# Fourier analysis

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Related to Fourier analysis: Fourier series

## 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

## Fou·ri·er a·nal·y·sis

(fūr-ē-ā' ă-nal'i-sis)A mathematical approximation of a function as the sum of periodic functions (sine waves) of different frequencies; used in reconstruction of magnetic resonance images and computed tomographs and analysis of any kind of signal for its frequency content.

## 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

## Fourier analysis

The mathematical breakdown of waveforms into simple sine wave constituents. Any complex waveform consists of sine waves of different frequencies: the slowest (fundamental) frequency and harmonics thereof (these are frequencies which are odd multiples of the fundamental frequency). It is used in analysis and reconstruction of waveforms as, for example, analysing the spatial frequency components of a visual image.

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