Models of Composite Harmonic Half-Waves and the Relationship of Time Sampling with the Entropy of Time Parameters of Signals

Abstract

The problem of finding the absolute error of stepwise and linear interpolation of the control signal from uniform samples from it using models of composite harmonic half-waves is solved. Previously, during the inspection of the control object, the maximum values of the signal parameters and half-waves are determined: speed, acceleration and sharpness, there are no spectrum parameters. To determine the values of the intervals of uniform sampling of time, two groups of models of "harmonic half-waves" are considered. The first group of models is described by harmonic time functions whose parameters are consistent. The second group of models is described by composite harmonic functions of time, thereby the time parameters of the signals are consistent. It is proved that with an increase in the entropy of the maximum values of the signal parameters, the value of the time sampling interval increases without increasing the interpolation error. Thus, the entropy value of the signal parameters serves as an indicator of their inconsistency. The results of modeling and graphs obtained in the environment of the mathematical package are presented. The results are intended to optimize the loading of input tasks and primary information processing of processors in robust real-time automation systems, for example, used to control high-speed trains when braking in sliding or skidding mode.