Fourier

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Fourier may refer to:

People named Fourier[edit]

  • Joseph Fourier (1768–1830), French mathematician and physicist
  • Charles Fourier (1772–1837), French utopian socialist thinker
  • Peter Fourier (1565–1640), French saint in the Roman Catholic Church and priest of Mattaincourt

Mathematics[edit]

  • 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
  • Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series
  • 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
  • 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

In physics and engineering[edit]

  • 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

See also[edit]