A Two-Stage Approach to the Establishment of State-Space Formulation of 2-D Frequency Transformation

This letter proposes a two-stage approach to the open problem of establishing state-space formulation of 2D frequency transformation for 2D digital filters. In the first stage, formulation of generating a 2D state-space representation that is not in the standard form of a Roesser model will be derived, while in the second stage, the desired state-space formulation to generate a 2D Roesser state-space representation will be established based on the results obtained in the first stage by utilizing certain linear transformation. Moreover, it will be seen that the proposed formulation includes the formulation of 1D frequency transformation for 2D digital filters given by Koshita and Kawamata as a special case, and thus can be viewed as a natural generalization of their result. Numerical examples are given to illustrate the effectiveness of the proposed formulation.