Multiplex signal transmission and the development of sampling techniques: the work of Herbert Raabe in contrast to that of Claude Shannon

Abstract

This 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.

Keywords:

• sampling theorem
• multiplexing
• Raabe's condition
• Nyquist rate
• Shannon theory
• historical review

AMS Subject Classifications:

• 01-02
• 01A60
• 94-03
• 94A20

Acknowledgements

The authors would like to thank Prof. Dr Ing. J.R. Ohm, Prof. Lüke's successor in the office of IENT, for giving them access to the exceptional library of his institute, and for kindly preparing the two Shannon photos (Figures 6 and 7) for publication, with the assistance of Mrs. Myrjam Schiermeyer. This work was partially supported by an FCT grant (PTDC/EEA-TEL/108568/2008, COMPETE reference FCOMP-01-0124-FEDER-009920).

Notes

1. The article by Butzer et al. 34, an in-depth study of the life and work of Raabe, contains an English translation of the relevant parts of Raabe's doctoral thesis 5; Raabe's contribution is analysed in detail, and the concepts used at the time are put into the present day terminology. This article is, in contrast, centred on the life and work of Shannon, which is described in some detail and set against the earlier work of Raabe.

2. William Robert Bennett was born on 5 June 1904, in Des Moines, Iowa. He received his BS degree in electrical engineering from Oregon State College, in 1925, and A.M. and PhD degrees from Columbia University, in 1928 and 1949, respectively. He joined the research department of Bell Labs in 1925 and worked in multichannel communication, including multiplex telephony. He also investigated the effects of nonlinear distortion and the spectra of quantized signals 104. His books on data transmission and noise include 102,105,106. He had a gift for exposition and could make a complex problem understandable to ‘even the most inexperienced beginner’ 107. He became a fellow of the IEEE in 1956 and retired from Bell Labs in 1965, as Head of the Data Theory Department. He accepted a Professorship at Columbia University and was appointed Charles Batchelor Professor of Electrical Engineering there in 1968; Emeritus, 1972. He received the Mervin J. Kelly Award in Telecommunications from IEEE in 1968 and died on 21 August 1983.

3. Karl Willi Wagner was removed from office in 1936 since he refused to dismiss his Jewish employees. He escaped being sent to a concentration camp in view of a thrombosis. His research assistant and later co-author of his well-known book on operational calculus, Dr Alfred Thoma, who denounced certain accusations made against his teacher, was fired immediately. This information was kindly supplied by his son Ulrich O.E. Thoma and is to be found in his father's autobiography; see http:/www.ulrichthoma.de/alfredthoma/.

4. See 108 and also the web link http:/www.nue.tu-berlin.de/history/, which includes biographies and other useful historical information pertaining to the TH/TU Berlin.

5. Leo Szilard was born on 11 February 1898, in Budapest. He moved to Germany in December 1919 and became a student of the TH Berlin. Divided among engineering and physics, he started to attend the physics colloquia at Berlin University in January 1920; joining this eminent circle of physicists changed Szilard's life. He obtained his PhD degree from Berlin University in 1922, officially under von Laue, but with the support of Einstein, with whom he had developed a close relationship. Of the several patents and inventions that he filed from 1926 onwards, several were joint work with Einstein. In 1933 Szilard left from Germany to England. Later on, in 1938, he moved to the USA. During that period he developed his ideas about nuclear chain reaction and critical mass, for which he would file a patent. With Wigner, he organized the letter of Einstein to Roosevelt that would initiate the atomic bomb project. However, in 1945 he started two versions of a petition to prevent the deployment of atomic bombs against Japan. He would defend nuclear weapon control until the end of his life. He was appointed Professor at the University of Chicago in 1946, a Fellow of the American Academy of Arts and Sciences in 1954 and a member of the National Academy of Sciences of the USA in 1961. He received the USA Atoms for Peace Award in 1960 (see also 11,109). Szilard died on 30 May 1964 in La Jolla, CA.

