Using of the Noise as Signal Enhancement Factor in Nonlinear System
Keywords:
stochastic resonance, nonlinear equation, signal to noise ratioAbstract
The stochastic resonance (SR) effect is considered, which makes it possible to stand out a weak signal from an additive mixture with noise. The strongest effect is shown to occur at certain well-defined, optimal noise intensity. The term SR was introduced during studies of the oscillator bistable model, which was proposed to analyze the glacial periods repeatability on Earth. The model described the particle motion in a symmetric one-dimensional bistable potential under the action of periodic force under strong friction conditions. In subsequent studies, the effect of stochastic resonance was found in many systems and not only physical. The known results of the approximate solution of the SR equation are considered. This equation is solved by two methods: the method of linear response and the theory of two states. In these studies, analytical expressions for the gain and signal-to-noise ratio are obtained using a number of approximations: restrictions on the signal amplitude when the response is linear, and restrictions on the frequency of the signal. In addition, when comparing the two methods considered, their use to calculate the noise variance at which the SR effect occurs, is shown to lead to different results. This necessitates further research to develop an analytical apparatus and verify its reliability by numerical calculations. The results of numerical simulation of the stochastic resonator response on the influence of an additive mixture harmonic signal and white Gaussian noise are presented. The enrichment of the output signal with harmonics and effective noise suppression are shown. The signal-to-noise ratio at the output numerical calculation results dependence on the input noise variance are presented. As it seen the dependence is complex, where you can select a local maximum at a point that does not correspond to the known values of the input noise variance at different approximate solutions of the equation SR. It is shown that the stochastic resonator acts as a low-pass filter, while providing a significant reduction in the output noise level.
References
Перелік посилань
Ширман Я. Д. Радиоэлектронные системы: основы построения и теория. (Справочник) / Я. Д. Ширман, Ю. И. Лосев, Д. И. Леховицкий и др. // М.: ЗАО «МАКВИС». — 1998. — 828 с.
Ширман Я. Д. Радиоэлектронные системы: основы построения и теория. (Справочник). Изд. 2-е перераб. и доп. / Я. Д. Ширман, С. Т. Багдасарян, Д. И. Леховицкий и др. // М.: «Радиотехника»/ — 2007. — 512 с.
Sklar B. Digital communication. Fundamental and Application. Second Edition // University of California, Los Angeles. — 2001. — 1104 p.
Kartashov V., et al. Use of Acoustic Signature for Detection, Recognition and Direction Finding of Small Unmanned Aerial Vehicles // 2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET). — 2020. — P. 1-4.
Постанова КМУ від 13 черня 2018 р. № 509 «Про внесення зміни до Плану використання радіочастотного ресурсу України».
Jerome, Moses M., Ramakalyan Ayyagari. A Brief Survey of Stochastic Resonance and Its Application to Control // IFAC Proceedings Volumes. — 2014. — Vol. 47, Iss. 1. — P. 313-320. doi:10.3182/20140313-3-IN-3024.00223.
Gammaitoni L., Hänggi P., Jung P., Marchesoni F. Stochastic Resonance: A remarkable idea that changed our perception of noise // The European Physical Journal B. — 2009. — Vol. 69. — P. 1–3. DOI: 10.1140/epjb/e2009-00163-x.
Budrikis Z. Forty years of stochastic resonance // Nature Reviews Physics. — 2021. — Vol. 3. — P. 771-780. https://doi.org/10.1038/s42254-021-00401-7.
Zhi-hui Lai, Yong-gang Leng. Weak-signal detection based on the stochastic resonance of bistable Duffing oscillator and its application in incipient fault diagnosis // Mechanical Systems and Signal Processing. — 2016. — Vol. 81. — Р. 60–74. https://doi.org/10.1016/j.ymssp.2016.04.002.
Benzi R., Sutera A., Vulpiani A. The mechanism of stochastic resonance // Journal of Physics A: mathematical and general. — 1981. — Vol. 14, Iss. 11. — P. 453. https://iopscience.iop.org/article/10.1088/0305-4470/14/11/006/meta.
