A numerical method of Fourier transform based on hyperfunction theory
For researchers needing accurate numerical Fourier transforms, this method offers a new approach with demonstrated efficiency gains.
The paper introduces a numerical Fourier transform method using hyperfunction theory, computing defining functions and then obtaining the transform via analytic continuation. Numerical examples demonstrate improved efficiency over previous methods.
In this paper, we propose a numerical method of Fourier transform based on hyperfunction theory. In the proposed method, we compute analytic functions called the defining functions, which give the desired Fourier transform as a hyperfunction, and then obtain the Fourier transform by the analytic continuation of the defining functions onto the real axis. Numerical examples show the efficiency of the proposed method compared to the previous methods.