Finite Fourier transforms computed by a modified Filon-Euler-Maclaurin method
The Filon-Euler-Maclaurin (FEM) method for computing the finite Fourier transform of a function in terms of the fast Fourier transform plus end point corrections is presented. Methods previously developed are derived within a unified framework. New methods of quadratic, quartic and quintic accuracy are given. Our formulation allows one to easily construct methods of higher order. (C) 2012 Elsevier B.V. All rights reserved.
fourier analysis numerical differentiation and integration finite-difference methods