Late nineteenth early twentieth centurytelephone and radio communications were rapidly developing. In 1882, the first telephone exchange in Russia was opened 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 to a distance of 250 meters, which consisted of only two words: "Heinrich Hertz".
The development of communications was at the head of technological progress. A little more than 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 a phone,radio communications, 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 carriers of useful signals, and in the theory of signal transmission, the theorem of a Russian scientist and engineer, academician Vladimir Alexandrovich Kotelnikov plays a fundamental role.
She entered science as the Kotelnikov theorem.
Vladimir Alexandrovich Kotelnikov
The future academician was born in 1908.in the family of teachers of Kazan University. He studied at MVTU them. Bauman attended his lectures in Moscow State University. In 1930, the Faculty of Electrical Engineering, where Kotelnikov studied, was transformed into the Moscow Energy Institute, and graduated from its Kotelnikov. 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 dealt with issues of secure communication channels, 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 dean of the radio engineering faculty. Later became the director of the Institute of Radio Engineering and Electronics, USSR Academy of Sciences.
All students of relevant specialties are still studying according to Kotelnikov’s textbook “Theoretical Foundations of Radio Engineering”.
Kotelnikov also dealt with radio astronomy problems, radiophysical studies of the oceans, and space research.
He did not have time to publish his latest work, Model Quantum Mechanics, written at almost 97 years old. She came out only in 2008.
V. Kotelnikov died in the 97th year of his life on February 11, 2005. He is twice the hero of socialist labor, awarded with many government awards. One of the minor planets is named in his honor.
Kotelnikov theorem
The development of communication systems has put manytheoretical issues. For example, signals of which frequency range can be transmitted over communication channels, of different physical structures, with different bandwidths, so as not to lose information when receiving.
In 1933, Kotelnikov proved his theorem, which is otherwise called the reading theorem.
Formulation of the Kotelnikov theorem:
If the analog signal has a finitespectrum (limited in width), it can be restored unambiguously and without loss in its discrete readings taken at a frequency strictly greater than twice the upper frequency.
Описывается идеальный случай, когда время signal duration is infinite. It has no interruptions, but has a limited spectrum (according to the Kotelnikov theorem). However, the mathematical model describing signals with a limited spectrum is also well applicable to real signals in practice.
Based on the Kotelnikov theorem, a method of discrete transmission of continuous signals can be implemented.
The physical meaning of the theorem
Theorem Kotelnikov simple words can beexplain as follows. If you need to transmit a signal, it is not necessary to transmit it entirely. You can send it instantaneous pulses. The transmission frequency of these pulses is called the sampling rate 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.
On discretization, the Kotelnikov theorem does veryimportant conclusions. For different types of signals there are different sampling rates. For voice (telephone) messages 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 channels.communication. At the physical level - wired, acoustic, optical, infrared and radio channels. And although the theorem is designed for an ideal communication channel, it is applicable to all other types of channels.
Multichannel telecommunication
Теорема Котельникова лежит в основе multi-channel telecommunications. When sampling and transmitting pulses, the period between pulses is much longer than their duration. This means that in the intervals of the pulses of one signal (this is called the duty cycle) it is possible to transmit pulses of another signal. Systems were implemented on 12, 15, 30, 120, 180, 1920 voice channels. That is, about 2 telephone conversations can be transmitted over one pair of wires simultaneously.
Based on the Kotelnikov theorem, in simple words one can say that almost all modern communication systems have emerged.
Harry nyquist
As it sometimes happens in science, scientists,dealing with similar problems come almost simultaneously to the same conclusions. This is quite natural. To this day, disputes are not dying down who discovered the law of conservation - Lomonosov or Lavoisier, who invented the incandescent lamp - Yablochkin or Edison, who invented radio - Popov or Marconi. This list goes on and on.
So, an American physicist of Swedish originHarry Nyquist in 1927 in the journal "Certain problems of telegraph transmission" published his research with the findings of Kotelnikov. His theorem is sometimes called the Kotelnikov-Nyquist theorem.
Harry Nyquist was born in 1907, defendeddissertation at Yale University, worked in the Bell lab. There he dealt with the problems of thermal noise in amplifiers, and participated in the development of the first photo telegraph. His works served as the basis for the further development of Claude Shannon. Nyquist died in 1976
Claude Shannon
Клода Шеннона иногда называют отцом information age - so great is his contribution to the theory of communications and computer science. Claude Shannon was born in 1916 in the USA. He worked in the laboratory of Bell and a number of American universities. During the war, together with Alan Turing was engaged in deciphering the codes of German submarines.
In 1948in the article "Mathematical Theory of Communication," he proposed the term bits to denote the minimum unit of information. He proved (independently of Kotelnikov) in 1949 to the theorem devoted to the recovery of a signal from its discrete readings. It is sometimes called the Kotelnikov-Shannon theorem. True, in the West, the Nyquist-Shannon theorem is more commonly accepted.
Shannon introduced the concept of entropy into communication theory. Engaged in the study of codes. Thanks to his work, cryptography has become a complete science.
Kotelnikov and cryptography
Котельников тоже занимался проблемами кодов и cryptography. Unfortunately, during Soviet times, everything related to codes, ciphers, was strictly classified. And open publications of many works of Kotelnikov could not be. However, he worked on the creation of closed communication channels, the codes of which the enemy could not crack.
18 июня 1941 года, практически перед самой by the war, Kotelnikov’s article “The Basic Provisions of Automatic Encryption” was published in the 2006 collection “Quantum Cryptography and Kotelnikov’s Theorem on One-Time Keys and Readings”.
Noise immunity
Through the work of Kotelnikov was developedPotential noise immunity theory, which determines what the maximum amount of interference can be in a communication channel so that information is not lost. Consider the option of an ideal receiver, which is far from real. But ways to improve the communication channel are clearly defined.
Space research
The team under the leadership of Kotelnikov introduceda great contribution to space communications, automation and telemetry systems. Sergei Pavlovich Korolev attracted Kotelnikov laboratory to solving problems of the space industry.
Dozens of control and measurement points were built, connected into a single control and measuring complex.
Radar equipment was developed forinterplanetary space stations, mapping is carried out at the opaque atmosphere of the planet Venus. With the help of devices developed under the guidance of Kotelnikov, from the Venus and Magellan space stations, the radar areas of the planet were radar in predetermined sectors. As a result, we know what lies behind Venus behind dense clouds. Also conducted studies of Mars, Jupiter, Mercury.
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 the prize of the International Academy of Astronautics, which is given to people with creative thinking for their significant contribution to space research.
Search for radio signals of extraterrestrial civilizations
International Radio Search ProgramWith the help of the largest radio telescopes, Seti's extraterrestrial civilizations were launched in the 90s. It was Kotelnikov who justified the need to use multi-channel receivers for this purpose. Modern receivers listen at the same time millions of radio channels, covering the entire possible range.
Also under his leadership, works were performed that define the criteria for a reasonable narrowband signal in general noise and interference.
Unfortunately, so far these searches have not been crowned with success. But on the scale of history, they are carried out very briefly.
Kotelnikov's theorem refers to the fundamental discoveries in science. It can be safely put on par with the theorems of Pythagoras, Euler, Gauss, Lorentz, etc.
В каждой области, где необходимо передавать или to accept any electromagnetic signals, we consciously or unknowingly use the Kotelnikov theorem. We talk on the phone, watch TV, listen to the radio, use the Internet. All this basically contains the principle of discretization of signals.