6. John von Neumann was born on 28 December 1903, in Budapest. In 1921 he enrolled in mathematics at the University of Budapest, but spent most of his time at the TU Berlin and the Zurich Polytechnic, where he studied mathematics and chemical engineering. He obtained his PhD degree in mathematics from the University of Budapest and the chemical engineering degree from Zurich at about the same time, in 1925. During the period 1927–1929 he taught as a Privatdozent at the University of Berlin. In 1929 he moved to the University of Hamburg, and in 1930 to the USA. In 1930 he became a visiting professor at Princeton University. He obtained a permanent position there in 1931 and in 1933 he was invited to join the Institute for Advanced Study, becoming the youngest of its six initial members. Von Neumann made fundamental contributions in a number of topics: the axiomatization of set theory, the mathematical foundations of quantum physics (included in this group is his famous book 75 on the mathematics of quantum mechanics), game theory and mathematical economics (among which stands out the influential book with Oskar Morgenstern on game theory and economic behaviour), spectral theory and operator algebras, ergodic theory and numerical mathematics and computer science. His contributions to modern computing are discussed in 17,19,110,111, among others. See also the paper by Ulam 112, which is part of a memorial issue of the Bulletin of the AMS that also includes an account written by Shannon 113 of von Neumann's work on automata theory. John von Neumann died on 8 February 1957, in Washington, DC.

7. Jean-Maurice-Émile Baudot (1845–1903) was born on 11 September 1845 in Magneux, France. A telegraph engineer and one of the pioneers of telecommunications, he worked in the development of fast telegraphy, and invented the Baudot system for simultaneous transmission of several signals over the same wire (Figure 4). Baudot's invention of 1875–1977 was based upon a distributor of B. Meyer of 1870/1871 and the code used by Gauss and Weber in their telegraph experiments of 1833 2,58. Baudot's name became attached to the Baudot code, a predecessor of the ASCII code. The term ‘baud’, a measure of the number of symbols transmitted per second, is named after him.

8. Patrick Bernard Delany (1845–1924) was born in King's County, Ireland, on 28 January 1845, and moved to the United States in 1854. By the age of 16 he was already an accomplished telegraphist and became Chief Operator of the Franklin Telegraph Company, Assistant General Superintendent of the Southern and Atlantic Telegraph Company and superintendent of the Automatic Telegraph Company. He left telegraphy and became a newspaper correspondent at Washington and subsequently Editor of Old Commonwealth, Harrisonburg, Virginia. From 1880 onwards he turned his attention to inventing. He obtained over 100 patents, mostly related to telegraphy. For his work in high speed and synchronous telegraphy, the Franklin Institut awarded Delany the John Scott Medal in 1885 and the Elliot Cresson Medal in 1886 and 1896, respectively.

9. Bernard Meyer (1830–1884) was a French telegraph operator. Meyer's distributor of 1870/1871, which influenced Baudot, led to a multiplexer that was first used on the Paris–Lyon line already in 1872.

10. Poul la Cour (1846–1908), a Danish meteorologist, invented and patented in 1874 (the year Edison invented quadruplex telegraphy) a telegraphic device based on tuning forks. Today the main idea behind la Cour's device would be described as frequency-domain multiplexing (see 30,31 for an account of other pioneering efforts at frequency-domain multiplexing). In the United States, la Cour's invention was credited to Elisha Gray, who had worked along similar lines. la Cour protested but found himself unable to support the legal battle and withdrew his claim. Nevertheless, in 1886, the Franklin Institute awarded la Cour the John Scott Medal for his phonic wheel of 1877.

11. Generalized sampling theory was developed at Aachen from 1977 onwards. It was first studied in the doctoral dissertation of Splettstößer 114, continued by Stens 115, Ries–Stens 116 and Butzer et al. 117; overview papers are [118–120]. Let us point out that it was Otto Lange who in 1975 introduced PLB and his research group, especially Wolfgang Splettstößer, to signal analysis, in particular to investigate Shannon's sampling theorem from a critical, mathematical point of view. It finally lead to some 150 papers in the broad area by this research group up to 1994 121. In 1970, while studying and doing graduate work in EE and information science at Aachen, Dr Lange obtained, in addition, his Dipl. Math. degree, one examiner being PLB.

