# 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 (FT)

[fo̅o̅ryā′]
Etymology: Jean B.J. Fourier, French mathematician, 1768-1830; L, transformare, to change form
a mathematical procedure that separates out the frequency components of a signal from its amplitudes as a function of time, or vice versa.

## 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 ?
Classical Fourier transform does not allow identification of these signals to distinguish them.
The Dunkl transform on the real line, which enjoys properties similar to those of Fourier transform, is generalization of the Fourier transform.
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].
Keywords: Circular convolution, circular deconvolution, discrete Fourier transform, circular convolution equations.
Nguyen, "An accurate algorithm for nonuniform fast Fourier transforms (NUFFT's)," IEEE Microwave and Guided Wave Letters, Vol.
If these Fourier transforms are replaced with the phase-only part of them then the NFCC becomes PhNFCC, otherwise is denoted as AmNFCC.
The Fourier Transform reveals any oscillation frequencies that are present in a time series.
Each Fourier transform F(Q) equals the volume integral [8] of the respective [rho](r)exp(-iQ * r), Q denoting the wave vector transfer.
where g*(w) and k*(w) are Fourier transforms of g(t) and k(t), g(t) = G(t)/[G.
6] have developed a new mathematical model for obtaining the fractional Fourier transforms of Dirichlet and Generalized "Hammimg" window functions and established the direct dependence of their FrFT on fractional angle a which can control the main-lobe width and stop-band attenuation of the resulting window function with the adjustable fractional parameter.
Fourier transforms in radar and signal processing, 2d ed.
He explains Fourier series on the circle, Fourier transforms on the line and space, Fourier analysis in LP spaces, the Poisson summation formula and multiple Fourier series, applications to probability theory, and a gentle introduction to wavelets.

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