VLADIMIR KOTELNIKOV AND MOSCOW POWER ENGINEERING INSTITUTE - SAMPLING THEOREM, RADAR

SYSTEMS... A FASCINATING AND EXTRAORDINARY LIFE

Mikhail K. Tchobanou1 and Nikolay N. Udalov2

1Dept of Electrical Physics 2Dept of Formation of Oscillations and Signals Generation

Moscow Power Engineering Institute 14 Krasnokazarmennaya st., 111250, Moscow, RUSSIA

{ChobanuMK, UdalovNN}@mpei.ru,

ABSTRACT

This paper is dedicated to V.A. Kotelnikov. Vladimir Alexandrovich Kotelnikov was a prominent Soviet and Russian scientist, the founder of the Soviet secret te-lephony, the creator of the theory of potential noise immunity. He was also a distinguished engineer, who had the capability to find optimal ways for application of complex theoretical results for specific targets. He was a good science organizer who headed important projects of national significance. Being a talented teacher he cre-ated a scientific school of highly qualified radio engi-neering and telecommunication specialists, set up effi-cient groups, nurtured a scientific school.

His life was inseparably linked with Moscow Power Engineering Institute. The personality of V.A. Kotel-nikov is so multilateral and significant, that even a quick enumeration of all fields of Kotelnikov’s activity will not be an easy task. In each of them he achieved a lot.

1. THE ROOTS

V.A. Kotelnikov (1908 – 2005) was a Full member of the Russian Academy of Science, twice Hero of the Socialist Labour, laureate of the Lenin and State (Stalin) Prizes, a prominent Russian scientist in the area of ra-diophysics, radio engineering, electronics, radio astron-omy and information theory.

He was born on the 6th of September, 1908, in Ka-zan, into a family of a professor at Kazan University, who was the prominent Russian mechanical engineer and mathematician – Kotelnikov Alexander Petrovich (1868 – 1944). His mother was Kotelnikova Varvara Petrovna (1876 – 1922). He was married to Bogatskaya Anna Ivanovna (1916 – 1990). He had three children: Kotelnikov Alexander Vladimirovich (1940 – 2000), Kotelnikova Natalia Vladimirovna (born 1942), and Koroleva Marina Vladimirovna (born 1956).

Vladimir grew up in a family of scientists. His father was a professor of mathematics and mechanics of the University of Kazan, and a member of the Mathematical

society. His aunt, Kotelnikova Elizaveta Petrovna, was also a mathematician as well. She was a teacher of phys-ics at the womens’ Department in Kazan. She was an energetic member of the Mathematical society.

Figure 1. Kotelnikov Alexander and Kotelnikova Varvara

The Mathematical society was formed from a Mathematical section of the Kazan Society of Naturalists and Doctors. The Mathematical section was set up by their father (V.A. Kotelnikov’s grandfather) – Petr Ivanovich Kotelnikov (1809 – 1879), a prominent scien-tist, honorary Professor of mathematics, and the Dean of the Department of physics and mathematics at the Uni-versity of Kazan. From his early childhood Volodya was in the very center of the scientific community – in the family, with friends, and professors who were visiting their home—there were lots of talks about the commu-nity’s problems.

After graduating from school in 1925 in Moscow, V.A. Kotelnikov entered the Technical School of Com-munication named after V.N. Podbel’skiy. Remaining faithful to his childhood’s hobby—science of radio en-gineering—he entered the Department of Electrical En-gineering at Moscow Higher Technical School (MHTS) named after N.E. Bauman.

2. MHTS – MPEIMoscow Power Engineering Institute was formed on

the basis of the Department of Electrical Engineering of MHTS. After 1995 it was named Moscow Power Engi-neering Institute – Technical University or MPEI (TU). In 1931 V.A. Kotelnikov graduated from MPEI and got a diploma in electrical engineering in the area of “radio engineering”.

Figure 2. The author of sampling theorem (1932).