12. The sinc function (which had been defined by Raabe's teacher Küpfmüller) is never mentioned by Raabe. However, it should be kept in mind that the ideal lowpass filter, and hence the sinc function, cannot be implemented. Therefore, it could not ever become part of the multiplexing system that Raabe was trying to design and build.

13. This subsection on distortion treats Sections 5 and 6 of Raabe's doctoral thesis 5 which were not discussed nor translated in 34. The authors are planning to present an online translation of the whole Raabe thesis.

14. Recorded at Winchester, MA, 28 February 1977. Other sources of information by Shannon himself include an interview with Robert Price (28 July 1982) and a Kyoto Prize speech draft that Shannon wrote in 1985. See also the comprehensive thesis of Hagemeyer 61 and that of Guizzo 16.

15. Shannon received this award (of DM 200,000) for his ‘fundamental research on information theory’. Prof. H.D. Lüke, chairman of the Board of Curators of the Eduard Rhein Foundation, had suggested Shannon for the Award. The foundation of Eduard Rudolph Rhein (1900–1993) is now managed by his nephew Dr Rolf Gartz.

16. Harry Nyquist was born on 7 February 1889 in Nilsby, Sweden. He emigrated to America, attended the University of North Dakota, Grand Forks, from 1912 to 1915, and received his BS and MS degrees in Electrical Engineering in 1914 and 1915, respectively. He attended Yale University, New Haven, Connecticut, from 1915 to 1917, and was awarded a PhD in 1917. From 1917 to 1934 Nyquist was employed by the American Telephone and Telegraph Company in the Department of Development and Research Transmission, where he was concerned with studies on telegraph picture and voice transmission. From 1934 to 1954 he was with the Bell Telephone Laboratories, Inc., where he continued in the work of communications engineering, especially in transmission engineering and systems engineering. When he retired he had obtained 138 US patents and published 12 technical articles. He received many honours for his outstanding work. He was the fourth person to receive the National Academy of Engineer's Founder's Medal, ‘in recognition of his many fundamental contributions to engineering’. In 1960, he received the IRE Medal of Honor ‘for fundamental contributions to a quantitative understanding of thermal noise, data transmission and negative feedback’. Nyquist was also awarded the Stuart Ballantine Medal of the Franklin Institute in 1960, and the Mervin J. Kelly award in 1961. He passed away on 4 April 1976.

17. Ralph Vinton Lyon Hartley was born on 30 November 1888 in Spruce, Nevada. He attended the University of Utah and received as a Rhodes Scholar the BA degree in 1912 and the BSc degree in 1913 from Oxford University. Upon returning to the USA, he worked for the Western Electric Company and was in charge of the Bell System's transatlantic radiotelephone tests. He invented the oscillating circuit that beared his name during that period. After World War I he worked at Bell Laboratories, doing research on repeaters and voice transmission. After a period of illness he returned to Bell Laboratories as a consultant. Hartley proposed the linear transformation that beared his name in 1942 122. He received the IRE Medal of Honor in 1946 ‘for his early work on oscillating circuits employing triode tubes and likewise for his early recognition and clear exposition of the fundamental relationship between the total amount of information which may be transmitted over a transmission system of limited band-width and the time required’. He retired in 1950 and died on 1 May 1970.

18. It is worth pointing out that McCulloch 123, a promoter of cybernetics, reports having received from Hartley in 1929 ‘a reference to the definition of information by C.S. Peirce’, which McCulloch calls ‘the bud of the American definition of information as a quantity’. C.S. Peirce (1839–1914), a philosopher and logician, was a co-founder of semiotics.

