editor-first5=Manju|chapter-url=https://books.google.com/books?id=FzGtDwAAQBAJ&pg=PA200}}</ref> [[PlayStation 4]]<ref name="playstation">{{cite web|url=https://doc.dl.playstation.net/doc/ps4-oss/|title=Open Source Software used in PlayStation 4|publisher=Sony Interactive Entertainment Inc.|access-date=2017-12-11}}</ref>

|-

| [[Dolby AC-4]]<ref>{{cite web |title=Dolby AC-4: Audio Delivery for Next-Generation Entertainment Services |url=https://www.dolby.com/us/en/technologies/ac-4/Next-Generation-Entertainment-Services.pdf |website=[[Dolby Laboratories]] |date=June 2015 |access-date=11 November 2019}}</ref>

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* {{Cite journal | last1 = Martucci | first1 = S. A. | title = Symmetric convolution and the discrete sine and cosine transforms | doi = 10.1109/78.295213 | journal = IEEE Transactions on Signal Processing | volume = 42 | issue = 5 | pages = 1038–1051 | date=May 1994 | bibcode = 1994ITSP...42.1038M }}

* {{Citation |last1=Oppenheim |first1=Alan |last2=Schafer |first2=Ronald |last3=Buck |first3=John |title=Discrete-Time Signal Processing |edition=2nd |publisher=Prentice Hall |___location=Upper Saddle River, N.J |year=1999 |isbn=978-0-13-754920-7 |url-access=registration |url=https://archive.org/details/discretetimesign00alan }}

* {{Cite journal | last1 = Frigo | first1 = M. | last2 = Johnson | first2 = S. G. | doi = 10.1109/JPROC.2004.840301 | title = The Design and Implementation of FFTW3 | journal = Proceedings of the IEEE | volume = 93 | issue = 2 | pages = 216–231| date=February 2005 | bibcode = 2005IEEEP..93..216F | url = http://fftw.org/fftw-paper-ieee.pdf| citeseerx = 10.1.1.66.3097 | s2cid = 6644892 }}

* {{Cite journal | last1 = Boussakta | first1 = Said. | last2 = Alshibami | first2 = Hamoud O. | doi = 10.1109/TSP.2004.823472 | title = Fast Algorithm for the 3-D DCT-II | journal = IEEE Transactions on Signal Processing| volume = 52 | issue = 4 | pages = 992–1000| date=April 2004| bibcode = 2004ITSP...52..992B | s2cid = 3385296 | url = http://eprints.whiterose.ac.uk/708/1/boussaktas2.pdf }}

* {{Cite journal | last1 = Cheng | first1 = L. Z.| last2 = Zeng | first2 = Y. H. | doi = 10.1109/TSP.2002.806558 | title = New fast algorithm for multidimensional type-IV DCT | journal = IEEE Transactions on Signal Processing| volume = 51 | issue = 1 | pages = 213–220| date=2003}}