A new family of semi-analytical recursive convolution algorithms (SARC) suitable for efficient numerical analysis of linear systems in the time domain is presented. Consecutive output samples in the SARC algorithms are calculated with higher accuracy than in other recursive convolution algorithms. The main idea and outline of an error analysis are presented and some areas of the SARC algorithm's application are considered. The application of SARC algorithms to the synthesis of discrete-time filters is pointed out as a method of filter design.
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