19. Karl Küpfmüller, born on 6 October 1897 in Nürnberg, was an Electrical Engineer and a pioneer in communication theory and control engineering 124, pp. 96–102], 125. After attending school, he received a practical engineering education in Siemens-Schuckert Werke in Nürnberg in 1914–1915 and attended until 1919 the Ohm-Polytechnikum in Nürnberg, the period 1916–1918 being spent with the armed forces. During 1919–1921 he was fortunate to be an assistant of Karl W. Wagner at the Telegraphentechnisches Reichsamt in Berlin and in 1921 he entered the Zentral-Laboratorium of Siemens & Halske AG as an engineer. During his years at Siemens he attended for three semesters a variety of university courses, and in 1928, as a non-academic, he received a full professorship for general communication engineering at the TH Danzig. In 1935 he was with the TH Berlin and in 1937 back again at Siemens & Halske, where he became Director of Research and Development for Communication Theory. He remained at the TH Berlin as honorary professor. After the war, he was with the firm Rohde & Schwarz during 1946–1948 in Munich (but interned until 1947 by the US occupational forces). In 1948–1952 he was with Standard Electric Lorenz AG, and finally from 1952 to 1963 as Full Professor and Director of the Institute for Telecommunication Engineering at the TH Darmstadt, perhaps the best in the field at that time. There he was a co-founder of the ITG (Informationstechnische Gesellschaft). Küpfmüller's classic textbook Einführung in die Theoretische Elektrotechnik (1st edition, Berlin 1932, 285pp.) is still in print after 18 editions 126. His Die Systemtheorie der elektrischen Nachrichtenübertragung (Stuttgart, 386pp.), which appeared in 1949, was based on lectures given from 1937 to 1943. He was highly honoured in his lifetime, being awarded, e.g. the Gauss-Weber Medal in 1932, honorary doctorates from the TH Danzig in 1944 and Erlangen in 1976, in addition to medals from Sweden and Austria. He died on December 26, 1977, in Darmstadt.

20. Fritz (Friedrich Heinrich) Lüschen, born on 19 March 1877 in Oldenburg, was one of the most important German communication engineers between WW I and WW II. He worked for 25 years for the Deutsche Reichspost, entering its administration as an 18 year old in 1895. After 10 years there, he spent five months at the École Supérieure des Postes et Télégraphes in Paris and then studied during 1905–1911 mathematics and physics at the University of Berlin, besides his work at the Reichspost. He also took in 1907 a nine-month engineering course at the Reichspostversuchsamt. Then in 1911 he became a telegraph engineering inspector. During WW I, he first served as a stage telegraph inspector and after 1917 as a second lieutenant at the headquarters of the German army in Turkey and Palestine. In 1920 Lüschen joined Siemens & Halske AG, first as Chief-Engineer of the laboratory for low-voltage cables, then in 1921 as Director of their Central Laboratory for Telecommunications, which he founded, and then in 1930 as director of their total cable community. Finally, in 1944 he was appointed by Albert Speer as Chairman of Development and Production of the entire German electrical engineering industry. On 18 June 1945 he committed suicide in Berlin. He was awarded honorary doctorates from Cologne University in 1925 and TH Danzig in 1929. He received the prestigious Gauss-Weber Medal from Göttingen in 1933 (see also 127).

