Butzer, P. L.P. L.ButzerDodson, M. M.M. M.DodsonFerreira, PauloPauloFerreiraHiggins, J. RowlandJ. RowlandHigginsLange, OttoOttoLangeSeidler, PeterPeterSeidlerStens, Rudolf L.Rudolf L.Stens2024-03-262024-03-262011Applicable Analysis 90 (3-4): 643-688 (2011)https://hdl.handle.net/11420/46719This article discusses the interplay between multiplex signal transmission in telegraphy and telephony, and sampling methods. It emphasizes the works of Herbert Raabe (1909-2004) and Claude Shannon (1916-2001) and the context in which they occurred. Attention is given to the role that the exceptional research atmosphere in Berlin during the 1920s and early 1930s played in the development of some of the ideas underlying these works, first in Germany and then in the USA, as some of the protagonists moved there. Raabe's thesis, published in 1939, describes and analyses a time-division multiplex system for telephony. In order to build his working prototype, Raabe had to develop the theoretical tools he needed and achieved a thorough understanding of sampling, including sampling with pulses of finite duration and sampling of low-pass and band-pass signals. His condition for reconstruction was known as 'Raabe's condition' in the German literature of the time. On the other hand, Shannon's works of 1948 and 1949 contain the classical sampling theorem, but go much further and lay down the abstract theoretical framework that underlies much of the modern digital communications. It is interesting to compare Raabe's very practical approach with Shannon's abstract work: Raabe independently developed his methods to the degree he needed, but his main purpose was to build a working prototype. Shannon, on the other hand, approached sampling independently of practical constraints, as part of information theory - which became tremendously influential. © 2011 Taylor & Francis.en0003-681120113-4643688Taylor & FrancisHistorical reviewMultiplexingNyquist rateRaabe's conditionSampling theoremShannon theoryMathematicsJournal Article10.1080/00036811.2010.549474Journal Article