Fourier

From Wikipedia, the free encyclopedia

Fourier (pronounced /ˈfʊərieɪ/, French pronunciation IPA: [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 x = sinθ, 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 (Fo) (also known as the Fourier modulus), a ratio αt / d² of the rate of heat conduction αt to the rate of thermal energy storage d²
      • 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