Kotel'nikov's theorem is the theoretical basis of modern information technologies

There are few achievements that have so strongly influenced the development of communication and modern information technologies, like Kotelnikov's theorem. By and large, this scientist glorified our country no less than S.P. Korolev, or A.S. Popov. It is possible that Kotelnikov is known outside of Russia even more than in the Fatherland.

Such glory has its own explanation. Kotel'nikov's theorem became the theoretical basis for all modern digital equipment used for communication. It is based on the principle of digitizing any signal or image. It creates the conditions for calculating multi-channel communication for one signal pair. Thanks to Kotel'nikov's theorem, it is possible to restore a noisy and "ragged" signal, to create noise-proof equipment. The encryption technique is also largely based on this theorem. It is possible that she will find other useful applications.

The author of theoretical labor, so significant for the development of radio engineering, was born in 1908 in Kazan. His father was a university professor, a well-known mechanic and mathematician Alexander Petrovich Kotelnikov, therefore, if we talk about genes, then Viktor Alexandrovich's science was "in the blood." After graduating from the Moscow Power Engineering Institute, the young man entered postgraduate study. That's when he got interested in the subject of the bandwidth of the communication line. Speaking more simply, he was curious how many people on each side can talk on the same telephone wire (without compromising mutual understanding and intelligibility of speech).

Assumptions about this have already been, and even, as it turned out, quite accurate. For example, Nyquist in 1928 suggested that if the signal rupture gap is equal to half the period of the maximum frequency, then it can be restored.

D = 1 / 2F,

Where:

D - admissible time of signal disappearance;

F- maximum frequency contained in the signal spectrum.

Nyquist reasonably suggested that a telephone audio signal having a frequency range of 3 kHz can be gated with a frequency of 6,000 times per second without losing any useful information.

Such bold and intuitive assumptions give modern historians of science from Western countries to replace the name of the author in the notion of "Kotelnikov's theorem". Nyquist's theorem is the name of Kotelnikov's theorem in many European and American textbooks. However, it is one thing to make an assumption, even if it is very bold and is confirmed by practice, and another thing is to prove it. The theorem of themes differs from an axiom or a hypothesis, which by definition needs proof.

We already have to pay tribute to our Western friends. Kotel'nikov's priority in the proof of the "Nyquist theorem" is unchallenged.

Without a sufficiently high level of knowledge of higher mathematics, it is impossible to understand how elegantly formulated Kotel'nikov's theorem is. The proof is based on the approximation of the waveform, which is given by the Kotel'nikov series (on its "drawing" on short pulses).

This theoretical justification of the minimum signal pulse duration allows us to use mobile communication today, as well as to digitize and process images, music and many other types of content.