Separable-denominator 2-D rational approximation via 1-D based algorithm

In this paper, an efficient technique is developed for the rational approximation of multi-input multi-output one-dimensional (1-D) digital filters. Then, after showing that a causal 2-D recursive digital filter with separable denominator can be characterized by two multi-output 1-D recursive digital filters, the 1-D technique is applied to approximate a 2-D digital filter by one being separable in the denominator. The parameters of the approximating filter can be obtained by solving linear equations by means of an efficient recursive algorithm. Moreover, the stability of the approximating filter is always ensured. Three examples are presented to illustrate the utility of the proposed technique.