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arXiv · 1812.10884

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

S. M. Abrarov·B. M. Quine
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Abstract

In our previous publications we have introduced the cosine product-to-sum identity [17] $$ \prod\limits_{m = 1}^M {\cos \left( {\frac{t}{{{2^m}}}} \right)} = \frac{1}{{{2^{M - 1}}}}\sum\limits_{m = 1}^{{2^{M - 1}}} {\cos \left( {\frac{{2m - 1}}{{{2^M}}}t} \right)} $$ 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 ${\sim 10^{ - 14}}$. 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.

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S. M. Abrarov, B. M. Quine. 2018-12-28. A rational approximation of the sinc function based on sampling and the Fourier transforms. https://doi.org/10.1016/j.apnum.2019.08.030

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