# Fourier transform

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Related to Fourier transform: Fourier series, Laplace transform, Fast Fourier transform, Discrete Fourier transform

## 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.

Synonym(s): Fourier transfer, Fourier transform

## Fourier transform (FT)

[fo̅o̅ryā′]

Etymology: Jean B.J. Fourier, French mathematician, 1768-1830; L,

*transformare,*to change forma 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

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