State-space realization theory of two-dimensional filters
State-space realization theory of two-dimensional filters
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DOI：
10.1109/tac.1976.1101305
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发表时间：
1976-08
影响因子：
6.8
通讯作者：
E. Fornasini;G. Marchesini
中科院分区：
文献类型：
--
作者：
E. Fornasini;G. Marchesini
从系统论的角度探讨了二维线性滤波器的实现问题。该系统的输入输出行为由两个变量的形式幂函数级数定义，并构造了一个零状态空间。一般说来，这种状态空间是无限维的。如果功率级数是有理的，则通过更新有限维局部状态空间上的方程来描述滤波器的动态特性。以自然的方式定义了局部可达性和能观性的概念，并给出了一种获得可达和能观实现的算法。一般来说，局部可达性和可观测性并不意味着实现的最小性。
The realization problem of two-dimensional linear filters is approached from a system theoretic point of view. The input-output behavior of such a system is defined by formal power series in two variables, and a Nerode state space is constructed. This state space is, in general, infinite dimensional. If the power series is rational, the dynamics of the filter is described by updating equations on finite-dimensional local state space. 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, local reachability and observability do not imply the minimality of the realization.