Matrix Formulation of Frequency Transformation for 2-D State-Space Digital Filters

Abstract: This paper proposes matrix formulation of fre-quency transformation for 2-D digital filters in terms of the state-space equations. In order to derive the formulation, we extend Mullis and Roberts ’ matrix formulation of 1-D fre-quency transformation to 2-D case. The proposed formula-tion 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 ob-tained by conventional formulation and consists of simple al-gebraic operations such as matrix addition, multiplication, in-verse and so on. Moreover, our formulation can be easily im-plemented in MATLAB without any complicated algorithm. 1.