For more than 75 years of his life, V.A. Kotelnikov was connected with MPEI. The graduation year of V.A. Kotelnikov in 1931 was a special one. Students who had been studying in one of the oldest institutes of higher education — MHTS named after N.E. Bauman—slowly “became” students of the new university. Their gradua-tion was “the first scream” of the “just born” MPEI. And that “scream” demonstrated MPEI’s strong and powerful will to enter its new life of science.

Figure 3. MHTS – MPEI, graduation year 1931.

MPEI played a big part in Kotelnikov’s destiny. This university challenged Kotelnikov’s direction sometimes and simultaneously helped him a lot.

He was accepted to do post-graduate studies at MPEI because he was one of the best students. In 1931, before post-graduate studies began, he had been working at the Scientific Research Institute of the Red Army.

Vladimir enrolled in the post-graduate course with-out exams in January 1931 and he became a Senior labo-ratory Assistant. This is how his MPEI working, scien-tific and teaching activities began. These activities lasted for about 50 years, with a stoppage during the Second World War from 1941 till 1944. In reality he was work-ing at the MPEI till his death.

In MPEI he met his wife to be and his real love, Anna Ivanovna Bogatskaya. They got married in 1938 and were together until her death in 1990.

Figure 4. Kotelnikovs (in 1948).

3. SAMPLING THEOREM

For his post-graduate studies in 1931-1933, Kotel-nikov chose the theme “power lines’ carrying capacity”. During this work he was the first in the world to formu-late with mathematical precision and to prove the “sam-pling theorem” (Kotelnikov theorem). This discovery became the basis of modern theory of information, the-ory of signals transmission and processing, in radio en-gineering, in radio location and radio astronomy.

In reality, post-graduate students didn’t have to per-form research work, but Vladimir decided to choose burning topics and to solve them. He analyzed all issues of radio and wired connections. As a result, 2 papers were published by him in 1932. In the same year he fin-ished his fundamental work, “About the carrying capac-ity of ether and wires in electrical communications”, which was about to be announced at the First All-Union Communications Technical Reconstruction and Feeble Current Industry Development Congress. Although the

Congress didn’t take place, all materials including his paper were published at the end of 1932.

Before graduating from the post-graduate course all students had to make a presentation of the work which they had been researching. Vladimir made papers about his two works, “Theory of non-linear filters”, and “About the carrying capacity of ether and wires in elec-trical communications”. The papers were approved but only a few appreciated the fundamental meaning of the second paper and of the sampling theorem. People were saying, “Everything seems to be correct but it looks like science fiction”.

The work was really outstanding in two aspects. It was a well-grounded program document which broke the deadlock and showed the real ways of future radio com-munication development in 1930s. It was aimed for the future. For the first time by informal demonstrating the informational aspect of communication problem the au-thor predicted and proved with mathematical accuracy the future of digital signals, and the possibility to trans-mit data using digital signals. Finally, the sampling theo-rem was proved. A more exact wording of this statement is known as Kotelnikov theorem in the textbooks.

Similar formulae were known before Kotelnikov, but his discovery is a good choice of functions class and un-derstanding of applications’ possibilities. The informa-tional aspect of communication problems was discussed for the first time. His idea became the basis of modern information theory.

Kotelnikov’s work was ahead of the time for at least 15 years. And it was fully evaluated at the end of the 1970s when analog systems began to be substituted by digital systems.

Vladimir Kotelnikov made attempts to publish his work in a popular magazine “Electrichestvo” (Electric-ity) in 1936. But his article was rejected! He remem-bered about that episode only in the 21st century when he saw a letter with the rejection which was found in his ar-chives.

Claude Shannon announced his sampling theorem only in 1948. In 1977 it was suggested to call this theo-rem a WKS theorem, which means Whittaker-Kotelnikov-Shannon theorem. In 1999 highlighting the priorities the fund of Edward Rhine awarded Kotelnikov V.A. the prize “for fundamental investigations” for “The first mathematically exact formulation and publishing of the ‘sampling theorem’ ” while summing up the most prominent achievements of 20th century.

