Matrix formulation of frequency transformation for 2D nonseparable denominator state-space digital filters

This paper proposes matrix formulation of frequency transformation for 2D digital filters in terms of the state-space equations. In order to derive the formulation, we extend Mullis and Roberts´ matrix formulation of 1D frequency transformation to 2D case. The proposed formulation is very suitable for both analysis and realization of the transformed state-space digital filters since the resultant state-space filter has smaller dimension than that of the filters obtained by conventional formulation and consists of simple algebraic operations such as matrix addition, multiplication, inverse and so on. Moreover, our formulation can be easily implemented in MATLAB without any complicated algorithm.