Precise Approximation Formula for Fourier Transform of Functions with Exponential Decay for the Whole Frequency

Abstract

Abstract. For Fourier transform with a limited frequency domain, an approximation formula using continuous Euler transform has been devised by Ooura, and its error analysis has been done by Tanaka. In this paper, we construct an approximation formula for Fourier transform in the whole frequency domain for an exponentially decreasing function by combining Sinc method, which is one of function approximation methods, and Ooura’s formula, perform error analysis and confirm its correctness by numerical experiments. As an extension, we also devise a method to achieve the given approximation error.