After graduating from his post-graduate course in 1933 and being a teacher in MPEI, V.A. Kotelnikov got a job in the USSR Peoples’ Commissariat of Communi-cations’ Central Scientific Research Institute of Com-munications as an engineer and later he became a head of the laboratory of the USSR Peoples’ Commissariat of Communications’ Institute of Radio (1933-1941). It be-came a new research scientific institute from the USSR Central Scientific Research Institute of Communications.

In 1936 he went on his first business trip abroad to the USA.

4. SECRET TELEPHONY AND TELEGRAPHY Kotelnikov created a number of outstanding engi-

neering projects before and during the Second World War. On his initiative and under his direction unique de-vices were created which were installed in a communica-tion line between Moscow and Khabarovsk. Such a communication-main creation was a very major break-through at that time domestically and internationally, in the sense of radio techniques. It wasn’t open and couldn’t be monitored or radio intercepted. An idea of changing in time voice frequency transformation was suggested and provided an acceptable disguise of speech signals.

Kotelnikov offered telegraph scramblers building principles. These principles were implemented in “Moskva” devices. It was the first time that superimposi-tion of a cipher onto a message was suggested and im-plemented in the USSR. A scheme of open message and cipher superimposition, which was suggested by Kotel-nikov, was very attractive and was used in many devices in subsequent generations. The cipher former (scram-bler) was very big and complicate and was constructed on electromechanical nodes. In the base of the construc-tion was a barrel filled with small balls. The barrel had several pins inside. The small balls rolled down onto 2 paper strips via 6 vertical pipes when the barrel re-volved. The small balls hit a ribbon. A paper tape was running under the ribbon. In such a way two copies of a paper tape were formed which were perforated ran-domly. These tapes were the keys. They were being sent to the transmission and receiving points to code and de-code information respectively. Such devices were tested on a line between Moscow and Komsomolsk on Amur. The pickup of the cipher from the key was performed by using photo-electronic elements.

It was a major breakthrough in USSR radio engineer-ing to put this line into operation. The line was one of the longest lines of that time. And it assisted in solving future problems in practical tasks.

Lots of MPEI students took part in that line design-ing and implementation and lots of them became scien-tists and prominent designer engineers in the area of fool-proof information transmission systems creation.

It is significant that that line was the first Kotelnikov “testing area” for designing new telephone and telegraph scramblers.

The requirements for absolute secrecy of the ci-phered materials were suggested and proved by Kotel-nikov in 1941. He gave the requirements that a mathe-matically non-breakable (non-decipherable) system should meet as well as the proof of the impossibility of its deciphering. This work and Kotelnikov theorem ap-peared to be the main basis in the USSR cryptography development.

While solving a problem of secure message passing V.A. Kotelnikov had formed his research work, “The fundamentals of automatic ciphering”, in June 1941, just 3 days before the Second World War started. The possi-ble creation of a device which could secure a perfect ci-

phering (impossible to read a message without a proper cipher) was proven. Also, conditions for designing such a device were found. This paper was published only in 1999 by Scientific Resesarch Committee of Cryptogra-phy Academy of Russian Federation during the celebra-tion of 90 years of V.A. Kotelnikov. It should be no-ticed that a secret paper, “Communication theory in se-cret systems”, written by Shannon much later on 1st of September, 1945, was published only in 1949 in English and in 1963 in Russian.

It’s interesting that areas of scientific interests of Ko-telnikov and Shannon intersected while creating a com-mon theory of communication, which was called “poten-tial noise-immune theory” by Kotelnikov.

Vladimir Kotelnikov understood that to ensure high stability and mask level of a voice signal it was neces-sary to design a vocoder, which could play a big part in voice spectrum compression (up to 10 times). Vocoder designing started in the laboratory of secret telephony. The war accelerated the work and by October 1941 mod-els of main units had been created. Vocoder started to “talk”. The only problem was it “talked” with a flick-ering voice and the quality of the reproduced voice wasn’t ideal.

