Fourier transform

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Fou·ri·er a·nal·y·sis

(fūr-ē-ā'),
a mathematical approximation of a function as the sum of periodic functions (sine and/or cosine waves) of different frequencies; a method of converting a function of time or space into a function of frequency; used in reconstruction of images in computed tomography and magnetic resonance imaging in radiology and in analysis of any kind of signal for its frequency content.

Fourier transform

A computational procedure used by MRI scanners to analyse and separate amplitude and phases of individual frequency components of the complex time varying signal, which allows spatial information to be reconstructed from the raw data.

Fou·ri·er trans·form

(fūr-ē-ā' trans'fōrm)
A mathematical technique of dividing a time-varying function or signal into components at different frequencies, giving the phase and amplitude of each; used in computed tomography and magnetic resonance image reconstruction transformation.

Fourier,

J.B.J., French mathematician and administrator, 1768-1830.
Fourier analysis - used in reconstruction of images in computed tomography and magnetic resonance imaging in radiology and in analysis of any kind of signal for its frequency content. Synonym(s): Fourier law; Fourier transform
Fourier law - Synonym(s): Fourier analysis
Fourier transform - Synonym(s): Fourier analysis
References in periodicals archive ?
The quaternion Fourier transform (QFT) is an extension of the classical two-dimensional Fourier transform (FT) [1-4] in the framework of quaternion algebra.
In this paper, we propose a method for resolving overlapping signals based on Fourier transform and inverse Fourier transform.
The special affine Fourier transform (SAFT) [3, 4], also known as the offset linear canonical transform [5, 6] or the inhomogeneous canonical transform [5], is a six-parameter (a, b, c, d, [u.sub.0], [w.sub.0]) class of linear integral transform.
In [7], the author studied that the fractional Fourier transform (FrFT) can be reduced to the classical Fourier transform.
Fourier Transform. This is an integral transform that transforms a function of one or more variables (in spatial domain) to another function (in frequency domain) of the same number of variables [3, 13, 14].
STEIDL, Fast Fourier transforms for nonequispaced data, in Approximation Theory IX, Vol.
Classical Fourier transform does not allow identification of these signals to distinguish them.
Fractional Fourier transform (FrFT) is a generalization of the Fourier transform, FrFT is a linear operator.
The Dunkl transform on the real line, which enjoys properties similar to those of Fourier transform, is generalization of the Fourier transform.
The specific goals of this study were to investigate the characteristic peaks of bimetallic catalysts and determine the bimetallic interactions semiquantitatively by phase-and-amplitude function corrected Fourier transform method.
This shows that Rxx(t) is an even and real function of time whose Fourier transform is also an even and real function of frequency [6].
Using discrete Fourier transform can be determined the circular deconvolution, ie the circular convolution inverse.

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