Fourier Expansion Method for Positive Real Approximation of Sampled Frequency Data

Abstract

Positive real approximation of sampled frequency data obtained from electromagnetic analysis or measurement is presented. The proposed two methods are based on the Fourier expansion method. The frequency data are approximated by the Laguerre series that becomes the Fourier series with an infinite interval at an imaginary axis of complex plane. The proposed methods do not require any passivity check algorithm. The first method approximates the real parts of sampled data by the piecewise linear matrix function. The second method uses discrete Fourier transform. It is here proven that the approximated matrix function is an interpolative function for the real parts of sampled data. The proposed methods are applied to the approximation of per unit length parameters of multi-conductor system. The capability of the proposed methods is demonstrated.