ESTUDO E DESENVOLVIMENTO DE UMA FAMILIA DE ALGORITMOS NÃO LINEARES PARA FILTRAGEM ADAPTATIVA

Abstract

In this work we develop a family of adaptive algorithms based on nonlinear functions as a criterion to be applied upon the error, that we want to minimize. Such a development is based upon the use of high order statistics to obtain additional information of the signals involved in the process, intending to enhance the adaptive filtering performance. We derive equations based upon the Taylor s series expansion of the nonlinear functions in order to obtain criterions that guarantee convergence. We also make a study about the covariance of the weight vector on steady state and determine equations that measure the time constant of the adaptive process. We present the sigmoidal algorithm that uses the function Ln(cosh ") as criterion. Simulations of this algorithm are performed to validate the theory and it is also applied to obtain the deterministic components of real impedance cardiographic signals.