Inverse two-sided z transform and moment problem

摘要

Numerical inversion of two-sided z transform F(z) is considered. The numerical inversion requires F(z) analyticity within an annular region which includes the unit circle |z|=1 and consequently the availability of a finite number of moments, related to the successive derivatives of F(z) at z=1. The approximate analytical form is obtained by resorting to the maximum entropy principle. Entropy and then L1 norm convergence are proved. Some numerical examples are illustrated.