FUNCTIONAL DIFFERENTIAL AND DIFFERENTIAL MODELS OF SYSTEMS WITH ACOUSTICAL FEEDBACK

The paper reports the investigations of the functional differential and differential models of system with acoustic feedback. The aim of the work is a for-mation, analysis and identification of linear and nonlinear functional differential models of echo, reverberation and acoustic feedback; the analysis of model sensitivity, the analysis of stability of telecommunication systems with the acoustic feedback. There is presented a mechanism of an acoustic feedback mechanism formation. At the analysis of sound propagation in closed rooms with the use of the geometric acoustics method there is obtained a nucleus equation which is approximated by nonnegative functions taking into account a model of reverberation and a model of multiple reflections. The considered procedure of echo formation and reverberation is an element of the feedback model common for warning systems and technological communication. There is investigated a model of acoustic systems with delayed feedback. A diagram of the kernel of a functional differential equation describing a system with feedback is shown. The models of systems with acoustic feedback presented in this work ensure the approximation to reality at that, an account of possibilities of the emergence in channels of non-linear distortion sound propagation are considered to be the next problem.