On the distribution of poles of Pade' approximants to the Z-transform of complex Gaussian white noise

In the application of Pad\'{e} methods to signal processing a basic problem is to take into account the effect of measurement noise on the computed approximants. Qualitative deterministic noise models have been proposed which are consistent with experimental results. In this paper the Pad\'{e} approximants to the $Z$-transform of a complex Gaussian discrete white noise process are considered. Properties of the condensed density of the Pad\'{e} poles such as circular symmetry, asymptotic concentration on the unit circle and independence on the noise variance are proved. An analytic model of the condensed density of the Pad\'{e} poles for all orders of the approximants is also computed. Some Montecarlo simulations are provided.