State-space formulation of 2-D frequency transformation base on Fornasini-Marchesini second model

This paper presents a state-space formulation of two-dimensional (2-D) frequency transformation for 2-D digital filters based on the Fornasini-Marchesini second (FM II) model. It will be shown that the FM II model can be interpreted as an equivalent model which has a similar form to the Roesser model. Then based on such a new equivalent model, the state-space formulation of the 2-D frequency transformation based on FM II model is derived by investigating the substantial input and output relations of the prototype filter, all-pass filters and the transformed filter such that the FM II model of the transformed filter can be directly obtained without using any realization approach. Moreover, it turns out that the resultant formulation owns a elegant and general expression so that it can be viewed as a natural extension of its counterpart in Roesser model. A non-trivial example is given to show the effectiveness of the proposed formulation.