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