Non-Linear Filtering of Chaotic Signal in the Presence of Noise
DOI:
https://doi.org/10.14529/ctcr180314Keywords:
stochastic resonance, chaotic dynamics, bistable system, Schmitt trigger, nonlinear dynamical system, optimal noise level, nonlinear filter, spectral analysis of the investigated oscillationsAbstract
The creation of radio engineering systems based on the effects of stochastic and chaotic dynamic is a promising direction. The task of developing such systems must be oriented toward using the results of theoretical studies of processes in nonlinear radiophysical systems. The subject of this study is the nonlinear filtering of a mixture of chaotic oscillations and noise based on the stochastic resonance effect occurring in a bistable system with the aim of isolating the information chaotic signal. Usually, noise is considered to be “white”, and the signal is narrow-banded. As a bistable system, a Schmitt trigger can be used. For narrowband signals, the stochastic resonance effect has been studied in sufficient detail theoretically, for broadband information signals, applied research is insufficient. The stochastic resonance effect is a phenomenon in which the response of a nonlinear system to a weak external signal amplifies with increasing noise intensity to some optimal value. In the study of radio engineering systems, chaotic oscillations can be used as information systems. Theoretical basis for research of information processing systems in radio engineering systems using chaotic signals is research in the field of nonlinear radiophysics. Of particular importance in this case is the selection of solutions at the model level, in particular, based on the results of circuit simulation of practically realized devices on the existing element base.
References
Lorenz E.N. Deterministic Nonperiodic flow. J. Atmos. Sci., 1963, vol. 20, рр. 130–133.
Rossler O.E. An Equation for Continuous Chaos. Phys. Lett. A., 1976, vol. 57A, 5, рр. 397–398.
Matsumoto T. A Chaotic Attractor from Chua’s Circuit. IEEE Trans. Circuits Syst., 1984, vol. CAS-31, pp.1055–1058.
Zlong G.-Q., Ayrom F. Experimental Confirmation of Chaos from Chua’s Circuit. Int. J. Circuit Theory Appl., 1985, vol. 13, pp. 93–98.
Carcasses J., Mira C., Bosch M., Simo C., Tatjer J.C. “Crossroad Area – Spring Area” Transition (I) Parameter Plane Representation. International Journal of Bifurcation and Chaos, 1991, vol. 1, no. 1, pp. 183–196.
Carcasses J., Mira C., Bosch M., Simo C., Tatjer J.C. “Crossroad Area – Spring Area” Transition (II). Foliated Parametric Representation. International Journal of Bifurcation and Chaos, 1991, vol. 1, no. 2, pp. 339–348.
Elhadj Z., Sprott J.C. A Minimal 2-Dquadratic Map with Quasi-periodic Route to Chaos. International Journal of Bifurcation and Chaos, 2008, no. 5, pp. 1567–1577. DOI: 10.1142/S021812740802118X
Froeschlé С., Lega E., Guzzo M. Analysis of the Chaotic Behaviour of Orbits Diffusing along the Arnold Web. Celestial Mechanics and Dynamical Astronomy, 2006, vol. 95, iss. 1-4, pp. 141–153. DOI: 10.1007/s10569-006-9004-2
Guzzo M., Lega E., Froeschlé С. First Numerical Evidence of Global Arnold Diffusion in QuasiIntegrable Systems. Discrete and Continuous DynamicalSystems – Series B, 2005, vol. 5, no. 3, pp. 687–698. DOI: 10.3934/dcdsb.2005.5.687
Richter H. The Generalized Henon Maps: Examples for Higher-Dimensional Chaos. International Journal of Bifurcation and Chaos, 2002, vol. 12, no. 6, pp. 1371–1384. DOI: 10.1142/s0218127402005121
Richter H. On a Family of Maps with Multiple Chaotic Attractors. Chaos, Solitons & Fractals, vol. 36, no. 3, 2008, pp. 559–571. DOI: 10.1016/j.chaos.2007.07.089
Elhadj Z., Sprott J.C. Classification of Three-Dimensional Quadratic Diffeomorphisms with Constant Jacobian. Frontiers of Physics in China, 2009, vol. 4, no. 1, pp. 111–121. DOI: 10.1007/s11467-009-0005-y
Kaneko K. Doubling of Torus. Progress of Theoretical Physics, 1983, vol. 69, no. 6, pp. 1806–1810. DOI: 10.1143/ptp.69.1806
Stagliano J., Wersingera Jr., Slaminkab E. Doubling Bifurcations of Destroyed T2 Tori. Physica D, 1996, vol. 92, no. 3-4, pp. 164–177. DOI: 10.1016/0167-2789(95)00273-1
Beck C., Schlogl F. Thermodynamics of Chaotic Systems. Cambridge. Cambridge Univ. Press, 1993. 461 p.
Kazimirov A.N., Telezhkin V.F. [Generator of Superbroadband Fractal Signal for Radio Engineering Communication Systems]. Doklady 16-y Mezhdunarodnoy konferentsii “Tsifrovaya obrabotka signalov i ikh primenenie” (DSPA-2014) [Reports of 16-th International Conference “Digital Processing of Signals and its Application”] (DSPA-2014). Vol. 1. Moscow, 2013, pp. 401–404. (in Russ.)
Dombrovsky A.N., Reshetnyak S.A. [Stochastic Resonance and Filtration of Signals in Nonlinear System of the Second Order]. Radio Engineering, 2007, no. 9. pp. 19–25. (in Russ.)
