Analytical and computational results on recurrent dynamic neural network for signal representation

This paper presents a recurrent dynamic neural network to solve signal representation and processing problems. The neural network is essentially composed of feedback-type connections, and arrays of integrators, linear gains, and nonlinear activation functions. By seeking a minimum energy state, the neural network solves for the sets of representation coefficients required to model a given signal in terms of elementary basis signals. An analytical model of the recurrent neural network was obtained through discretization of the integrator blocks and linearization of the activation function. Continuity of the algorithm when segment boundaries are crossed is made possible by varying the slope of the linearized activation function. The proposed approach results in a closed analytical form of the recurrent neural network solution. The perceived advantages are estimation of robustness, prediction of convergence by examining the eigenvalues of the analytical state matrix, and increase of computational speed. Moreover, unlike classical traditional methods, the approach offers the possibility of handling time-varying signals with uncertainties and considerable noise