Benzi R., Parisi G., Sutera A., Vulpiani A. Stochastic resonance in climatic change // Tellus. — 1982. — Vol. 34, Iss. 1. — P. 10-16 doi:10.3402/tellusa.v34i1.10782.
Anishchenko V. S., Neiman A. B., Moss F., Schimansky-Geier L. Stochastic resonance: noise-enhanced order // Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences. — 1999. — Vol. 42, Iss. 1. — P.7-34. https://iopscience.iop.org/article/10.1070/PU1999v042n01ABEH000444/meta.
Bruno A., Graziani S. Stochastic resonance. Theory and application // Kluwer Academic Publishers. — 2000. — 220 p.
Hänggi P. Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing // Chemphyschem. — 2002. — Mar 12; 3(3). — Р. 90-101. DOI: 10.1002/1439-7641(20020315)3:3<285::AID-CPHC285>3.0.CO;2-A.
Демидович Б. П., Моденов В. П. Дифференциальные уравнения / изд-во Лань. — 2020. — 280 с.
Миддлтон Д. Введение в статистическую теорию связи / Пер. с англ./ Под ред. Б.Р. Левина, М.:«Советское радио», T. 1. — 1961. — 791 с.
Gammaitoni L., Hänggi P., Jung P., Marchesoni F. Stochastic resonance // Reviews of Modern Physics. — 1998. — Vol. 70, No. 1. — P. 223. DOI: 10.1103/RevModPhys.70.223.
Iannelli J. M., Yariv A., Chen T. R., and Zhuang Y. H. Stochastic resonance in a semiconductor distributed feedback laser // Appl. Phys. Lett. — 1983 (1994, 1998). — Vol. 65, — P. 2626. doi:10.1063/1.112838.
Hanggi P. Stochastic processes I: Asymptotic Behaviour and Symmetries // Helv. Phys. Acta. — 1978. — Vol. 51. — P. 183-201. http://doi.org/10.5169/seals-114941.
Толстов Е. Ф., Филончиков В. Д., Школьный Л. А. Радиотехнические цепи и сигналы / Учебник. — М.: ВВИА им. Н. Е. Жуковского. — 1993. — 720 с.
Risken H. Fokker-Planck Equation. Methods of Solution and Applications // Berlin: Springed-Verlad, 1989. 472 p.
Харченко О. И. Выделение синусоидальных составляющих в случайном сигнале // Радиотехника: Всеукр. межвед. науч.-техн. сб. — 2010. — Вып. 160. — С. 247–252. https://openarchive.nure.ua/bitstream/document/15053/1/RT_2010_160_247-252.pdf
Williams D. Understanding, Calculating, and Measuring Total Harmonic Distortion (THD) // All About Circuits.
References
Shirman Y. D., et al. (1998). Radio electronic systems: fundamentals of construction and theory (Reference book) [Radioelektronnye sistemy: osnovy postroeniya i teoriya. (Spravochnik)]. Moscow: ZAO ''MAKVIS'', 828 p. [In Russian].
Shirman Y. D., et al. (2007). Radio electronic systems: construction principles and theory. (Reference book). Ed. 2nd revision. and additional [Radioelektronnye sistemy: osnovy postroeniya i teoriya. (Spravochnik). Izd. 2-e pererab. i dop.]. M.: ''Radiotechnique'', 512 p.
Sklar B. (2001). Digital communication. Fundamental and Application. Second Edition. University of California, Los Angeles, 1104 p.
Kartashov V., et al. (2020). Use of Acoustic Signature for Detection, Recognition and Direction Finding of Small Unmanned Aerial Vehicles. 2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), pp. 1-4, doi:10.1109/TCSET49122.2020.235458.
Resolution of the CMU of June 13, 2018 No. 509 ''On Amendments to the Plan for the Use of Radio Frequency Resources of Ukraine'' [Postanova KMU vid 13 chernia 2018 r. № 509 «Pro vnesennia zminy do Planu vykorystannia radiochastotnoho resursu Ukrainy»]. [In Ukrainian].