5. SECOND WORLD WAR Kotelnikov’s laboratory was evacuated to Ufa in the

autumn of 1941. It became a part of the State Industrial-Experimental Union Institute #56 of the Ministry of Electrical Industry which had been evacuated from Len-ingrad earlier.

Figure 5. Kotelnikov laboratory in Ufa (1943).

First models of secret telephony were created there, in difficult conditions of evacuation. In 1942, a connec-tion with Transcaucasia was broken during the battles around Stalingrad but the communication was reestab-lished by the radio channel. At the Institute, Kotelnikov was a head of a group of scientists, and then the head of the laboratory. The creation of new secret communica-tion systems, which were immune to interception, con-tinued in Ufa. Production of the designed devices estab-lished in blockade Leningrad in factory #209. Kotel-nikov took part in it too. At the same time he had to handle scientific, technical and organizational problems.

Non-breakable communication systems created by Kotelnikov were used to connect Moscow with battle-

fronts in 1942-1945, as well as with front-line forces. It was used to connect Soviet delegation with Moscow during the unconditional surrender of the fascist Ger-many. Kotelnikov V.A. was awarded twice the Stalin Prize of the 1st degree in 1943 and 1946. He donated his prize money for the battle-front’s needs. A tank was built with his money.

After coming back to Moscow from Ufa, Kotel-nikov’s laboratory was moved to the Department of People's Commissariat of Internal Affairs of the USSR.

In 1944 he got back to MPEI as a professor, Dean of the Department of Radio Engineering, head of the Chair of the Fundamentals of radio engineering. Vladimir Ko-telnikov worked there until 1980. There were a lot of useful transformations in MPEI when he was a Dean, he set up a new teaching specialization – “radiophysics and electronics”.

Figure 6. Twice Laureat of State (Stalin) Prizes (1946).

Kotelnikov V.A. was one of the founders (May 1945) and honorary members of the All-Russian Scien-tific and Technical Society of Radio Engineering, Elec-tronics and Telecommunications named after Alexander Stepanovich Popov. Popov’ Society was created on the day of the 50th anniversary of invention of radio by Popov (7th of May, 1895). The Government celebrated this event on a large scale because radio communications was of great importance in Second World War. Kotel-nikov was the President of the Society during a very long period of time.

That time he formulated a statement about the possi-bility for creation of telephone ciphering devices based on vocoder and steady scrambler. To achieve it, it was

necessary to transform a compressed voice spectrum into a sequence of discrete impulses and to accomplish a scrambling using a telegraph scrambler model.

6. THEORY OF NOISE IMMUNITY Working actively in the area of radio communication

V.A. Kotelnikov made significant improvements in the methods of small signal receiving. The results of his in-vestigations were generalized in his Doctoral thesis de-fended in 1947 in MPEI. In it he stated the principles of potential noise-immunity that became later classical. This work initiated a new direction of science - statisti-cal radiophysics. It was published only in 1956 and it gave a worldwide recognition to the author.

Figure 7. The Deans of Radio Engineering Department of MPEI (1998).

The work touched upon a sensitive and eternal radio communication subject. If a communication chan-nel has a narrow transmission band, then a receiving sig-nal is unreadable due to a lack of high frequencies. If a wide transmission band is used then noises and inter-ferences appear. There were attempts to circumvent these difficulties using some transformations of a trans-mitting signal. Kotelnikov successfully explained that there is no sense in working out any kinds of transforma-tions, stopping useless activity of inventors of informa-tional “perpetuum mobile”.

Figure 8. In the laboratory in MPEI (1946).

The history of the defense is the next. The head of MPEI of those times V.A. Golubtsova made an offer to Kotelnikov to defend a doctoral thesis. At first he didn’t have any ideas about a theme of his future thesis.

