Editing Transform coding (section)

==Digital==
The term is much more commonly used in [[digital media]] and [[digital signal processing]]. The most widely used transform coding technique in this regard is the [[discrete cosine transform]] (DCT),<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><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> proposed by [[N. Ahmed|Nasir Ahmed]] in 1972,<ref name="Ahmed">{{cite journal |last=Ahmed |first=Nasir |author-link=N. Ahmed |title=How I Came Up With the Discrete Cosine Transform |journal=[[Digital Signal Processing (journal)|Digital Signal Processing]] |date=January 1991 |volume=1 |issue=1 |pages=4–5 |doi=10.1016/1051-2004(91)90086-Z |url=https://www.scribd.com/doc/52879771/DCT-History-How-I-Came-Up-with-the-Discrete-Cosine-Transform|url-access=subscription }}</ref><ref name="Stankovic">{{cite journal |last1=Stanković |first1=Radomir S. |last2=Astola |first2=Jaakko T. |title=Reminiscences of the Early Work in DCT: Interview with K.R. Rao |journal=Reprints from the Early Days of Information Sciences |date=2012 |volume=60 |url=http://ticsp.cs.tut.fi/reports/ticsp-report-60-reprint-rao-corrected.pdf |access-date=13 October 2019}}</ref> and presented by Ahmed with T. Natarajan and [[K. R. Rao]] in 1974.<ref name="pubDCT">{{Citation |first1=Nasir |last1=Ahmed |author1-link=N. Ahmed |first2=T. |last2=Natarajan |first3=K. R. |last3=Rao |title=Discrete Cosine Transform |journal=IEEE Transactions on Computers |date=January 1974 |volume=C-23 |issue=1 |pages=90–93 |doi=10.1109/T-C.1974.223784|s2cid=149806273 }}</ref> This DCT, in the context of the family of discrete cosine transforms, is the DCT-II. It is the basis for the common [[JPEG]] [[image compression]] standard,<ref name="t81">{{cite web |title=T.81 – Digital compression and coding of continuous-tone still images – Requirements and guidelines |url=https://www.w3.org/Graphics/JPEG/itu-t81.pdf |publisher=[[CCITT]] |date=September 1992 |access-date=12 July 2019}}</ref> which examines small blocks of the image and transforms them to the [[frequency domain]] for more efficient quantization (lossy) and [[data compression]]. In [[video coding]], the [[H.26x]] and [[MPEG]] standards modify this DCT image compression technique across frames in a motion image using [[motion compensation]], further reducing the size compared to a series of JPEGs.

In [[audio coding]], MPEG audio compression analyzes the transformed data according to a [[psychoacoustic model]] that describes the human ear's sensitivity to parts of the signal, similar to the TV model. [[MP3]] uses a hybrid coding algorithm, combining the [[modified discrete cosine transform]] (MDCT) and [[fast Fourier transform]] (FFT).<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 |access-date=14 July 2019}}</ref> It was succeeded by [[Advanced Audio Coding]] (AAC), which uses a pure MDCT algorithm to significantly improve compression efficiency.<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|archive-url=https://web.archive.org/web/20170213191747/https://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf|archive-date=2017-02-13}}</ref>

The basic process of [[digitizing]] an analog signal is a kind of transform coding that uses [[Sample (signal)|sampling]] in one or more domains as its transform.