Fourier

Fourier ( /ˈfʊəri.eɪ/; ) 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: In mathematics:

  • 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
  • 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

In physics and engineering:

  • The Fourier number (also known as the Fourier modulus), a ratio of the rate of heat conduction to the rate of thermal energy storage
  • 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

Read more about Fourier:  People Named Fourier

Other articles related to "fourier":

Sine And Cosine Transforms
... In mathematics, the Fourier sine and cosine transforms are forms of the Fourier integral transform that do not use complex numbers ... They are the forms originally used by Joseph Fourier and are still preferred in some applications, such as signal processing or statistics ...
Mark Pinsky - Selected Publications
... Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics), 2002, ISBN 978-0-534-37660-4 Fourier series of radial functions in several ...
Structure Factor - Derivation
... We can define its Fourier transform ... Using the property that the Fourier transform of a convolution product is simply the product of the Fourier transforms of the two factors, we have, such that (2 ...
Angle-resolved Low-coherence Interferometry - History - Fourier-domain Implementation
... However, it has been demonstrated that it is possible to use a Fourier domain implementation to yield depth resolution in a single data acquisition ... Finally the data is Fourier transformed on a line-by-line basis to generate scattering intensity as a function of OPL and angle ...
People Named Fourier
... Joseph Fourier (1768–1830), French mathematician and physicist Charles Fourier (1772–1837), French utopian socialist thinker Peter Fourier (1565–1640 ...