Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2023. №6
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DOI: https://doi.org/10.30898/1684-1719.2023.6.7

 

STOCHASTIC RESONANCE IN A DIGITAL FILTER

BASED ON THE LYAPUNOV CHARACTERISTIC FUNCTION

 

Yu. M. Veshkurtsev 1, D. A. Titov 2, A. S. Tabakova 2

 

1 Institute of Radioelectronics, service and diagnostics

644077, Russia, Omsk, pr. Mira, 57

2 Omsk State Technical University

644050, Russia, Omsk, pr. Mira, 11

 

The paper was received March 9, 2023.

 

Abstract. The phenomenon of stochastic resonance in a radio engineering system, similar in structure to a digital filter based on the Lyapunov characteristic function, is considered. The physical meaning of stochastic resonance is revealed and the hypothesis of its existence in a radio engineering system is confirmed. In the process of modeling a digital filter, the effect and indicators of stochastic resonance were established when filtering an additive mixture of a quasi-deterministic signal and "white" noise. An improvement in the signal-to-noise ratio at the output of the system by a factor of 634 compared to the signal-to-noise ratio at its input was obtained when filtering an additive mixture of a centered quasi-deterministic signal and "white" noise. When filtering an additive mixture of a non-centered quasi-deterministic signal and "white" noise, the indicated stochastic resonance index is lower and amounts to 174 times. It is proposed to consolidate the phenomenon of stochastic resonance for a radio engineering system with such new definitions as the band and bandwidth of the resonance. Noise immunity increases noticeably in the resonance band in a digital modem with a circuit similar to a digital filter based on the Lyapunov characteristic function. The purpose of this work is to present a hypothesis with a future perspective, revealing the possibility of using a new effect in the construction of radio engineering systems.

Key words: stochastic resonance, Lyapunov characteristic function, digital filter, quasi-deterministic signal, digital filter noise immunity.

Corresponding author: Titov Dmitry Anatolievich, dtitov2@yandex.ru

References

1.  Anishchenko V.S., Neiman A.B., Moss F., Schimansky-Geier L. Stochastic resonance: noise enhanced order. Uspekhi fizicheskikh nauk [Advances in Physical Sciences]. 1999. V.169. №1. P.7-38. https://doi.org/10.3367/UFNr.0169.199901c.0007 (In Russian)

2. Klimontovich, Yu.L. What are stochastic filtration and stochastic resonance? Uspekhi fizicheskikh nauk [Advances in Physical Sciences]. 1999. V.169. №1. P.39-47. https://doi.org/10.3367/UFNr.0169.199901d.0039 (In Russian)

3. Veshkurtsev Yu.M., Veshkurtsev N.D., Titov D.A. Filtering in the space of probability additive mixture of eccentric quasideterminants signal-to-noise. Pribory i sistemy. Upravlenie, kontrol', diagnostika [Instruments and Systems: Monitoring, Control, and Diagnostics]. 2018. №3. P.18-23. (In Russian)

4. Veshkurtsev Yu.M., Titov D.A. Determination of the sampling rate of a random process. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2022. №6. https://doi.org/10.30898/1684-1719.2022.6.2 (In Russian)

5. Veshkurtsev Yu.M. Prikladnoi analiz kharakteristicheskoi funktsii sluchainykh protsessov [Applied analysis of the characteristic function of random processes]. Moskow, Radio i svyaz' Publ. 2003. 204 p. (In Russian)

6. Imanbayeva A.K., Tokmyrzaeva Zh.B. The signal-to-noise ratio in bistable stochastic resonators. Vestnik KaZNU. Seriya: fizicheskaya [Recent Contributions to Physics]. №2(61). 2017. P.100-107. (In Russian)

7. Veshkurtsev Yu.M. Osnovy teorii postroeniya modemov novogo pokoleniya [Fundamentals of the theory of building modems of a new generation]. Novosibirsk, SibAK Publ. 2020. 184p. (In Russian)

8. Patent RF №2626332. Veshkurtsev Yu.M., Veshkurtsev N.D., Algazin E.I., Sposob demodulyatsii signala [Method of Demodulation of Signal]. Application Date: 27.07.2016. Publication Date: 26.07.2017. 5p. URL: https://i.moscow/patents/ru2626332c1_20170726 (In Russian)

9. Veshkurtsev Yu.M. Generalization of the theory of a new method of modulation and demodulation of a random signal. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2022. №12. https://doi.org/10.30898/1684-1719.2022.12.8 (In Russian)

For citation:

Veshkurtsev Yu.M., Titov D.A., Tabakova A.S. Stochastic resonance in a digital filter based on the Lyapunov characteristic function. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2023. №6. https://doi.org/10.30898/1684-1719.2023.6.7 (In Russian)