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| '''Fourier''' ({{IPAc-en|ˈ|f|ʊər|i|.|eɪ}}; {{IPA-fr|fuʁie|lang}}) most commonly refers to [[Joseph Fourier]] (1768–1830), French mathematician and physicist, or the mathematics, physics, and engineering terms named in his honor for his work on the concepts underlying them:
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| In '''mathematics''':
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| *[[Fourier series]], a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function
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| *[[Fourier analysis]], the description of functions as sums of sinusoids
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| *[[Fourier transform]], the type of linear canonical transform that is the generalization of the Fourier series
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| *[[Fourier operator]], 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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| *[[List of Fourier-related transforms]], a list of linear transformations of functions related to Fourier analysis
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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]] (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
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| *[[Discrete-time Fourier transform]] (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]] (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
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| In '''physics''' and '''engineering''':
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| *The [[Fourier number]] (<math>\mathit{Fo}</math>) (also known as the Fourier modulus), a ratio <math>\alpha t/d^2</math> of the rate of heat conduction <math>\alpha t</math> to the rate of thermal energy storage <math>d^2</math>
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| *[[Fourier transform spectroscopy]], a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source, using time-domain measurements of the electromagnetic radiation or other type of radiation, including several methods such as the continuous wave Michelson or Fourier transform spectrometer and the pulsed Fourier transform spectrograph
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| ==People named Fourier==
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| *[[Joseph Fourier]] (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
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| {{disambiguation}}
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| [[Category:Fourier analysis]]
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