A method for realizing separable-denominator two-dimensional transfer function matrices

We propose a method for realizing separable-denominator two-dimensional transfer function matrices (2DTFM), and we present an upper bound of the realization dimension. Moreover, we suggest that, in the case that the input number is equal to the output number, it is possible that it can be realized with a minimal dimension with respect to both of the two variables. Also, we present two types of state-space realization form. They can be directly obtained from each coefficient of the separable-denominator 2DTFM.