A state-space realization form of two-dimensional digital filters

In this paper, we propose a method for obtaining the state-space realization form of two-dimensional digital filters (2DDF). By using our method, realization form can be directly obtained from the coefficients of the transfer functions of 2DDF, without performing canonical decomposition of the state equations and solving nonlinear equations. Consider the possibility of reducing the realization dimension in our state-space realization form, and obtain conditions imposed on the transfer functions of 2DDF for the reduction. Moreover, we present a class of transfer functions of 2DDF that can be realized with a minimal dimension with respect to both of two variables.