Editing Nyquist–Shannon sampling theorem (section)

===Other discoverers===
Others who have independently discovered or played roles in the development of the sampling theorem have been discussed in several historical articles, for example, by Jerri<ref>{{cite journal | last=Jerri | first=Abdul | author-link=Abdul Jerri | title=The Shannon Sampling Theorem—Its Various Extensions and Applications: A Tutorial Review | journal=Proceedings of the IEEE | volume=65 | issue=11 | pages=1565–1596 | date=November 1977 | doi=10.1109/proc.1977.10771 | bibcode=1977IEEEP..65.1565J | s2cid=37036141 }} See also {{cite journal | last=Jerri | first=Abdul | title=Correction to 'The Shannon sampling theorem—Its various extensions and applications: A tutorial review' | journal=Proceedings of the IEEE | volume=67 | issue=4 | page=695 | date=April 1979 | doi=10.1109/proc.1979.11307 }}</ref> and by Lüke.<ref>{{cite journal | last=Lüke | first=Hans Dieter | title =The Origins of the Sampling Theorem | journal =IEEE Communications Magazine | pages =106–108 | date =April 1999 | issue=4 | doi =10.1109/35.755459 | volume=37| url=http://www.hit.bme.hu/people/papay/edu/Conv/pdf/origins.pdf | citeseerx=10.1.1.163.2887 }}</ref> For example, Lüke points out that H. Raabe, an assistant to Küpfmüller, proved the theorem in his 1939 Ph.D. dissertation; the term ''Raabe condition'' came to be associated with the criterion for unambiguous representation (sampling rate greater than twice the bandwidth).  Meijering<ref name="EM">{{cite journal | last =Meijering | first =Erik | title =A Chronology of Interpolation From Ancient Astronomy to Modern Signal and Image Processing | journal =Proceedings of the IEEE | volume =90 | issue =3 | pages =319–342 | date =March 2002 | doi =10.1109/5.993400 | url =http://bigwww.epfl.ch/publications/meijering0201.pdf }}</ref> mentions several other discoverers and names in a paragraph and pair of footnotes:

{{blockquote|
As pointed out by Higgins, the sampling theorem should really be considered in two parts, as done above: the first stating the fact that a bandlimited function is completely determined by its samples, the second describing how to reconstruct the function using its samples. Both parts of the sampling theorem were given in a somewhat different form by J. M. Whittaker and before him also by Ogura. They were probably not aware of the fact that the first part of the theorem had been stated as early as 1897 by Borel.{{refn|group= Meijering|Several authors, following Black, have claimed that this first part of the sampling theorem was stated even earlier by Cauchy, in a paper published in 1841. However, the paper of Cauchy does not contain such a statement, as has been pointed out by Higgins.}} As we have seen, Borel also used around that time what became known as the cardinal series. However, he appears not to have made the link. In later years it became known that the sampling theorem had been presented before Shannon to the Russian communication community by [[Vladimir Kotelnikov|Kotel'nikov]]. In more implicit, verbal form, it had also been described in the German literature by Raabe. Several authors have mentioned that Someya introduced the theorem in the Japanese literature parallel to Shannon. In the English literature, Weston introduced it independently of Shannon around the same time.{{refn|group= Meijering|As a consequence of the discovery of the several independent introductions of the sampling theorem, people started to refer to the theorem by including the names of the aforementioned authors, resulting in such catchphrases as "the Whittaker–Kotel'nikov–Shannon (WKS) sampling theorem" or even "the Whittaker–Kotel'nikov–Raabe–Shannon–Someya sampling theorem". To avoid confusion, perhaps the best thing to do is to refer to it as the sampling theorem, "rather than trying to find a title that does justice to all claimants".}}

{{reflist|group= Meijering}}|Eric Meijering, "A Chronology of Interpolation From Ancient Astronomy to Modern Signal and Image Processing" (citations omitted)
}}

In Russian literature it is known as the Kotelnikov's theorem, named after [[Vladimir Kotelnikov]], who discovered it in 1933.<ref>Kotelnikov VA, ''On the transmission capacity of "ether" and wire in electrocommunications'', [http://ict.open.ac.uk/classics/1.pdf (English translation, PDF)] {{Webarchive|url=https://web.archive.org/web/20210301042517/http://ict.open.ac.uk/classics/1.pdf |date=2021-03-01 }}, Izd. Red. Upr. Svyazzi RKKA (1933), Reprint in ''[http://www.ieeta.pt/~pjf/MSTMA/ Modern Sampling Theory: Mathematics and Applications]'', Editors: J. J. Benedetto und PJSG Ferreira, Birkhauser (Boston) 2000, {{ISBN|0-8176-4023-1}}.</ref>