# 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 ?
The Fast Fourier Transformation (FFT) which is obtained by making use of DFT's periodical characteristic and performs transformation with a less processing is however obtained as [1-6];
When the input sampling shifts one sample, the first component of the sum value is deleted according to the direct Fourier transformation which has a zero angle; and one new component is added.
The algebraic frame generated by the Fourier transformation consists of unbounded linear functionals; however, although the frequency of the signal is uncontrollable, the doubly boundedness of the analysis operator controls the energy of the processed signal.
Using the angular spectrum method, we establish a relationship between the bistatic radar cross section and the two-dimensional Fourier transformation of the scattered near-field.
The Fourier transformation of a private fieldof a particle does two things.
Comparison of the results calculated by the Short Time Fourier Transformation and by the array of resonators shown very good conjunction in the results.
The time window for the Fourier transformation and the frequency range, over which coherency is evaluated, are different in Figs.
Fourier transformation mass spectrometer (FTMS), coupled with a rotary vane pump;
For frequency-domain HRV parameters analysis, spectral power was quantified both by fast Fourier transformation and autoregressive method for the following frequency bands: 0.
This global formulator and manufacturer of thermoset molding compounds has enhanced its comprehensive test laboratory with the acquisition of a Fourier Transformation Near Infrared Spectrometer.
Multi-channel display options include bargraphs, trend plots, oscilloscope view, and discrete Fourier transformation for harmonic analysis.
Computational effort with the newly implemented one-dimensional Fast Fourier Transformation (FFT) algorithm scales linearly with the number of analysis frequencies, while conventional methods require effort squarely proportional to the number of frequencies.

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