A realization method of three-dimensional digital filters

The author proposes a method for realizing three-dimensional digital filters (3DDFs) by the state space method. If one extends the past methods for realizing two-dimensional digital filters to 3DDFs, complicated matrix calculation (canonical decomposition of variable coefficient state equations) is necessary or enormous equations have to be solved. Therefore, in the present work, the denominator and numerator of the given 3DDF are realized independently. By using this method, the above-mentioned difficulties can be avoided. The authors also show that the separable-denominator 3DDF can be realized with a minimal dimension with respect to two variables