The thesis was completed in the autumn. That was a great work about “Potential noise immunity the-ory”, which brought him world fame. However, the de-fense was delayed. The work passed ahead of it’s time approximately on 10 years. Only a few scientists could understand his work and it was difficult to find an oppo-nent for the defense. A request was made to academician Papalexi but he rejected to be an opponent because he also didn’t fully understand Kotelnikov’s thesis.

Figure 9. During the lesson in MPEI (1947).

Finally the thesis was defended. It was given to the State Library named after Lenin and only a short article was published –“Noise Immune Radio Communication Problems”—in 1947.

Kotelnikov released his monograph “Potential Noise Immunity Theory” in 1956 and this monograph created a furor in all world of radio engineering. World recogni-tion came to Kotelnikov!

7. EXPERIMENTAL DESIGN BUREAU OF MPEI

A gripping work over the Rocket Space Program of the USSR started in 1947 and MPEI took an active part in it. Within an extremely short period of time on the Government decree, which was signed by Stalin, a super secret “Sector of Special Works” was created for con-ducting scientific research works over jet armament, which afterwards became an Experimental Design Bu-reau (EDB) of MPEI. As the MPEI Sector was created in 1947 and till 1953, Kotelnikov V.A. did everything in his power to organize and to develop the MPEI EDB—he was the first leader and chief designer of this organi-zation, which started to work over the Rocket Space Pro-gram of the USSR immediately.

The Sector’s members created their own test studios (which became an MPEI Pilot Plant with complete pro-duction cycle) when they achieved independence from Industrial Ministries to manufacture systems they de-

sign. They managed to keep their balance notwithstand-ing competition with powerful industrial plants. The Special Sector was solving tasks, which were beyond Industry’s strength or were refused by the Industry.

V.A. Kotelnikov was a member of General Design-ers Council, which head was Sergei Pavlovich Korolev. MPEI EDB group became one of the largest designers and creators of space radio electronics.

Figure 10. The Day of Cosmonautics (12th of April).

Kotelnikov V.A. was enlist in the Government Tech-nical Commission to accept the first-ever-designed se-cure phone ciphering equipment based on vocoder and stable scrambler, in which it’s practically implemented Kotelnikov’s suggestion to design and create devices based on vocoder. The commission appreciated the ex-perimental devices very highly and decided to use them in the Government communications. The only thing the Commission wished was devices’ sound quality im-provement based on increased speech naturalness.

Being a prominent specialist in the area of secret te-lephony, Vladimir Kotelnikov took part in work of the second Government Technical Commission, which task was to choose only one device from several for serial production. It was the most authoritative commission, which consisted of Ministers of the USSR.

The Commission’s choices were two devices for se-rial production: the device M803-5 for most critical, in-cluding overseas, routes and the device M503 for do-mestic ones.

In the beginning of the 1990s V.A. Kotelnikov be-came one of the founders of the Cryptography Academy of the Russian Federation. He actively participated in the Academy temporary groups’ works, committees, coun-cils and expert-examinations of cryptographic re-searches.

8. ACADEMY OF SCIENCES OF USSR

In 1953, at the age of 45, Kotelnikov was elected as a Full member of the USSR Academy of Science, bypass-ing phase of Corresponding member. In that very year, Kotelnikov became a Deputy Head of had just founded USSR Academy of Science Institute of Radio Electron-ics (IRE), a bit later he became its Head (1954-1987)

and, finally, from 1987 he was its Honorary Head. He conducted colossal work over creation of the Institute, involving the best scientists, selecting the scientific sub-jects, which strongly impacted on the Institute’s “coming out” to the leading scientific institutions in the area of radio engineering.

