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Instruments and Systems: Monitoring, Control, and Diagnostics

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Probability Density or Lyapunov Characteristic Function is a Leader in Solving Problems in Statistical Decision Theory
Yu.M. VESHKURTSEV, D.A. TITOV

Discovered at the end of the 20th century, the effect of stochastic resonance in nonlinear systems is now becoming widely known, the
number of publications describing it is growing. Among the publications there are works in which, without mentioning a new effect, the
hypothesis of the presence of some kind of resonance was expressed during the study of the system. The purpose of this work is to confi rm the
validity of the hypotheses about resonance, which made it possible to expand the understanding of physical processes in a nonlinear system
and eliminate doubts about the reliability of the high results obtained by the authors earlier. It is established that the Lyapunov characteristic
function and its accompanying stochastic resonance effect can be used to construct nonlinear signal detection systems against a background
of noise. A special property of a digital fi lter based on the Lyapunov characteristic function is manifested when fi ltering an additive mixture
of signal and noise, as well as in cases when this digital fi lter is used as part of other devices, for example, as part of a signal detection unit
against a background of noise.
Keywords: stochastic resonance, Lyapunov characteristic function, digital fi lter, quasi-deterministic signal, signal detection.


DOI: 10.25791/pribor.8.2024.1520

Pp. 42-46.

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