D.V. Beylekchi1, V.A. Ermolaev2, A.A. Kolpakov3, A.Yu. Proskuryakov4

1–4 Murom Institute of Vladimir State University (Murom, Russia)
1 desT.087@gmail.com

The task of designing telecommunication systems of acoustic signal exchange with increased noise immunity refers to the solution of signal processing problems, with the purpose of information extraction and interference suppression by methods of adaptive filtering, adaptive interference compensation and system identification, and the tasks are set and solved:

- identification of non-stationary signals and creation of non-stationary models based on the observed data;

- adaptive compensation of acoustic interference and echo-signals.

Methods of adaptive filtering, adaptive interference compensation and system identification, methods of increasing noise immunity of information exchange systems are based on the theory of random processes and mathematical statistics, on the theory of linear and nonlinear systems. One of the problems is to ensure the stability of loudspeaker and public address systems, which are characterized by the presence of acoustic channels of delayed, usually distributed feedback, modeling the phenomena of echo and reverberation. There are two approaches to modeling systems with concentrated and distributed delays in the feedback loop: the approach based on the ideology of multilink models and the approach originating from the theory of variable structure systems, which, respectively, implement the ideas of invariance and sliding modes of optimization and control.

The main goals and objectives of the research are the development of new methods, models and algorithms for processing acoustic signals and control information that improve the efficiency of operational-command, dispatching and information-management telecommunication systems in the presence of external interference. The purpose of this paper is to construct and analyze multi-connection models of systems with concentrated and distributed delay in the feedback loop. The structure of resonant models of reverberation (multiple reflections) is considered: with fixed delays, with variable delays, with distributed, on finite or unlimited intervals, delays. In this case, distributed delays are considered only on a finite interval.

It is shown that in multilink models of resonant modes of multiple reflections, the phenomenon of multiple reflections, defined in acoustics as reverberation, consists in the mixing of distorted copies of the same signal to be extracted. This poses the problem of creating a model that helps to reveal the composition of resonant modes and their parameters. It seems that the realization of such models is possible both in the class of multi-connected and distributed systems, including systems with delay, which always accompanies the phenomenon of multiple reflections at their subsequent superposition. The model of systems with distributed delay described by the modified Hutchinson equation is investigated. It is found that the model is described by a linear differential equation whose solution at each of the specified intervals can be obtained, provided that the function h(τ) and the initial conditions given at the initial interval are known.

In the course of the research it is shown that the graph of the multilink system actually coincides with the graph of interconnections of the artificial neural network. The model of the system with distributed delay described in the paper has been tested using Scilab and can be applied for further developments.

Beylekchi D.V., Ermolaev V.A., Kolpakov A.A., Polyakova T.R., Proskuryakov A.Yu. Problems of analysis and modeling of non-stationary systems and signals with delay in a feedback loop. Science Intensive Technologies. 2024. V. 25. № 1. P. 25−34. DOI: https://doi.org/10.18127/ j19998465-202401-03 (in Russian)

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