He continued to head the Special Sector of MPEI and the Foundations of Radio Engineering Chair of the De-partment of Radio Engineering till 1955 and 1980, re-spectively. At that time he was the USSR Academy of Science Vice-President already. The USSR Academy of Science President, A.P. Alexandrov, once informed V.A. Kotelnikov about a new decree against combining jobs and he had to leave MPEI according to “his own initia-tive”. But the connection between Kotelnikov and MPEI didn’t break.

Figure 11. The President and the Vice-President ofAcademy of Sciences of USSR – A. Alexandrov and V. Kotelnikov

Being a Professor in MPEI from 1968 till 1988, Ko-telnikov was also a Professor, Chair Head at Moscow Physical & Engineering Institute.

9. PLANETS RADIO LOCATION

Formation and developing of a new direction in the Space research—planets radio location—is tightly con-nected with his name. Kotelnikov’s ideas are being used in spacecrafts control and monitoring systems designing. Radiolocation of Venus (1961-1964), Mercury (1962), Mars (1963), Jupiter (1963) was conducted under his di-rection. He was conferred on Lenin’s prize for that re-search work in 1964.

Integrated studies over the Venus radiolocation preparation were started under Kotelnikov’s direction in 1960, in which specialists of many institutions partici-pated. They needed to design a receiving and transmit-ting complex and, also, a plant for received signals proc-essing, which let make necessary measurements with a great and never seen before precision.

Pictures of the northern part of Venus, which were taken in 1983-1984 using the apparatus “Venera-15” and “Venera-16”, which were equipped with MPEI EDB de-vices, became world outstanding achievements. The

spacecrafts succeeded to take radio images on a substan-tial scale of the northern part of Venus, the size was ap-proximately 115 million km2 with resolution approxi-mately 1 km. A first in the history of science Atlas of Venus surface was created due to the conducted re-searches, its editor-in-chief was V.A. Kotelnikov.

Figure 12. Members of Venus and other planets location group.

V.A. Kotelnikov was a prominent organizer of the Soviet and Russian science. Being a Vice-President of the USSR Academy of Science, he was a Head of Physi-cal & Engineering and Mathematical Science in USSR Academy of Science Section from 1970 to 1975. After-wards, he became the first Vice-President of the USSR Academy of Science (1975-1988). From 1988 he was Academy of Science of Russia (ASR) Presidium Coun-cilor.

V.A. Kotelnikov founded the journal “Radio Engi-neering and Electronics” and was it’s editor-in-chief for a long time. He was the Head of Research Council of the Academy on “Radio astronomy” problem. He had been a Head of the “Interkosmos” International Cooperation Council in the area of researching and using the Outer Space during several years (at the moment, it’s an RAS Council Section “International cooperation” on the Space).

In 1973-1980 he was a Chairman of the Supreme Soviet of the Russian Soviet Federative Socialist Repub-lic (RSFSR), it was the highest legislative body of the Soviet Union that time.

10. HONORARY TITLES AND AWARDS

Kotelnikov’s merits were marked with high awards. He was twice Hero of Socialist Labour, he was rewarded with: 6 Orders of Lenin, the Order of the October Revo-lution, 2 Orders of the Labour Red Flag, and the Orders “Honour sign” and “For Services to Motherland” (of the Second degree).

At 21st of September 2003, the President of the Rus-sian Federation, Vladimir Putin, signed a decree about decorating academician Vladimir Kotelnikov with the Order “For Services to Motherland” of the First degree. He became one of the first knights of this Order in Rus-sia. The presentation of the Order took place at 10th of October, 2003 in Catherine hall of Kremlin.

Figure 13. V. Kotelnikov became the Full knight of the Order “For Services to Motherland” (2003)

He was awarded with the Prize of Lenin, twice State Prize of the USSR. The USSR Academy of Science con-ferred him to: a Golden Medal named after A.S. Popov (in 1974), a Golden Medal named after M.V. Lo-monosov, a Prize and a Golden Medal named after M.V. Keldysh.

