Finite-Frequency Model Reduction of Two-Dimensional Digital Filters

This technical note is concerned with the model reduction problem of two-dimensional (2-D) digital filters over finite-frequency ranges. The 2-D digital filter is described by the Fornasini-Marchesini local state-space (FM LSS) model. With the aid of the generalized Kalman-Yakubovich-Popov (GKYP) lemma for 2-D systems, sufficient conditions for the finite-frequency model reduction problem are derived. Compared with full-frequency methods, the proposed finite-frequency method can get a better approximation performance over finite-frequency ranges. An example is given to demonstrate the effectiveness of the proposed method.