Nyquist theorem - the theoretical basis of modern information technologies

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Few achievements so strongly influenced the development of modern communication and information technologies, as the Nyquist theorem.By and large, this scientist glorified our country no less than SPQueens, or ASPopov.Perhaps Kotelnikov known outside Russia, even more than in the Fatherland.

Such fame has its explanation.Nyquist 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 multichannel audio communication signal pair.Due to Nyquist theorem, you can restore noisy and "ragged" signal, creating immunity of.Cryptographic equipment is also largely based on this theorem.Maybe she can find other useful applications.

author of such significance for the development of radio theoretical work was born in 1908 in Kazan.His father was a university professor, a famous engineer and mathematician Alexander P. Kotelnikov, so if we talk about genes, science Victor Alexandrovich was "in the blood".After graduating from the Moscow Energy Institute, the young man went to graduate school.Here then are interested in its theme bandwidth link.Simply put, he wondered how many people from each side can speak the same telephone wire (without prejudice to mutual understanding and speech).

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

D = 1 / 2F,


D - allowed time signal disappears;

F- maximum frequency contained in the signal spectrum.

Nyquist reasonable to assume that the telephone audio signal having a frequency range of 3 kHz, it is possible to gate a frequency of 6,000 times per second with no loss of useful information.

Such bold and intuitive assumptions give modern historians of science from Western countries to replace the notion of "Nyquist theorem" the author's name.Nyquist theorem - that's the name of Nyquist theorem in many European and American textbooks.However, it is one thing to suggest, even if it is very bold, and confirmed by the practice, and another thing - to prove it.Theorem differs from axioms or hypotheses that by definition requires proof.

you already have to pay tribute to our Western friends.Priority Nyquist in the proof of "Nyquist Theorem" no one disputes.

Without a sufficiently high level of knowledge of higher mathematics is impossible to understand how delicately worded Nyquist theorem.The proof is based on an approximation of the waveform, which sets the number of Nyquist (his "plotting" by short pulses).

Such a theoretical basis the minimum duration of the pulse signal gives us the opportunity now to use mobile phones as well as digitized and processed images, music, and many other types of content.