Jerome, Moses M., Ramakalyan Ayyagari. (2014). A Brief Survey of Stochastic Resonance and Its Application to Control. IFAC Proceedings Volumes, Vol. 47, Iss. 1, pp. 313-320. doi: 10.3182/20140313-3-IN-3024.00223.
Gammaitoni L., Hänggi P., Jung P., Marchesoni F. (2009). Stochastic Resonance: A remarkable idea that changed our perception of noise. The European Physical Journal B, Vol. 69, pp. 1–3. DOI: 10.1140/epjb/e2009-00163-x.
Budrikis Z. (2021). Forty years of stochastic resonance. Nature Reviews Physics, Vol. 3, pp. 771-780. DOI: 10.1038/s42254-021-00401-7.
Zhi-hui Lai, Yong-gang Leng. (2016). Weak-signal detection based on the stochastic resonance of bistable Duffing oscillator and its application in incipient fault diagnosis. Mechanical Systems and Signal Processing, Vol. 81, Р. 60–74. doi:10.1016/j.ymssp.2016.04.002.
Benzi R., Sutera A., Vulpiani A. (1981). The mechanism of stochastic resonance. Journal of Physics A: mathematical and general, Vol. 14, Iss. 11, p. 453.
Benzi R., Parisi G., Sutera A., Vulpiani A. (1982). Stochastic resonance in climatic change. Tellus, Vol. 34, Iss. 1, pp. 10-16. doi:10.3402/tellusa.v34i1.10782.
Anishchenko V. S., Neiman A. B., Moss F., Schimansky-Geier L. (1999). Stochastic resonance: noise-enhanced order. Physics-Uspekhi, Russian Academy of Sciences, Vol. 42, Iss. 1, pp.7-34.
Bruno A., Graziani S. (2000). Stochastic resonance. Theory and application. Kluwer Academic Publishers, 220 p.
Hänggi P. (2002). Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing. Chemphyschem, Mar 12; 3(3), pp. 285-90. DOI: 10.1002/1439-7641(20020315)3:3<285::AID-CPHC285>3.0.CO;2-A.
Demidovich B. P., Modenov V. P. (2020). Differential equations [Differencial'nye uravneniya]. Publishing house Lan, 280 p. [In Russian].
Middleton D. (1961). An Introduction to Statistical Communication Theory. Transl. from English / Ed. B.R. Levin, M.: ''Soviet radio'', Vol. 1, 791 p. [In Russian].
Gammaitoni L., Hänggi P., Jung P., Marchesoni F. (1998). Stochastic resonance. Reviews of Modern Physics, Vol. 70, No. 1, pp. 223. DOI: 10.1103/RevModPhys.70.223.
Iannelli J. M., Yariv A., Chen T. R., and Zhuang Y. H. (1983 (1994) 1998). Stochastic resonance in a semiconductor distributed feedback laser. Appl. Phys. Lett., Vol. 65, P. 2626. doi:10.1063/1.112838.
Hanggi P. (1978). Stochastic processes I: Asymptotic Behaviour and Symmetries. Helv. Phys. Acta, Vol. 51, pp. 183-201. doi:10.5169/seals-114941.
Tolstov E. F., Filonchikov V. D., Shkolny L. A. (1993). Radio circuits and signals. Textbook [Radiotekhnicheskie cepi i signaly. Uchebnik]. M .: VVIA im. N. E. Zhukovsky, 720 p. [In Russian].
Risken H. (1989). Fokker-Planck Equation. Methods of Solution and Applications. Berlin: Springed-Verlad, 472 p.
Kharchenko O. I. (2010). Isolation of sinusoidal components in a random signal [Vydelenie sinusoidal'nyh sostavlyayushchih v sluchajnom signale]. Radio engineering: Vseukr. interdepartmental sci.-tech. collection, Iss. 160, pp. 247–252. [In Russian].
Williams D. (2017). Understanding, Calculating, and Measuring Total Harmonic Distortion (THD). All About Circuits.
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