This is a list of things named after Joseph Fourier:
Mathematics
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Budan–Fourier theorem, see
Budan's theorem
In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan de Boislaurent.
A similar theorem was publish ...
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Fourier's theorem
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Fourier–Motzkin elimination
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Fourier algebra
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Fourier division
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Fourier method
Analysis
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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 Joseph Fo ...
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Fourier series
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems ...
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Fourier–Bessel series
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Fourier sine and cosine series
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Generalized Fourier series
**Laplace–Fourier series, see
Laplace series
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Fourier–Legendre series
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Fourier transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
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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 ...
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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 discrete values.
The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers ...
(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 Sampling (signal processing), samples of a function (mathematics), function into a same-length sequence of equally-spaced samples of the discre ...
(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). A Fourier transform converts a signal from its original domain (often time or space) to a representation in ...
(FFT), a fast algorithm for computing a Discrete Fourier transform
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Finite Fourier transform
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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' ...
(FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
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Fourier–Deligne transform
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Fourier–Mukai transform
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Fourier inversion theorem
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Fourier integral theorem
In physics and engineering
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Fourier's law of heat conduction
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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 optics
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Fourier-transform spectroscopy
Fourier-transform spectroscopy (FTS) is a measurement technique whereby Spectrum (physics), spectra are collected based on measurements of the coherence (physics), coherence of a Radiation, radiative source, using time-domain or space-domain meas ...
, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source
Other
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Joseph Fourier University
Joseph Fourier University (UJF, , also known as Grenoble I) was a French university situated in the city of Grenoble and focused on the fields of sciences, technologies and health. It is now part of the Université Grenoble Alpes.
Importance
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10101 Fourier
See also
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Fourier (disambiguation)
*{{Intitle, Fourier
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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 ...
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List of Fourier analysis topics
Fourier
Joseph Fourier