Herbert Raabe's work in multiplex signal transmission and his development of sampling methods

This paper discusses the work of Herbert Raabe (1909-2004) and its significance in terms of sampling. Raabe's thesis, published in 1939, represents a milestone in the development of sampling, as pointed out in the historical works of Luke. Raabe built and analysed the first time-division multiplex system for telephony, a task that required of him a thorough understanding of sampling, including sampling with pulses of finite duration and sampling of low-pass and band-pass signals. We analyse his approach, its significance from the viewpoint of sampling, the generality of its conclusions, and also the milieu that lead to his remarkable achievements: the exceptional research climate existing in Berlin at the time he worked. We also examine the connection between ''Raabe's condition'', the work of Harry Nyquist (1924, 1928) on telegraphy and the so-called ''Nyquist rate''. An English translation of the sections of Raabe's dissertation more closely related to sampling is included as an appendix.