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Views Read Edit View history. Instead of requiring an optical filter, the graphics processing unit of smartphone cameras performs digital signal processing to remove aliasing with a digital filter.

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Let f t contain no frequencies over W. 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 [16] and by Lüke.

Raabe, an assistant to Küpfmüller, proved the theorem in his Ph. Meijering [18] mentions several other discoverers and names in a paragraph and pair of footnotes:. As pointed out by Higgins [], the sampling theorem should really be considered in two parts, as done above: Both parts of the sampling theorem were given in a somewhat different form by J.

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 by Borel [25]. 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 Kotel'nikov [].

In more implicit, verbal form, it had also been described in the German literature by Raabe []. Several authors [33, ] 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. However, the paper of Cauchy does not contain such a statement, as has been pointed out by Higgins [].

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" []. Exactly how, when, or why Harry Nyquist had his name attached to the sampling theorem remains obscure. The term Nyquist Sampling Theorem capitalized thus appeared as early as in a book from his former employer, Bell Labs , [19] and appeared again in , [20] and not capitalized in In , Blackman and Tukey cited Nyquist's article as a reference for the sampling theorem of information theory , [23] even though that article does not treat sampling and reconstruction of continuous signals as others did.

Their glossary of terms includes these entries:. This explains Nyquist's name on the critical interval, but not on the theorem. Similarly, Nyquist's name was attached to Nyquist rate in by Harold S. According to the OED , this may be the origin of the term Nyquist rate. In Black's usage, it is not a sampling rate, but a signaling rate.

From Wikipedia, the free encyclopedia. Proceedings of the Institute of Radio Engineers. Reprint as classic paper in: Nonuniform Sampling, Theory and Practice. Universal minimum-rate sampling and spectrum-blind reconstruction for multiband signals. Compressed Sensing for Analog Signals". Elektrische Nachrichtentechnik in German.

Bell System Technical Journal. Proceedings of the IEEE. Archived from the original on A tutorial review " ". Transmission Systems for Communications.

Theory of Linear Physical Systems. Theory of Signal Detectability: Composite Deferred Decision Theory. The Measurement of Power Spectra: Five short stories about the cardinal series , Bulletin of the AMS 12 Küpfmüller, Karl , "Utjämningsförlopp inom Telegraf- och Telefontekniken", "Transients in telegraph and telephone engineering" , Teknisk Tidskrift , no. The Art of Scientific Computing 3rd ed.

Sampling Years after Shannon , Proc. Detection theory Discrete signal Estimation theory Nyquist—Shannon sampling theorem. Audio signal processing Digital image processing Speech processing Statistical signal processing. Compression formats Compression software codecs. Retrieved from " https: Digital signal processing Information theory Theorems in Fourier analysis Mathematical theorems in theoretical computer science Claude Shannon Telecommunication theory.

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