A state-space design of two-dimensional digital filters

In this paper, the authors propose a method for obtaining the state-space design of two-dimensional digital filters (2DDF). By using their method, design 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 design dimension in their state-space design, and obtain conditions imposed on the transfer functions of 2DDF for the reduction. Moreover, they present a class of transfer functions of 2DDF that can be designed with a minimal dimension with respect to both of two variables