Pole Reconstruction of Systems from Laguerre Basis Representations

摘要

This paper investigates an opportunity to identify poles of systems with unknown structure on the basis of discrete-time spectral signal representations generated on the basis orthogonal Laguerre systems. The convergence of the Laguerre representation coefficients is analyzed within the framework of a hyperbolic metrics generated by the Blaschke functions associated with the Laguerre system, and a conceptual base is given to solve the task of finding the poles of the system. An algorithm is proposed to find the poles, and a discussion is given upon the criteria of finding all of them. An efficient implementation of the algorithm based upon frequency domain measurement is available for practical computations.