A: Cambridge, Massachusetts, United States

7/23/1940 to 1/1949

In 1949 American mathematician, electrical engineer, and cryptographer Claude Shannon published *Communication in the Presence of Noise*in the Janauary 1949 issue of the Proceedings of the I.R.E*. *A footnote preceding the publication indicated that the original manuscript was "received by the Institute, July 23, 1940," but obviously publication was delayed because of World War II. Then in 1947 Shannon presented the paper to the IRE New York Section, and at the IRE National Convention in March, 1948. These details confirm that the content remained current during the eight years between the time it was written and final publication.

"The sampling theorem was implied by the work of Harry Nyquist in 1928 ('Certain topics in telegraph transmission theory'), in which he showed that up to 2B independent pulse samples could be sent through a system of bandwidth B; but he did not explicitly consider the problem of sampling and reconstruction of continuous signals. About the same time, Karl Küpfmüller showed a similar result, and discussed the sinc-function impulse response of a band-limiting filter, via its integral, the step response Integralsinus; this bandlimiting and reconstruction filter that is so central to the sampling theorem is sometimes referred to as a Küpfmüller filter (but seldom so in English).

"The sampling theorem, essentially a dual of Nyquist's result, was proved by Claude E. Shannon in 1949 ('Communication in the presence of noise'). V. A. Kotelnikov published similar results in 1933 ('On the transmission capacity of the 'ether' and of cables in electrical communications', translation from the Russian), as did the mathematician E. T. Whittaker in 1915 ('Expansions of the Interpolation-Theory', 'Theorie der Kardinalfunktionen'), J. M. Whittaker in 1935 ('Interpolatory function theory'), and Gabor in 1946 ('Theory of communication')" (Wikipedia article on Nyquist-Shannon Sampling Theorem, accessed 01-04-2010).