At the end of the nineteenth and beginning of the twentieth century, telephone and radio communications developed rapidly. In 1882, the first telephone exchange in Russia was launched in St. Petersburg. This station had 259 subscribers. And in Moscow at about the same time there were 200 subscribers.
In 1896, Alexander Popov transmitted the first radio signal over a distance of 250 meters, consisting of only two words: "Heinrich Hertz".
The development of communications has been at the forefront of technological progress. A little over a century has passed since then, and thanks to the work of scientists and engineers in this industry, we see how the world has changed.
We can't imagine our life without telephone, radio communication, television and the Internet. This is based on the propagation of electromagnetic waves, the theory of which was developed by James Clerk Maxwell in the middle of the nineteenth century. Electromagnetic waves are the carrier of useful signals, and in the theory of signal transmission, the theorem of the Russian scientist and engineer, academician Vladimir Alexandrovich Kotelnikov plays a fundamental role.
It entered science under the name of Kotelnikov's theorem.
Vladimir AleksandrovichKotelnikov
The future academician was born in 1908 in a family of Kazan University teachers. Studied at MVTU im. Bauman, attended lectures of interest to him at Moscow State University. In 1930, the electrical engineering faculty, where Kotelnikov studied, was transformed into the Moscow Power Engineering Institute, and Kotelnikov graduated from it. After graduation, he worked in various universities and laboratories. During the war, he headed the laboratory of a closed research institute in Ufa, where he de alt with issues of secure communication channels and message encoding.
Approximately such developments are mentioned by Solzhenitsyn in his novel "In the First Circle".
For about forty years he was in charge of the Department of "Fundamentals of Radio Engineering", and was the Dean of the Faculty of Radio Engineering. Later he became director of the Institute of Radio Engineering and Electronics of the USSR Academy of Sciences.
All students of the relevant speci alties are still studying according to Kotelnikov's textbook "Theoretical Foundations of Radio Engineering".
Kotelnikov also de alt with the problems of radio astronomy, radiophysical research of the oceans, and space research.
He did not have time to publish his last work "Model Quantum Mechanics", written already at the age of almost 97. It only came out in 2008
V. A. Kotelnikov died at the age of 97 on February 11, 2005. He was twice a hero of socialist labor, was awarded many government awards. One of the minor planets is named after him.
Kotelnikov's theorem
Development of communication systemsraises many theoretical questions. For example, signals of what frequency range can be transmitted over communication channels, of different physical structure, with different bandwidth, so as not to lose information during reception.
In 1933, Kotelnikov proved his theorem, which is otherwise called the sampling theorem.
Formulation of Kotelnikov's theorem:
If an analog signal has a finite (limited in width) spectrum, then it can be reconstructed unambiguously and without loss from its discrete samples taken at a frequency strictly greater than twice the upper frequency.
Describes the ideal case when the signal duration time is infinite. It has no interruptions, but it has a limited spectrum (by Kotelnikov's theorem). However, the mathematical model describing limited-spectrum signals is well applicable to real signals in practice.
Based on the Kotelnikov theorem, a method for discrete transmission of continuous signals can be implemented.
Physical meaning of the theorem
Kotelnikov's theorem can be explained in simple terms as follows. If you need to transmit a certain signal, then it is not necessary to transmit it in its entirety. You can transmit its instantaneous impulses. The transmission frequency of these pulses is called the sampling frequency in the Kotelnikov theorem. It should be twice the upper frequency of the signal spectrum. In this case, at the receiving end, the signal is restored without distortion.
Kotelnikov's theorem draws very important conclusions about discretization. There are different sampling rates for different types of signals. For a voice (telephone) message with a channel width of 3.4 kHz - 6.8 kHz, and for a television signal - 16 MHz.
In communication theory, there are several types of communication channels. At the physical level - wired, acoustic, optical, infrared and radio channels. And although the theorem was developed for an ideal communication channel, it is applicable to all other types of channels.
Multichannel telecommunications
Kotelnikov's theorem underlies multichannel telecommunications. When sampling and transmitting pulses, the period between pulses is much greater than their duration. This means that in the intervals of pulses of one signal (this is called duty cycle), it is possible to transmit pulses of another signal. Systems for 12, 15, 30, 120, 180, 1920 voice channels were implemented. That is, about 2000 telephone conversations can be transmitted simultaneously over one pair of wires.
