Optimum generalized orthonormal basis networks for a class of discrete-time systems

The aim of this paper is to establish analytical equations for the problem of finding optimum real poles of the generalized orthonormal basis (GOB) for the class of discrete time systems which unit sample response is of the form h(k)=∑i=1PAibik, where Ai and -1<bi,<1 are real numbers. These equations are written only in terms of the unknown poles. This is achieved by minimizing the mean square error (MSE) between the given system and its GOB counterpart.