Asymptotic behaviour of transfer function synthesis methods

Abstract

Abstract This paper presents an analysis of the asymptotic behaviour of the solutions to various iterative linear least-squares methods that synthesize transfer functions from frequency-response data. The methods of Sanathanan and Koerner and Lawrence and Rogers are shown to possess asymptotic solutions that do not coincide with the solution to a fundamental non-linear least-squares criterion. Several methods with more appropriate asymptotic behaviour are then suggested. The analytical tools presented should allow analysis of conditions for the convergence of iterative linear least-squares methods.