Abstract. A technique for synthesis of various complex discrete linear systems on the base of differential equations for continuous analog filters is considered. The systems include low and high frequency filters, vibrational links, rejection and selective filters.  To derive the difference equations describing the operation of synthesized linear systems, the derivatives of differential equations are replaced by their analogs in the form of complex difference equations. With the correct choice of discretization period, the frequency properties of synthesized discrete filters coincide practically with the frequency properties of the respective continuous filters. Specific examples of design of complex discrete filters of low and high frequencies using the method of invariant selective differential equations are presented. 

Keywords: complex discrete filter, differential equation, separation equation, frequency transfer function

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