# 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.

## 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. Syn. Fourier transform. See contrast sensitivity.
References in periodicals archive ?
The digitized male genitalia were prepared for the elliptic Fourier analysis with Paint.
The Fourier analysis tells us about cycles, and neural networks about the most probable events to happen in the near future, and both reach a common conclusion: at most 2 years before 2020, the DJIA/GF will have a sustained recovery to give birth to a new cycle.
Application of elliptical Fourier analysis of otolith form as a tool for stock identification.
When morphometry meets genetics: inferring the phylogeography of Carabus solieri using Fourier analysis of pronotum and male genitalia.
To verify whether Fourier analysis could capture Bayer's (1961) qualitative interpretation of sclerites's shapes, we started with the taxonomy favored by that author.
We first use Fourier analysis to gain some insight into the behavior of the Chambolle iterations and the associated Algorithm 3.
Wavelet-based methods offer a viable alternative to the ubiquitous Fourier analysis (e.
4) The Fourier analysis will yield the steady-state waveforms of the circuit, while the transient simulation will follow the time-domain waveform evolution of the circuit.
Automated Fourier Analysis (FFT) routines offer a level of diagnosis that removes a good deal of the guesswork as to the origin of machine related variations," he said.
Some of these include peak, valley and zero finding, Fourier analysis, smoothing, interpolating and extracting sections of data.
On one page, an engineer describes how she applies the Fourier analysis techniques she learned in math class to the work she does now.
The net constructed this generating function in a method somewhat analogous to the mathematical technique called Fourier analysis, which enables scientists to approximate any curve by adding together sine waves of different frequency, phase and amplitude Instead of sine waves, however, the net used another trigonometric function, hyperbolic tangents (tanh).

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