• Fourier series
  Fourier series
  In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
  
  , 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
  Fourier transform
  In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
  
  , the type of linear canonical transform that is the generalization of the Fourier series
• Fourier operator
  Fourier operator
  The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform.It may be thought of as a limiting case for when the size of the discrete Fourier transform increases without bound while its spatial resolution also increases without bound,...
  
  , the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform
• Fourier inversion theorem
  Fourier inversion theorem
  In mathematics, Fourier inversion recovers a function from its Fourier transform. Several different Fourier inversion theorems exist.Sometimes the following expression is used as the definition of the Fourier transform:...
  
  , 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
  Short-time Fourier transform
  The short-time Fourier transform , or alternatively short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time....
  
   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
  Fractional Fourier transform
  In mathematics, in the area of harmonic analysis, the fractional Fourier transform is a linear transformation generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power where n need not be an integer — thus, it can transform a function to an...
  
   (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
• Discrete-time Fourier transform
  Discrete-time Fourier transform
  In mathematics, the discrete-time Fourier transform is one of the specific forms of Fourier analysis. As such, it transforms one function into another, which is called the frequency domain representation, or simply the "DTFT", of the original function . But the DTFT requires an input function...
  
   (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
  Discrete Fourier transform
  In mathematics, the discrete Fourier transform is a specific kind of discrete transform, used in Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function...
  
   (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
  Fast Fourier transform
  A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
  
   (FFT), a fast algorithm for computing a Discrete Fourier transform
• Generalized Fourier series
  Generalized Fourier series
  In mathematical analysis, many generalizations of Fourier series have proved to be useful.They are all special cases of decompositions over an orthonormal basis of an inner product space....
  
  , generalizations of Fourier series that are special cases of decompositions over an orthonormal basis of an inner product space

• The Fourier number
  Fourier number
  In physics and engineering, the Fourier number or Fourier modulus, named after Joseph Fourier, is a dimensionless number that characterizes heat conduction. Conceptually, it is the ratio of the heat conduction rate to the rate of thermal energy storage. Together with the Biot number, it...
  
   () (also known as the Fourier modulus), a ratio of the rate of heat conduction to the rate of thermal energy storage
• Fourier transform spectroscopy
  Fourier transform spectroscopy
  Fourier transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the electromagnetic radiation or other type of radiation....
  
  , 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

People named Fourier

• Joseph Fourier
  Joseph Fourier
  Jean Baptiste Joseph Fourier was a French mathematician and physicist best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's Law are also named in his honour...
  
   (1768–1830), French mathematician and physicist
• Charles Fourier
  Charles Fourier
  François Marie Charles Fourier was a French philosopher. An influential thinker, some of Fourier's social and moral views, held to be radical in his lifetime, have become main currents in modern society...
  
   (1772–1837), French utopian socialist thinker
• Peter Fourier
  Peter Fourier
  Saint Peter Fourier, C.R.S.A., was a French canon regular who is honored as a saint in the Roman Catholic Church, who had served as a pastor in Mattaincourt , and who also helped to found a religious congregation of canonesses dedicated to the care of poor children...
  
  (1565–1640), French saint in the Roman Catholic Church and priest of Mattaincourt