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 (1772–1837), French utopian socialist thinker
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Peter Fourier (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 compl ...
, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform
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Fourier inversion theorem In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information ...
, any one of several theorems by which Fourier inversion recovers a function from its Fourier transform
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Short-time Fourier transform 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
In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the ''n''-th power, where ''n'' n ...
(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 (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
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in th ...
(FFT), a fast algorithm for computing a discrete Fourier transform
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Generalized Fourier series, 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)
Occupational surnames
{{disambiguation, surname
French-language surnames
Surnames of French origin
Surnames of Belgian origin