Choice of Basis Functions for Continuous and Discrete System Modelling

Abstract This paper discusses the role played by basis functions in continuous and discrete system modelling. We show that the choice of basis functions can significantly reduce the number of terms necessary to achieve a given level of approximation to the true signal spectrum and can substantially improve numerical properties. Emphasis is placed on the approximation of ARMA models of stationary stochastic processes by linearly parameterized models of AR type. Connections with the Levinson algorithm for order recursive estimation are also briefly explored.