ANALYTICAL DESCRIPTION OF NONLINEAR OBJECT WHEN MODELING SYSTEMS OF INFORMATION TRANSFER

Abstract

The paper proposes an analytical tool in the form of a point interpolation method that allows describing transition processes in nonlinear objects taking into account the shape of the signals and the minimum number of discrete samples (minimizes the number of terms in the general expression describing the behavior of the signal in its domain). In addition, the proposed method of describing the signals provides their compression, which is important in the transmission of signals and their storage. The gain in the sampling interval, compared with polynomial approximation, is shown when providing a given error of signal reproduction by discrete values. A mathematical apparatus for determining the error of the proposed interpolation is developed. The error of the proposed interpolation is compared with the known polynomial ones. A classification of signals at the output of the simulated nonlinear object is proposed and a mathematical apparatus for calculating the error of modeling and reproduction of each type of signals in this classification is developed. The proposed method allows describing analytically the response of the investigated nonlinear object to the produced effect on the numerical values of the ordinates of this response in modeling of information transmission systems. This ensures acceptable accuracy by increasing the sampling interval and reducing the number of discrete samples. The proposed method of analytical description of signal can be used not only in modeling nonlinear object, but also in signal recovery from discrete samples in the case where the signal is stored as discrete samples, as well as when reproducing the signal by an information receiver in the case, when in the form of discrete counts, a signal is transmitted over the communication channel.