Fourier
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'''Fourier''' ({{pronEng|ˈfʊərieɪ}}, French pronunciation {{IPA2|fuʁie}}) may refer to:
*[[Charles Fourier]] (1772–1837), a French utopian socialist thinker
*[[Joseph Fourier]] (1768–1830), a French mathematician and physicist
**Mathematics, physics, and engineering terms named in his honor for his work on the concepts underlying them:
***Mathematics tools:
****The [[Fourier mode]], a simple sinusoidal function such as <math>x = sin \theta</math>, in its role as a component of a Fourier series
****The [[Fourier series]], a series, a weighted sum of component normal Fourier modes, the result of Fourier analysis
****[[Fourier analysis]], the analysis of a periodic function by decomposition into a Fourier series
****The [[Fourier transform]], the type of linear canonical transform that is the generalization of the Fourier series
****The [[Fourier operator]], the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform
****[[Fourier inversion theorem]], any one of several theorems by which Fourier inversion recovers a function from its Fourier transform
****[[List of Fourier-related transforms]], a list of linear transformations of functions related to Fourier analysis
****[[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
****[[Fractional Fourier transform]] (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
****[[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
****[[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
****[[Fast Fourier transform]] (FFT), a fast algorithm for computing a Discrete Fourier transform
****[[Generalized Fourier series]], generalizations of Fourier series that are special cases of decompositions over an orthonormal basis of an inner product space
***Physics and engineering:
****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>
****[[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
*[[Peter Fourier]] (1565–1640), a French saint in the Roman Catholic Church and priest of Mattaincourt
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