System theoretical consideration on n‐point padé approximation

Abstract In the field of system modelling, circuit synthesis and filter design, it is very important to approximate a given characteristic function by a rational function of an appropriate order. Padé approximation has been known for a long time and is one of the rational function approximation methods used extensively because of its simplicity. This paper proposes to investigate N‐point Padé approximation which is an extension of Padé approximation, from the system‐theoretic viewpoint. The N‐point Padé approximation is a rational function interpolation including the derivative of arbitrary order and, compared to regular Padé approximation and rational Hermite interpolation, it can cope with more diverse demands. In this paper we discuss the following subjects on rational function approximation of given characteristic function: its explicit form, minimal order realization problem, Nuttall's compact form, its relation to continued fractions, and the numerical efficient iterative algorithm. These are more general discussions, even including regular Padé approximation. Also, we give numerical results of the approximation of a transfer function for continuous and discrete systems as an example of application of N‐point Padé approximation.