A rational approximation of the sinc function based on sampling and the Fourier transforms

In our previous publications we have introduced the cosine product-to-sum identity [17] Pi(M)(m=1) cos(t/2(m)) = 1/2(M-1) Sigma(2M-1)(m=1) cos(2m - 1/2(M)t) and applied it for sampling [1,2] as an incomplete cosine expansion of the sinc function in order to obtain a rational approximation of the Voigt/complex error function that with only 16 summation terms can provide accuracy similar to 10(-14). In this work we generalize this approach and show as an example how a rational approximation of the sinc function can be derived. A MATLAB code validating these results is presented. Crown Copyright (C) 2019 Published by Elsevier B.V. on behalf of IMACS. All rights reserved.