Fourier

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 series, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function
****Fourier analysis, the description of functions as sums of sinusoids
****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 ($mathit\{Fo\}$) (also known as the Fourier modulus), a ratio $alpha\; t/d^2$ of the rate of heat conduction $alpha\; t$ to the rate of thermal energy storage $d^2$
****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