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Identification of the acoustic signal models of audio exchange systems under conditions of interference and acoustic feedback
V.A. Ermolaev 1, Y.A. Kropotov 1, A.Y. Proskuryakov 1

1 Murom Institute (branch) of Vladimir State University, Murom, Russia

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DOI: 10.18287/2412-6179-CO-655

Pages: 454-465.

Full text of article: Russian language.

Abstract:
In this paper questions of building models of information exchange systems with discrete and distributed delay and with delayed feedback by methods of the theory of linear functional differential equations are investigated. When solving the said equations, it is necessary to consider restrictions caused by the uncertainties in the system under modeling, such as the absence of the exact data on the parameters of the model elements, their natural spread and temporal variations, thus requiring the solution of an identification problem. The models with continuous aftereffect introduced in this work take a fuller account of reflected signal characteristics in closed space, which increases the reliability of modeling results in comparison with the known differential models. At the same time, there is a problem of finding functions that characterize the value distribution of the echo delay. In this work, these functions (kernels) are approximated by a number of exponents, which simplifies the equations and allows the assumption that the aftereffect can be concentrated on both final and infinite intervals. The echo components caused by closed-space resonances are modeled by transfer functions of the corresponding linear links. In numerical modeling, a single-channel model represented by a second-order resonance link and a pulse-shaped kernel described by a sum of two decreasing exponents is considered. The analysis of stability of the models of systems with delayed feedback is conducted by a frequency method. In the paper an approach to estimating the correlation and spectral functions of signals and noise components based on the parametric representation of the latter is considered. The paper also considers issues relating to the practical significance of the research results.

Keywords:
functional differential equations, model of systems with acoustic feedback, echo signals, voice communication, sound, acoustic signals, approximation of distribution functions, correlation function, adaptive filter.

Citation:
Ermolaev VA, Kropotov YA, Proskuryakov AY. Identification of the acoustic signal models of audio exchange systems under interference and acoustic feedback conditions. Computer Optics 2020; 44(3): 454-465. DOI: 10.18287/2412-6179-CO-655.

