Fast algorithms for the special case convolution and deconvolution calculations

The method and algorithms for special-case convolution and deconvolution calculations are presented. The method is applicable when one of the functions to be convolved is a sum of exponential terms with real or complex coefficients. It is shown that the algorithms based on the proposed method are numerically simpler than the known, direct algorithms of convolution and deconvolution in the time domain. The accuracy of the proposed algorithms and direct algorithms is practically the same, but in the case of the new algorithms it can be further improved if the modified procedure of calculating coefficients is used