Research of methods of transformation of chaotic signals in radio engineering systems

Abstract

Results of mathematical modelling of the phenomena of a stochastic resonance and stochastic filtration are submitted at influence on two-state output system — the Shmitt trigger of a mix of a signal and noise. Physical studies of stochastic resonance usually deal with real or numerical experiments. Theoretical approaches face a number of difficulties. To describe the diffusion system, one needs to solve the corresponding Fokker-Planck equation. In case of one-dimensional diffusion and white noise, this equation is two-dimensional due to the time-dependence of the potential. Despite the time-periodicity of the potential, in general, it is difficult to study the solutions of the Fokker-Planck equation as functions of the noise intensity. The Schmitt trigger provides another interpretation to the phenomenon of stochastic resonance. A system displaying stochastic resonance can be considered as a type of a random amplifier. The weak periodic signal, which cannot be detected in the absence of noise, can be successfully recovered if the system is appropriately tuned. Stochastic resonance provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. As signals, harmonious or chaotic fluctuation were used, which can be considered (examined) as information. The effect of a stochastic filtration is observed for chaotic fluctuation too.