A numerical method of Fourier transform based on hyperfunction theory

TL;DR

This paper introduces a novel numerical Fourier transform method utilizing hyperfunction theory, which computes the transform through analytic continuation of defining functions, demonstrating improved efficiency over existing techniques.

Contribution

The paper presents a new numerical Fourier transform approach based on hyperfunction theory, offering a different perspective and potentially more efficient computations.

Findings

Demonstrates the efficiency of the proposed method through numerical examples.

Provides a new framework for Fourier transform computation using hyperfunctions.

Shows improved performance compared to previous methods.

Abstract

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.