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Signals and Processes Sampling under the Theorem of Kotelnikov Subject to the Maximum Values of their Derivatives on Time


B. G. Majorov

Theorems of Kotelnikov and the maximum deviation criterion of Temnikov are considered in the article. They are intended for definition of the maximum permissible time interval sampling. Theorem of Kotelnikov' feature is a theoretical necessity of signal restoration by trigonometrical series of Kotelnikov. Practically it is connected with technical difficulties; therefore they apply restoration by linear approximation or step approximation in the information technology. Such unreasonable combination leads to unreasonable definition of interval range of time sampling. It also leads to opinion that the theorem of Kotelnikov is intended for application in radio engineering and the maximum deviation criterion are applied in information-measuring technology. It is necessary to solve the contradiction. It is offered to use mathematical model of signal behavior between the beginning and the end of time interval of sampling. It’s termed a trajectory of the maximum deviation (ТMD) in the form of sinusoidal function half wave. Nine physical and mathematical Requirements to ТMD are put forward. They allow providing the maximum permissible value of time interval sampling. The expressions are received that connect TMD characteristics among themselves: the maximum spectrum frequency of sampling signal, an absolute error of approximation, the maximum: speed, acceleration, sharpness and other derivatives on time from the signal. These expressions are termed as signal characteristics coordination criterion. Expressions (in a general view) for theorem of Kotelnikov specification are received. They are similar to expressions of the maximum deviation criterion (contain necessary quantity of the maximum values of signal derivatives on time). The received scientific results allow using the theorem of Kotelnikov as equal to the maximum deviation criterion in the information technology for well-founded definition of time fixed-rate sampling interval at signal linear and step approximation on its measured values.
May 29, 2020

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