Minimum order input-output equation for LTV digital filters with time-varying state dimension

Abstract This paper develops a connection between linear time-varying state equations and minimum order input–output equations for linear time-varying digital filters. A procedure is presented for computing a minimum order input–output equation from a given linear time-varying state equation. The linear time-varying input–output equations and state equations considered in this paper have time-varying orders and time-varying state dimensions, respectively. These models are appropriate for representing practical signal processing systems and are efficient in the computation and implementation of digital filters. It is shown that, in contrast to linear time-invariant filters, the solution for the minimum time-varying order input–output equation can be non-unique.