Mathematica 9 is now available

Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

Numerical computation of multidimensional Fourier integrals

Gordon Inverarity
Organization: Met Office, U.K.
Old MathSource #

Revision date


The NFourierIntegral package adaptively computes multidimensional Fourier integrals over finite integration ranges. Each integral is evaluated over sets of equally-spaced values in each dimension whose Cartesian product spans an arbitrary region of transform variable space. With suitable truncation, the package can be used to approximate multidimensional Fourier transforms. The underlying algorithm is that of Inverarity (2002), which generalizes the one-dimensional algorithm of Bailey and Swarztrauber (1994). For a given number of function evaluations, the multidimensional midpoint rule is used to approximate the integral as a multidimensional circular convolution, which is then evaluated using fast Fourier transforms. It is implemented adaptively using Richardson extrapolation, also known as extrapolation to the limit.


Bailey, D.H. and Swartrauber, P.N., "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms", SIAM J. Sci. Comput., 15, 1105-1110 (1994)

Inverarity, G.W., "Fast computation of multidimensional Fourier integrals", SIAM J. Sci. Comput., 24, 645-651 (2002) (

(c) British Crown Copyright 2002

*Mathematics > Calculus and Analysis

Fourier, Fourier transform, Fourier integral, multi-dimensional, numerical integration

INSTALL.txt (1.1 KB) - Text file
Calculus.sit (17.3 KB) - Macintosh Stuffit archive
Calculus.tar.gz (16.5 KB) - GZIP archive
Download (18.7 KB) - ZIP archive