At the end of the nineteenth beginning of the twentieth century, telephone and radio communications rapidly developed. 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 to a distance of 250 meters, which consisted of only two words: “Henry Hertz”.
The development of communications was at the head 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 cannot imagine our life without a telephone, 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 mid-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, is of fundamental importance.
She entered the science under the name of Kotelnikov's theorem.
Vladimir Alexandrovich Kotelnikov
The future academician was born in 1908 in a family of teachers at Kazan University. He studied at the Moscow Technical University. Bauman, attended lectures of interest to him at Moscow State University. In 1930, the Faculty of Electrical Engineering, where Kotelnikov studied, was transformed into the Moscow Power Engineering Institute, and he graduated from 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 headed the department "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 Academy of Sciences of the USSR.
All students of relevant specialties are still studying according to the textbook Kotelnikov "Theoretical Foundations of Radio Engineering".
Kotelnikov also dealt with the problems of radio astronomy, radiophysical research of the oceans, space research.
He did not have time to publish his latest work, Model Quantum Mechanics, already written at almost 97 years old. She was released only in 2008.
V. A. Kotelnikov died in his 97th year of life on February 11, 2005. He is twice a hero of socialist labor, and has been awarded many government awards. One of the minor planets is named after him.
Kotelnikov Theorem
The development of communication systems posed many theoretical questions. For example, the signals of which frequency range can be transmitted over communication channels of different physical structures, with different bandwidths so as not to lose information during reception.
In 1933, Kotelnikov proved his theorem, which is also called the sampling theorem.
The statement of the Kotelnikov theorem:
If an analog signal has a finite (limited in width) spectrum, then it can be restored unambiguously and without loss from its discrete samples taken with a frequency strictly exceeding twice the upper frequency.
An ideal case is described when the signal duration time is infinite. It has no interruptions, but has a limited spectrum (by Kotelnikov's theorem). However, the mathematical model describing signals with a limited spectrum is in practice well applicable to real signals.
Based on the Kotelnikov theorem, a method of discrete transmission of continuous signals can be implemented.
The physical meaning of the theorem
Kotelnikov's theorem in simple words can be explained 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 instant 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.
On discretization, Kotelnikov’s theorem makes very important conclusions. For different types of signals, there are different sampling frequencies. For voice (telephone) communication 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. Although the theorem was developed for an ideal communication channel, it is applicable to all other types of channels.
Multichannel telecommunication
Kotelnikov's theorem underlies multichannel telecommunications. When sampling and transmitting pulses, the period between pulses is much longer than their duration. This means that in the intervals of 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, one pair of wires can transmit about 2,000 telephone calls simultaneously.
On the basis of the Kotelnikov theorem, in simple words we can say that almost all modern communication systems have arisen.
Harry Nyquist
As is sometimes the case in science, scientists dealing with similar problems come to almost the same conclusions. This is quite natural. There is still no debate about who discovered the conservation law - Lomonosov or Lavoisier, who invented the incandescent lamp - Yablochkin or Edison, who invented the radio - Popov or Marconi. This list goes on and on.
Thus, Harry Nyquist, an American physicist of Swedish descent, published his research in 1927 in the journal "Defined Problems of Telegraphic Transfer" with the conclusions of Kotelnikov. His theorem is sometimes called the Kotelnikov-Nyquist theorem.
Harry Nyquist was born in 1907, defended his thesis at Yale University, worked in Bell's laboratory. There he studied the problems of thermal noise in amplifiers, participated in the development of the first photo telegraph. His works served as the basis for the further development of Claude Shannon. Nyquist passed away in 1976.
Claude Shannon
Claude Shannon is sometimes called the father of the information age - his contribution to the theory of communications and computer science is so great. Claude Shannon was born in 1916 in the United States. He worked in the laboratory of Bell and a number of American universities. During the war, along with Alan Turing, he decrypted 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. He proved the theorem on reconstructing a signal from its discrete samples (independently of Kotelnikov) in 1949. It is sometimes called the Kotelnikov-Shannon theorem. True in the West, the name Nyquist-Shannon theorem is more commonly accepted.
Shannon introduced the concept of entropy into the theory of communication. Engaged in the study of codes. Thanks to his work, cryptography has become a full-fledged science.
Kotelnikov and cryptography
Kotelnikov also dealt with problems of codes and cryptography. Unfortunately, in the days of the USSR, everything related to codes, ciphers, was strictly classified. And open publications of many works by Kotelnikov could not be. However, he worked on creating closed communication channels, the codes of which the enemy could not crack.
June 18, 1941, almost before the war, was written by Kotelnikov's article "The Basic Provisions of Automatic Encryption", published in the 2006 collection "Quantum Cryptography and Kotelnikov's One-Time Keys and Counts Theorem".
Noise immunity
Using the work of Kotelnikov, a theory of potential noise immunity was developed, which determines how much maximum interference can be in the communication channel so that information is not lost. The option of an ideal receiver that is far from real is being considered. But ways to improve the communication channel are clearly defined.
Space exploration
The team led by Kotelnikov made a great contribution to the space communications, automation and telemetry systems. Sergey Pavlovich Korolev involved the Kotelnikov laboratory in solving the problems of the space industry.
Dozens of control points were built, connected to a single control and measuring 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, from the space stations "Venus" and "Magellan" radar was carried out areas of the planet in predefined sectors. As a result, we know what is hiding on Venus behind dense clouds. Also, research was conducted on 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 from extraterrestrial civilizations
Seti, the international program for searching for radio signals from extraterrestrial civilizations with the help of 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 simultaneously to millions of radio channels, covering the entire possible range.
Also, under his leadership, work was performed that defines the criteria for a reasonable narrowband signal in general noise and interference.
Unfortunately, so far these searches have not been successful. But on the scale of history, they are not very long.
Kotelnikov's theorem relates to fundamental discoveries in science. It can be safely put on a par with the theorems of Pythagoras, Euler, Gauss, Lorentz, etc.
In each 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 TV, listen to the radio, use the Internet. All this basically contains the principle of discretization of signals.