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ON SOME CLASSES OF LINEAR TIME-VARYING PARAMETRIC FILTERS

In this paper we investigate linear time-varying filters characterized by temporaland spectral-domain parameters. Existence and uniqueness properties are presented for four classes of parametric time-varying filters: (1) the rational class; (2) the rational adjoint class; (3) the well-known ARMA class; and (4) the ARMA adjoint class. In previous work on nonstationary processes [1], we presented membership conditions on the Green’s function for each of these classes. These conditions were used to determine when minimum-order parameterizations are unique and to give precise conditions under which a unique minimum-order filter is a member of one or more of these classes. In this paper, we present these results in a system theoretic framework.