21. Felix (Alexander Philipp) Strecker, born on 27 February 1892 in Dembno (Jarotschin District, now Poland), was an authority in communication theory, a subject to which he contributed substantially. He studied botany and zoology during 1910–1914 at the University of Halle and the TH Munich. He joined the armed forces during WW I, then he studied in 1921–1923 at Halle, receiving his Dr. rer. nat. in physics under Karl E.F. Schmidt in 1923. In that same year he joined Siemens & Halske AG, the main laboratory of which was just coming into being and would gather names like Lüschen, Bruno Pohlmann (1884–1958), Küpfmüller and Dennis Gabor. Strecker worked first as a Patent Engineer, then in 1929 he became in charge of the Zentrallabor headed by Fritz Berger, in 1934 he became Chief-Engineer and in 1935 head of the long distance telephone laboratory, among other duties. From 1937 to 1944 he was the authorized person (Bevollmächtigter) of the Siemens & Halske AG, Berlin-Siemensstadt. During this period alone he published more than 20 papers. After the war his health deteriorated, but he wrote two books and returned to the Zentrallabor. In 1950 he settled in Munich, where he passed away in 1951. Let us just mention two prominent results (see [128–132] for more information). In 1929 Strecker introduced together with Richard Feldtkeller (1901–1981) matrix calculus into the theory of linear networks and amplifiers, giving it the present form; he had been introduced to the calculus by his teacher Prof. H. Jung at Halle. In 1930 he discovered the stability criterion usually associated with the name of Nyquist. He lectured on it in 1931 and wrote a manuscript entitled ‘Die Bedingungen der Selbsterregung in linearen Gebilden’ which the journal Elektrische Nachrichtentechnik did not publish (the journal still exists). As a result, the first publication on the subject was Nyquist's paper of 1932 133, who found the criterion independently. Strecker was able to publish his result of 1931 only in 1947 in his book ‘Die elektrische Selbsterregung’ 134 (see also 135).

22. Dennis Gabor was born on 5 June 1900, in Budapest, Hungary. Already in high school he was demonstrating a deep understanding of physics. He attended the Budapest Technical University, and obtained a degree in Mechanical Engineering. Because he opposed the monarchy that had come to power in 1920, he fled to Germany and studied at the Technical University of Berlin, from which he received the Diploma in Engineering in 1924 and the doctorate in 1927. During this period, he invented a fast-response cathode-ray oscilloscope. After graduation he worked in the physics laboratory of Siemens and Halske but was forced to return to Hungary in 1933: the Nazi regime had started and his contract was terminated because he was not German. He emigrated to the UK and got a job at the British Thomson-Houston Company. During the war, his Hungarian citizenship proved to be an obstacle and his scientific work did not go well. The breakthrough occurred in 1947, when he invented holography. Although the potential of his invention was not fully appreciated until the invention of the laser, its importance would be recognized. He was awarded the Nobel Prize for Physics in 1971 as a result of his pioneering work in holography. He received other honours, including the Albert Michelson Medal of the Franklin Institute, in 1968, and the Medal of Honour of the IEEE, in 1970. He died on 9 February 1979, in London.

23. Vladimir Alexandrovich Kotel'nikov (1908–2005) was born on 6 September 1908 in Kazan, the capital of what was then the Republic of Tatarstan. He graduated from the Moscow Power Engineering Institute (MEI) in 1930. He became a postgraduate at MEI, and was promoted to Senior Laboratory Assistant and then to Assistant Professor. His doctor of science thesis of 1946, translated in 1959 136, is another of his pioneering works that drew little attention at the time it appeared despite the importance of the results it contained (see, in this respect, 137). Kotel'nikov also worked in cryptography and planetary radar. He was elected a full member of the USSR Academy of Sciences in 1953, received the State Prize (twice, in 1943 and 1946), the Lenin prize (1964), the Eduard Rhein Foundation award (in 1999, at age 91, following a proposal made by Hans Dieter Lüke), the IEEE Alexander Graham Bell Medal (2000) and several other honours.

24. As late as 1995, Vladimir Tichomirow, the great Russian expert in the broad areas of signal analysis and approximation, and a student of Kolmogorov, told one of the authors (P.L.B.) at Aachen that this paper was not available in Moscow; he himself had never seen it.

25. In PCM, or pulse code modulation, an analogue signal is represented by uniformly sampling it and then quantizing the samples to a fixed, finite precision. In the compact disc, for example, the sampling rate is 44.1 kHz and the samples are quantized to 16 bits.

26. In PPM, or pulse position modulation, a message is conveyed by varying the position of a pulse. If the pulse can occupy any of 2 ⁿ equally likely positions, each message will consist of n bits.

27. We have slightly simplified Bennett's equations by taking his ν = 0 and using complex exponentials.