Abstract
The input-output behaviour of a two-dimensional linear filter is defined by a formal power series in two variables- If the power series is rational, the dynamics of the filter is described by updating equations on finite dimensional local state spaces. The notions of local reachability and observability are defined in a natural way and an algorithm for obtaining a reachable and observable realization is given. In general reachability and observability do not imply the minimality of the realization. Nevertheless the dimension of a minimal realization is the least rank in a family of Hankel matrices.
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