Fourier may refer to:
People named Fourier
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Joseph Fourier
Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French people, French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier an ...
(1768–1830), French mathematician and physicist
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Charles Fourier
François Marie Charles Fourier (;; 7 April 1772 – 10 October 1837) was a French philosopher, an influential early socialist thinker and one of the founders of utopian socialism. Some of Fourier's social and moral views, held to be radical in ...
(1772–1837), French utopian socialist thinker
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Peter Fourier
Peter Fourier (french: link=no, Pierre Fourier, ; 30 November 15659 December 1640) was a French canon regular who is honored as a saint in the Roman Catholic Church. Foregoing offers of high office, he served for many years as an exemplary past ...
(1565–1640), French saint in the Roman Catholic Church and priest of Mattaincourt
Mathematics
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Fourier series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''p ...
, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function
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Fourier analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...
, the description of functions as sums of sinusoids
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Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
, the type of linear canonical transform that is the generalization of the Fourier series
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Fourier operator
The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional function when it corresponds to the Fourier transform of one-dimensional functions. It is complex ...
, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform
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Fourier inversion theorem, any one of several theorems by which Fourier inversion recovers a function from its Fourier transform
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Short-time Fourier transform
The short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divi ...
or short-term Fourier transform (STFT), a Fourier transform during a short term of time, used in the area of signal analysis
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Fractional Fourier transform (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
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Discrete-time Fourier transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values.
The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the ...
(DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane
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Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex- ...
(DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies
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Fast Fourier transform (FFT), a fast algorithm for computing a discrete Fourier transform
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Generalized Fourier series
In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions de ...
, generalizations of Fourier series that are special cases of decompositions over an orthonormal basis of an inner product space
In physics and engineering
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Fourier number (
) (also known as the Fourier modulus), a ratio
of the rate of heat conduction
to the rate of thermal energy storage
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Fourier transform spectroscopy
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It ca ...
, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source
See also
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List of Fourier-related transforms
This is a list of linear transformations of function (mathematics), functions related to Fourier analysis. Such transformations Map (mathematics), map a function to a set of coefficients of basis functions, where the basis functions are trigonomet ...
, a list of linear transformations of functions related to Fourier analysis
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Fourier (crater)
Fourier is a Lunar craters, lunar impact crater that is located in the southwestern part of the Moon's near side, just to the southeast of the crater Vieta (crater), Vieta. To the northeast is the Mare Humorum. The rim of this crater is roughly cir ...
Occupational surnames
{{disambiguation, surname
French-language surnames
Surnames of French origin
Surnames of Belgian origin