Data-dependent Orthogonal Polynomials on Generalized Circles: A Unified Approach Applied to Δ-Domain Identification

The performance of algorithms in system identification and control, depends on their implementation in finite-precision arithmetic. The aim of this paper is to develop a unified approach for numerically reliable system identification that combines the numerical advantages of data-dependent orthogonal polynomials and the discrete-time δ-domain parametrization. In this paper, earlier results for discrete orthogonal polynomials on the real-line and the unit-circle are generalized to obtain an approach for the construction of orthogonal polynomials on generalized circles in the complex plane. This enables the formulation of a unified framework for the numerically reliable identification of systems expressed in the δ-domain, as well as in the traditional Laplace and Z-domains. An example is presented which shows the significant numerical advantages of the δ-domain approach for the identification of fast-sampled systems.