Academician Kotelnikov deserved authority not only in Russia, but overseas too. He was the member of many organizations: IEEE member (elected in 1964, from 1.01.1987 – Fellow); foreign member of Czechoslovak Academy of Science (1965); honorary doctor of Czech Higher Technical School (the honorary degree was given in 1967); foreign member of the Academy of Sci-ence of Democratic Republic of Germany (1974-1992) and of the Academy of Science of Poland (1974); Corre-sponding Member of the International Astronautics Academy (1981); Full Member of the International As-tronautics Academy (1982); Vice-President of the Inter-national Astronautics Academy (1983-1995); foreign member of Mongolia Academy of Science (1983); for-eign member of Bulgaria Academy of Science (1987); honorary doctor of Saint-Petersburg State University of Electrical Engineering (1995). Besides, academician Ko-telnikov was a member of the Russian Association of Astronautics International Academy members. He was also a full member of the Engineering Academy and of the Academy of Arts.

His scientific and social activity was marked with overseas rewards and prizes. He was awarded by: the IEEE (USA) with a medal named after H. and S. Ben and with Golden medal named after A.G. Bell; the Fund of Edward Rhine (Germany) – the main prize for the fundamental investigations; Czechoslovakia Academy of Science – Golden medal “The merits for Science and Humanity” and Golden medal named after Fr. Krzhiz-hek; Slovak Academy of Science – Golden medal “Mer-its for Science”; Polish Electricians Society – medal named after Professor Y. Groshkovskiy as a recognition of his contribution to the cooperation between Soviet and Polish scientists; Space Research Scientific Unions International Council Committee – medal named after Vikhram Sarabhaya; International Prize name after J. Neru and etc.

Kotelnikov V.A. was the author of three monographs and of many scientific articles.

The International Conference “Modern radio engi-neering in sights of V.A. Kotelnikov” took place in MPEI (TU) in 2003. It was timed to his 95th Birthday, to the 70th anniversary of Kotelnikov theorem (sampling theorem), to the 50th anniversary of him being a Full member of the USSR Academy of Science, to the 50th

anniversary of the USSR Academy of Science IRE, which was created and headed for a long time by him.

Figure 14. Academician Vladimir Kotelnikov

The conference appeared to be the last chord in his Symphony, the beautiful leitmotif of which is Moscow Power Engineering Institute and it could be heard during all last 75 years of Vladimir Kotelnikov life.

11. ACKNOWLEDGMENTS

The references [1, 2, 3, 4, 5, 6] were used to prepare this paper.

Special thanks are addressed to Helen Roudneva and Dmitry Kislov for their assistance during the preparation of the paper.

12. REFERENCES[1] S. A. Bukashkin, “V.A. Kotelnikov – the founder of secret

telephony,” Radiotechnicheskie tetradi (Radio Engineer-ing Books), vol. 27, pp. 22–25, 2003 (in Russian).

[2] N. S. Kardashev, Yu. N. Pariyskii, G. Ya. Smolkov, B.A. Dubinskii, “V.A. Kotelnikov and radio astronomy devel-opment,” Radiotechnicheskie tetradi (Radio Engineering Books), vol. 27, pp. 25–31, 2003 (in Russian).

[3] A. G. Vitushkin, Half a century – as one day // Mathe-matical events of 20th century. Moscow, FAZIS, 2003 (in Russian).

[4] N. V. Kotelnikova, “Vladimir Alexandrovich Kotelnikov (on the 95th anniversary),” Radiotechnicheskie tetradi (Radio Engineering Books), vol. 27, pp. 7–10, 2003 (in Russian).

[5] N. V. Kotelnikova, “The path of the scientist. Alma mater of Vladimir Alexandrovich Kotelnikov,” Radiotech-nicheskie tetradi (Radio Engineering Books), vol. 31, pp. 9–19, 2005 (in Russian).

[6] VLADIMIR ALEXANDROVICH KOTELNIKOV. On the 95th anniversary. Moscow, MPEI Publishing House, 2003, 76 p. (in Russian).