Editing Linear predictive coding (section)

==Early history==

Linear prediction (signal estimation) goes back to at least the 1940s when [[Norbert Wiener]] developed a mathematical theory for calculating the best [[Wiener filter|filters]] and predictors for detecting signals hidden in noise.<ref>{{cite journal | author=B.S. Atal | title=The history of linear prediction | year=2006 | pages=154–161 | volume=23 | issue=2 | journal=IEEE Signal Processing Magazine| doi=10.1109/MSP.2006.1598091 | bibcode=2006ISPM...23..154A | s2cid=15601493 | url=https://www.researchgate.net/publication/3321695}}</ref><ref name="Sasahira">{{cite journal |author1=Y. Sasahira |author2=S. Hashimoto | title=Voice pitch changing by Linear Predictive Coding Method to keep the Singer's Personal Timbre | year=1995 | format=pdf| publisher = Michigan Publishing|url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/voice-pitch-changing.pdf?c=icmc;idno=bbp2372.1995.118;format=pdf}}</ref> Soon after [[Claude Shannon]] established a [[A Mathematical Theory of Communication|general theory of coding]], work on predictive coding was done by [[C. Chapin Cutler]],<ref>{{cite patent | inventor=C. C. Cutler | title=Differential quantization of communication signals | pubdate=1952-07-29 | country=US|number=2605361}}</ref> [[Bernard M. Oliver]]<ref>{{cite journal | author=B. M. Oliver | title=Efficient coding | journal = The Bell System Technical Journal |year=1952 | volume=31 | issue=4 | pages=724–750 | publisher=Nokia Bell Labs| doi=10.1002/j.1538-7305.1952.tb01403.x }}</ref> and Henry C. Harrison.<ref>{{cite journal | author=H. C. Harrison | title=Experiments with linear prediction in television | year=1952 | volume=31 | pages=764–783 | journal=Bell System Technical Journal| issue=4 | doi=10.1002/j.1538-7305.1952.tb01405.x }}</ref> [[Peter Elias]] in 1955 published two papers on predictive coding of signals.<ref>{{cite journal | author=P. Elias | title=Predictive coding I | year=1955 | pages=16–24 | volume=IT-1 no. 1 | journal=IRE Trans. Inform.Theory| doi=10.1109/TIT.1955.1055126 }}</ref><ref>{{cite journal | author=P. Elias | title=Predictive coding II | year=1955 | pages=24–33 | volume=IT-1 no. 1 | journal=IRE Trans. Inform. Theory| doi=10.1109/TIT.1955.1055116 }}</ref>

Linear predictors were applied to speech analysis independently by [[Fumitada Itakura]] of [[Nagoya University]] and Shuzo Saito of [[Nippon Telegraph and Telephone]] in 1966 and in 1967 by [[Bishnu S. Atal]], [[Manfred R. Schroeder]] and John Burg. Itakura and Saito described a statistical approach based on [[maximum likelihood estimation]]; Atal and Schroeder described an [[adaptive filter|adaptive linear predictor]] approach; Burg outlined an approach based on [[maximum entropy spectral estimation|principle of maximum entropy]].<ref name="Sasahira" /><ref>{{cite journal |author1=S. Saito |author2=F. Itakura | title=Theoretical consideration of the statistical optimum recognition of the spectral density of speech | date=Jan 1967 | journal=J. Acoust. Soc. Jpn.}}</ref><ref>{{cite journal |author1=B.S. Atal |author2=M.R. Schroeder | title=Predictive coding of speech | year=1967 | journal=Conf. Communications and Proc}}</ref><ref>{{cite journal | author=J.P. Burg | title=Maximum Entropy Spectral Analysis | year=1967 | journal=Proceedings of 37th Meeting, Society of Exploration Geophysics, Oklahoma City}}</ref>

In 1969, Itakura and Saito introduced method based on [[partial correlation]] (PARCOR), [[Glen Culler]] proposed real-time speech encoding, and [[Bishnu S. Atal]] presented an LPC speech coder at the Annual Meeting of the [[Acoustical Society of America]]. In 1971, realtime LPC using [[16-bit computing|16-bit]] LPC hardware was demonstrated by [[Philco-Ford]]; four units were sold.<ref name="Gray">{{cite journal |last1=Gray |first1=Robert M. |author1-link=Robert M. Gray |title=A History of Realtime Digital Speech on Packet Networks: Part II of Linear Predictive Coding and the Internet Protocol |journal=Found. Trends Signal Process. |date=2010 |volume=3 |issue=4 |pages=203–303 |doi=10.1561/2000000036 |url=https://ee.stanford.edu/~gray/lpcip.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://ee.stanford.edu/~gray/lpcip.pdf |archive-date=2022-10-09 |url-status=live |issn=1932-8346|doi-access=free }}</ref> LPC technology was advanced by Bishnu Atal and [[Manfred Schroeder]] during the 1970s{{ndash}}1980s.<ref name="Gray"/> In 1978, Atal and Vishwanath ''et al.'' of BBN developed the first [[variable bitrate|variable-rate]] LPC algorithm.<ref name="Gray"/> The same year, Atal and [[Manfred R. Schroeder]] at Bell Labs proposed an LPC speech [[codec]] called [[adaptive predictive coding]], which used a [[psychoacoustic]] coding algorithm exploiting the masking properties of the human ear.<ref name="Schroeder2014">{{cite book|last1=Schroeder|first1=Manfred R.|title=Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder|date=2014|publisher=Springer|isbn=9783319056609|chapter=Bell Laboratories|page=388|chapter-url=https://books.google.com/books?id=d9IkBAAAQBAJ&pg=PA388}}</ref><ref>{{cite book|last1=Atal|first1=B.|last2=Schroeder|first2=M.|title=ICASSP '78. IEEE International Conference on Acoustics, Speech, and Signal Processing |chapter=Predictive coding of speech signals and subjective error criteria |date=1978|volume=3|pages=573–576|doi=10.1109/ICASSP.1978.1170564}}</ref> This later became the basis for the [[perceptual coding]] technique used by the [[MP3]] [[audio compression (data)|audio compression]] format, introduced in 1993.<ref name="Schroeder2014"/> [[Code-excited linear prediction]] (CELP) was developed by Schroeder and Atal in 1985.<ref>{{cite book|last1=Schroeder|first1=Manfred R.|author1-link=Manfred R. Schroeder|last2=Atal|first2=Bishnu S.|title=ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing |chapter=Code-excited linear prediction(CELP): High-quality speech at very low bit rates |author2-link=Bishnu S. Atal|date=1985|volume=10|pages=937–940|doi=10.1109/ICASSP.1985.1168147|s2cid=14803427}}</ref>

LPC is the basis for [[voice-over-IP]] (VoIP) technology.<ref name="Gray"/> In 1972, [[Bob Kahn]] of [[Defense Advanced Research Projects Agency|ARPA]] with Jim Forgie of [[Lincoln Laboratory]] (LL) and Dave Walden of [[BBN Technologies]] started the first developments in packetized speech, which would eventually lead to voice-over-IP technology. In 1973, according to Lincoln Laboratory informal history, the first real-time 2400&nbsp;[[bit]]/[[Second|s]] LPC was implemented by Ed Hofstetter. In 1974, the first real-time two-way LPC packet speech communication was accomplished over the [[ARPANET]] at 3500&nbsp;bit/s between Culler-Harrison and Lincoln Laboratory.