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

In the application of Pade 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 Pade approximants to the Z-transform of a complex Gaussian discrete white noise process are considered. Properties of the condensed density of the Pade 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 Pade poles for all orders of the approximants is also computed. Some Monte Carlo simulations are provided.

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