Matrix algorithm of the digital recursive filters synthesis

Problem of a digital recursive filter (DRF) synthesis is considered, which is solved by finding its system function on given transfer function of an analog-filter-prototype (AFP). Matrix algorithm for known methods of Z-transform of an analog filter into a digital one and V.V. is obtained. Suggested matrix algorithm permits, from a general point of view, synthesis of DRF and continuous approximation of difference equations on the base of difference methods of Z-transform. It allows to simplify algorithmic methods and computer codes for P-plane transformation into Z-plane and V.V. Expressions for polynomials Rk(k=1; 2; 3; 4; 5) matrices U and U-1 for standard Z-transform, the Tsypkin-Holdenberg methods, bilinear Z-transform, Medved-Traxsel method and Boker-Taler method are presented.