Generation of Random Signals in Control Units and Systems Research

The article deals with the problems of generating stationary signals with desired characteristics of the spectral density. For that purpose, the resulting signal is represented as a sum of the following type x(t)sin(ω_smt + φ) + y(t)cos(ω_smt + φ). If we compare this expression with the well-known ones, we can see its distinctive feature: x(t) and y(t) are independent random piecewise-linear processes, they are formed by the signals from random number generators. Spectral density the signal of this type is well approximated by triangles. This way of approximation reflects peaks existence in real spectral density characteristics which becomes apparent in different frequencies. In general it gives a good opportunity to make approximation of initial spectral density by the set of such triangles. Furthermore, unlike the wide spread forming filter approach, in the case under consideration it is possible to avoid transient responses and begin to generate the proper random signal. Applying the traditional approach we make the comparison of spectral density modeling results with the explicit peak using the forming filter and relying on the proposed method. Moreover, we show a possible approximation of the real record of the transport machine vibration acceleration.

References

[1] Ermakov S.M., Mikhaylov G.A. Statisticheskoe modelirovanie [Statistical Modeling]. Moscow, Nauka Publ., 1982. 296 p.

[2] Radchenko Yu.S., Radchenko T.A. Osnovy statisticheskogo modelirovaniya. Ch. 1. Modelirovanie sluchaynykh velichin [Principles of Statistical Modeling. Part 1. Simulation of Random Variables]. Voronezh, Voronezhskiy gos. univ. Publ., 2010. 30 p.

[3] Radchenko Yu.S., Radchenko T.A. Osnovy statisticheskogo modelirovaniya. Ch. 2. Modelirovanie sluchaynykh protsessov [Principles of Statistical Modeling. Part 2. Simulation of Random Processes]. Voronezh, Voronezhskiy gos. univ. Publ., 2010. 50 p.

[4] Peled Abraham, Liu Bede. Digital Signal Processing. Theory, Design, and Implementation. John Wiley & Sons, 1976. 304 p.

[5] Sveshnikov A.A. Prikladnye metody teorii sluchaynykh funktsiy [Applied Methods of the Random Function Theory]. Leningrad, Sudprom Publ., 1961. 252 p.

[6] Levin B.R. Teoreticheskie osnovy statisticheskoy radiotekhniki. Kn. 1 [Statistical Communication Theory]. Moscow, Sov. Radio Publ., 1969. 752 p.

[7] Shakhtarin B.I. Sluchaynye protsessy v radiotekhnike. T. 1. Lineynye preobrazovaniya [Stochastic Processes in Radio Engineering. Vol. 1. Linear Transformations]. Moscow, Goryachaya liniya - Telekom Publ., 2010. 512 p.