Based on the Kotelnikov theorem, in simple words, almost all modern communication systems arose.
Harry Nyquist
As is sometimes the case in science, scientists dealing with similar problems arrive almost simultaneously at the same conclusions. This is quite natural. Until now, disputes have not subsided about who discovered the law of conservation - Lomonosov or Lavoisier, who invented the incandescent lamp - Yablochkin or Edison, who invented the radio - Popov or Marconi. This list is endless.
Yes,the American physicist of Swedish origin Harry Nyquist in 1927 published his research in the journal Certain Problems of Telegraph Transmission with conclusions similar to those of Kotelnikov. His theorem is sometimes called the Kotelnikov-Nyquist theorem.
Harry Nyquist was born in 1907, did his PhD at Yale University, and worked at Bell Labs. There he studied the problems of thermal noise in amplifiers, participated in the development of the first phototelegraph. His works served as the basis for the further developments of Claude Shannon. Nyquist passed away in 1976
Claude Shannon
Claude Shannon is sometimes called the father of the information age - so great is his contribution to the theory of communication and computer science. Claude Shannon was born in 1916 in the USA. He worked at the Bell Lab and at a number of American universities. During the war, he worked with Alan Turing to decipher the codes of German submarines.
In 1948, in the article "Mathematical Theory of Communication", he proposed the term bit as a designation of the minimum unit of information. In 1949, he proved (independently of Kotelnikov) a theorem dedicated to the reconstruction of a signal from its discrete samples. It is sometimes called the Kotelnikov-Shannon theorem. True, in the West the name of the Nyquist-Shannon theorem is more accepted.
Shannon introduced the concept of entropy into communication theory. I studied codes. Thanks to his work, cryptography has become a full-fledged science.
Kotelnikov and cryptography
Kotelnikov also de alt with problems of codes andcryptography. Unfortunately, in the days of the USSR, everything related to codes, ciphers, was strictly classified. And open publications of many of Kotelnikov's works could not be. However, he worked to create closed channels of communication, the codes of which the enemy could not crack.
June 18, 1941, almost before the war, Kotelnikov's article "Basics of automatic encryption" was written, published in the 2006 collection "Quantum cryptography and Kotelnikov's theorem on one-time keys and readings".
Noise immunity
With the help of Kotelnikov's work, a theory of potential noise immunity was developed, which determines the maximum amount of interference that can be in a communication channel so that information is not lost. A variant of an ideal receiver, which is far from the real one, is considered. But ways to improve the communication channel are clearly defined.
Space exploration
The team led by Kotelnikov made a great contribution to the systems of space communications, automation and telemetry. Sergei Pavlovich Korolev involved the Kotelnikov laboratory in solving the problems of the space industry.
Dozens of control and measurement points were built, linked into a single control and measurement complex.
Radar equipment for interplanetary space stations was developed, mapping was carried out in the opaque atmosphere of the planet Venus. With the help of devices developed under the direction of Kotelnikov, space stations "Venera" and "Magellan" carried outradar areas of the planet in predetermined sectors. As a result, we know what is hidden on Venus behind dense clouds. Mars, Jupiter, Mercury were also explored.
Kotelnikov's developments have found application in orbital stations and modern radio telescopes.
In 1998, V. A. Kotelnikov was awarded the von Karman Prize. This is an award from the International Academy of Astronautics, which is given to people with creative thinking for a significant contribution to space research.
Search for radio signals from extraterrestrial civilizations
The international program to search for radio signals of extraterrestrial civilizations Seti using the largest radio telescopes was launched in the 90s. It was Kotelnikov who justified the need to use multichannel receivers for this purpose. Modern receivers listen to millions of radio channels simultaneously, covering the entire possible range.
Also, under his leadership, work was carried out that defines the criteria for a reasonable narrowband signal in general noise and interference.
Unfortunately, so far this search has not been successful. But on the scale of history, they are conducted for a very short time.
Kotelnikov's theorem refers to fundamental discoveries in science. It can be safely put on a par with the theorems of Pythagoras, Euler, Gauss, Lorentz, etc.
In every area where it is necessary to transmit or receive any electromagnetic signals, we consciously or unconsciously use the Kotelnikov theorem. We talk on the phone, watch TVlisten to the radio, use the Internet. All this basically contains the principle of sampling signals.
