Abstract
This paper proposes modifications to a numerical convolution algorithm, which theoretically has to be most precise amongst three convolution methods but has so far been avoided because of its poor accuracy in the numerical applications. In the paper, the three algorithms are to be examined to analyse one of the most difficult response computations for the input impulse, the ideal front-chopped impulse, and numerical results are compared with the analytically obtained values. The reason for the poor numerical performance in the method is investigated and new additional terms are to be derived so that the conventional inadequate method can yield the most precise results. Numerical analyses show that, with the proposed techniques, the accuracy of 10-5 can easily be attained in the response calculations for the input impulse. Also in the paper, it is demonstrated that the number of the multiplications involved in the convolution integral almost dominates the numerical precision for the computed response.
