Properties of Harmonic and Composite Half-Waves, Determination of the Uniform Time Sampling Interval of Digital Signal Processors

Abstract

When building autonomous real-time systems (RTS), it is necessary to solve the problem of optimal multitasking loading of a number of parallel functioning digital signal processors. One of the reserves for achieving the desired result is the implementation of samples from the sensor signals of information about the magnitude of the signal most rarely in time. In this case, it is necessary to provide a linear or stepwise approximation of the signal by samples with an acceptable reconstruction error. One of the system tasks of these processors is filtering signals or limiting the spectrum to the cutoff frequency. A distinctive feature of the approach proposed in the article is the fulfillment of the condition: if the measurement of this frequency is difficult (for example, in the electromechanical means of the RTS), then for such signals it is proposed to match the maximum values of the harmonic half-wave parameters: approximation error, speed and acceleration. The study opens up the prospect of applying new approaches to sampling the time of signals in the amplitude-time domain and determining the equivalent cutoff frequency of the signal spectrum for such signals. In this article, the dependences of the value of the unit of system time for input-output of data on the degree of agreement between the maximum values of the signal parameters are obtained. A mathematical model of the extreme behavior of a signal between two adjacent samples is given in the form of a harmonic half-wave. The study is also extended to convex composite harmonic functions, according to which the signal can deviate from the results of a linear or stepwise approximation of the signal for these samples. The comparison of the models by the value of the relative time sampling intervals, depending on the degree of matching of the maximum parameters of the harmonic half-wave, is carried out. When comparing, in addition to these maximum parameters, the relationship of the maximum signal speed with the error of approximating the samples by steps and the relationship of the maximum acceleration of the signal with the maximum error of the linear approximation was taken into account. The results make it possible to determine the duration of the intervals of uniform sampling of the signal time based on the results of the inspection of the control object, substantiate a significant increase in the sampling interval of time or a similar increase in the number of tasks to be solved per unit of system time.