References:
  1. Guretsky H. Analysis and synthesis of control systems with delay [In Russian]. Moscow: "Mashinostroenie" Publisher; 1974.
  2. Rezvan V. Absolute stability of automatic systems with delay [In Russian]. Moscow: "Nauka" Publisher; 1983.
  3. Tsykunov AM. Robust synchronization of a network of objects with distributed delay. Autom Remote Control 2015; 6(11): 1952-1965.
  4. Tsykunov AM. Robust control of nonlinear objects with the distributed delay single class [In Russian]. Probl Upr 2016; 3: 16-22.
  5. Tchangani AP, Dambrine M, Richard JP. Robust stabilization of delay systems with discrete or distributed delayed control. Proc 37th IEEE Conference on Decision & Control 1998: 4051-4056.
  6. Khartovskii VE. Controllability and identifiability of multi-delay dynamic systems. Autom Remote Control 2005; 66(9): 1396-1408.
  7. Khartovskii VE. Problems of identification and control of the output for time lag systems. Autom Remote Control 2011; 72(5): 914-928.
  8. Erneux T. Applied delay differential equations. New York, Springer, 2009.
  9. O'Brien D. Optical communications through free space. In Book: Dakin JP, Brown RGW, eds. Handbook of optoelectronics. Applications of optoelectronics: Vol 3. Ch 31. Broken, NY: CRC Press; 2018: 413-427.
  10. Mbe JHT, Talla AF, Chengui GRG, Coillet A, Larger L, Yanne PW, Chembo YK. Mixed-mode oscillations in slow-fast delayed optoelectronic systems. Phys Rev E 2015; 91: 012902.
  11. Marquez BA, Larger L, Brunner D, Chembo YK, Jacquot M. Interaction between Lienard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback. Phys Rev E 2016; 94: 062208.
  12. Illing L, Hoth G, Shareshian L, May C. Scaling behavior of oscillations arising in delay-coupled optoelectronic oscillators. Phys Rev E 2011; 83: 026107.
  13. Martines-Llinas J, Colet P, Erneux T. Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems. Phys Rev E 2014; 89: 042908.
  14. Lenstra D. Relaxation oscillation dynamics in semiconductor diode lasers with optical feedback. IEEE Photon Tech-nol Lett 2013; 25(6): 591-593.
  15. Peil M, Jacquot M, Chembo YK, Larger L, Erneux T. Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators. Phys Rev E 2009; 79: 026208.
  16. Loiko NA, Samson AM. Nonlinear dynamics of laser systems with a delay [In Russian]. Kvantovaya Elektronika 1994; 21(8): 713-728.
  17. Kouomou YC, Colet P, Larger L, Gastaud N. Chaotic breathers in delayed electro-optical systems. Phys Rev Lett 2005; 95: 203903.
  18. Belousov PP, Belousov PYa, Dubnishchev YuN. Laser Doppler visualisation of the velocity field [In Russian]. Kvantovaya Elektronika 1999; 29(2): 157-162.
  19. Dubnishcheva YuN, Chuguib YuV, Kompenhansc J. Laser Doppler visualisation of the velocity field by excluding the influence of multiparticle scatterin [In Russian]. Kvantovaya Elektronika 2009; 39(10): 962-966.
  20. Glyzin SD, Kolesov AYu, Rozov NKh. Self-excited relaxation oscillations in networks of impulse neurons. Russian Mathematical Surveys 2015; 70(3): 383-452.
  21. Glyzin SD, Kolesov AYu, Rozov NH. The theory of non-classical relaxation oscillations in singularly perturbed delay systems. Sbornik: Mathematics 2014; 205(6): 781-842.
  22. Myshkis AD. Linear differential equations with lagged argument [In Russian]. Moscow, Leningrad: "Gostehizdat" Publisher, 1951.
  23. Kolmanovskii V, Myshkis A. Introduction to the theory and applications of functional differential equations. Dordrecht, Boston, London: Kluwer Academic Publishers; 1999.
  24. Krasovsky NN. Some problems of the theory of motion stability [In Russian]. Moscow: "Fizmatlit" Publisher; 1959.
  25. Bellman R, Cooke KL. Differential-difference equations. New York, London: Academic Press; 1963.
  26. Elsholtz LE. Introduction to the theory of differential equations with a divergent argument [In Russian]. Moscow: "Nauka" Publisher, 1971.
  27. Hale J. Theory of functional differential equations. New York, Heidelberg, Berlin: Springer-Verlag; 1977.
  28. Pinney E. Ordinary difference-differential equations. University of California Press; 1958.
  29. Hansler E, Schmidt G, eds. Topics in acoustic echo and noise control: Selected methods for the cancelation of acoustic echoes, the reduction of background noise, and speech processing. Berlin, Heidelberg: Springer; 2006.
  30. Kuttruff H. Room acoustics. London, New York: Spon Press; 2009.
  31. Kanev NG. Reverberation in a trapezoidal room [In Russian]. Akusticheskij Zhurnal 2013; 59(5): 607-612.
  32. Kanev NG. About the maximum sound absorption by a Helmholtz resonator in a room at low frequencies [In Russian]. Acusticheskij Zhurnal 2018; 64(6): 752-755.
  33. Bobrovnitskiy YuI, Morozov KD, Tomilina TM. Impedance approach to the design of the effective absorbers of the vibrational energy [In Russian]. Akusticheskij Zhurnal 2017; 63(2): 137-144.
  34. Bobrovnitskii YuI. Models and general wave properties of two-dimensional acoustic metamaterials and media [In Russian]. Akusticheskij Zhurnal 2015; 61(3): 283-294.
  35. Bobrovnitskii YuI. Hysteretic damping and causality [In Russian]. Akusticheskij Zhurnal 2013; 59(3): 291-295.
  36. Akhunov KhG, Kravtsov YuA. Conditions for the coherent summation of waves in the backscattering of sound in multipath-transmission channels [In Russian]. Akusticheskij Zhurnal 1984; 30(2): 145-148.
  37. Min Q, He W-Q, Wang Q-B, Tian J-J, Zhang Q-Y. Study of stepped acoustic resonator with transfer matrix method. Acoustical Physics 2014; 60(4): 492-498.
  38. Sysoev IV, Prokhorov MD, Ponomarenko VI, Bezruchko BP. Parameter determination of the elements and architecture of the bonds in the ensembles of the connected systems with time lag [In Russian]. Zhurnal Tekhnicheskoi Fiziki 2014; 84(10): 16-26.
  39. Sysoev IV, Ponomarenko VI, Prokhorov MD. Reconstruction of the oscillator ensembles with nonlinear delayed connections [In Russian]. Pisma v Zhurnal Tekhnicheskoi Fiziki 2018; 44(22): 57-64.
  40. Sysoev IV, Ponomarenko VI, Prokhorov MD. Identification of the interaction structure and the element eigenfre-quency parameters in the networks consisting of the delay systems [In Russian]. Pisma v Zhurnal Tekhnicheskoi Fiziki 2016; 42(1): 95-102.
  41. Ponomarenko VI, Kulminskiy DD, Karavaev AS, Prokhorov MD. Collective dynamics of the identical bistable auto-generator with a delay connected through the common field [In Russian]. Pisma v Zhurnal Tekhnicheskoi Fiziki 2017; 43(6): 64-71.
  42. Ermolaev VA, Kropotov YuA. Methods of local analysis and smoothing of time series and discrete signals [In Russian]. Matem Mod 2017; 29(2): 119-132.
  43. Ermolaev VA, Karasev OE, Kropotov YA. Interpolation filtering method in the tasks of processing speech signals in the time domain [In Russian]. Herald of computer and information technologies 2008; 7: 12-17.
  44. Ermolaev VA, Kropotov YA, Eremenko VT, Karasev OE. Identification of discrete linear systems models with variable, slowly changing parameters [In Russian]. Radiotekhnika i Elektronika 2010; 55(1): 57-62.

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