# 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 ?
Method for eliminating zero spectrum in Fourier transform profilometry, Optics and Lasers in Engineering, 43(11), 1267-1276.
Analysing non-stationary signals, in a narrow frequency range the preference should be given to the windowed Fourier transform, and when wide frequency range, to the wavelet transformations.
This paper presents a new procedure to obtaining on-line transformer Frequency Response by applying controlled pulses and using the Wavelet Transform as an improved alternative to the Fourier Transform.
Using the discrete Fourier transform method, we solve as example a circular convolution equation:
The Fourier transform of function x is the function [?
Now it is ready to summarize the 2D conformal Fourier transform (2D CFT) algorithm with the following steps:
The discrete Fourier transforms of these GC-spectra, denoted as Ref(u) and NRef(u), are given by (Teusdea, 2009)
However, Varian is the only company in the market offering nanoLC paired with a Fourier Transform triple quadrupole, MS.
Evaluation of barometric-corrected head data by a Fast Fourier Transform method identified periodicities of water-level changes at 12.
Each Fourier transform F(Q) equals the volume integral [8] of the respective [rho](r)exp(-iQ * r), Q denoting the wave vector transfer.
Fast Fourier transform (FFT) and autocorrelation functions were used to find the dominating wavelength of the sheet, but more than one wavelength may be significant.

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