# Fourier transform

(redirected from Fourier integral)
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Related to Fourier integral: Fourier series

## Fourier transform

n.
An operation that maps a function to its corresponding Fourier series or to an analogous continuous frequency distribution.

[After Baron Jean Baptiste Joseph Fourier.]

## Fourier transform

n
(Mathematics) an integral transform, used in many branches of science, of the form F(x) = [1/√(2π)]∫eixyf(y)dy, where the limits of integration are from –∞ to +∞ and the function F is the transform of the function f
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive ?
Introduction to Pseudodifferential Operators and Fourier Integral Operators.
YING, A fast butterfly algorithm for the computation of Fourier integral operators, Multiscale Model.
In , we find that [X.sub.[alpha]] is related to the mapping properties of the fractional integral operators, the convolution operators and the Fourier integral operators in r.i.q.B.f.s.
The use of Fourier integral transform gives the opportunity to conduct research in the field of images, thereby isolate the effect of the time factor.
Keywords: Taylor expansion, Fourier integral, Aboodh Transform Method, Differential Transform Method
In any case, due to the potentialities of the reproducing kernel Hilbert spaces and the use of the Fourier integral transformation, we will be able to use Proposition 2.3 and obtain analytical conclusions and approximate expressions for the solutions of the integral equations under study.
In the expression of the Fourier integral for lattice fields, the momentum integration with respect to wave-vector components [k.sub.[mu]]([mu] = 1, 2, 3, 4) is restricted by the Brillouin zone [k.sub.[mu]] [member of] [-[pi]/[a.sub.[mu]][pi]/[a.sub.[pi]]], where [a.sub.[mu]] are the lattice constants.
This assumption allowed bypassing traditional mathematical problem, which is raised in the study of transient dynamic problems for finite two-dimensional domains, and allowed further application of Fourier integral transform for the spatial variable.
 Norbert Wiener, The Fourier Integral and Certain of its Applications, New York, Dover Publications, 1958.
The origin of a new integral transform is traced back to the classical Fourier integral.
The wave equations concerning both the single-phase elastic layer and the saturated half-space a resolved using a Fourier integral transform technique.
The scalar Green's function can be represented as two-dimensional Fourier integral
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