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Mathematical Models of Telecommunication Systems with Acoustic Feedback

In this paper, mathematical models of telecommunication systems with acoustic feedback are investigated, stability issues are investigated on the basis of the construction of functional differential and differential-difference models. The aim of the work is the construction, analysis and identification of linear and nonlinear functional differential models of echo, reverberation and acoustic feedback; sensitivity analysis of models, stability analysis of telecommunication systems with acoustic feedback. A mechanism for the formation of acoustic feedback is presented. When analyzing the propagation of sound in closed rooms using the method of geometric acoustics, an equation of the nucleus was obtained, which is approximated by non-negative functions taking into account the reverberation model and the multiple reflection model. The considered scheme for the formation of echo and reverberation is an element of the acoustic feedback model, characteristic of alert systems and technological communication. A model of acoustic systems with delayed feedback was investigated. A graph of the kernel of a functional differential equation describing a system with feedback is given. The models of systems with acoustic feedback presented in the paper provide an approximation to reality, while taking into account the possibilities of occurrence in the propagation paths of sound of nonlinear distortion is considered as the next task.