Fourier

Fourier may refer to:

• Fourier (surname), French surname

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
• 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 (${\displaystyle {\mathit {Fo}}}$) (also known as the Fourier modulus), a ratio ${\displaystyle \alpha t/d^{2}}$ of the rate of heat conduction ${\displaystyle \alpha t}$ to the rate of thermal energy storage ${\displaystyle d^{2}}$
• Fourier-transform spectroscopy, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source

See also

• List of Fourier-related transforms, a list of linear transformations of functions related to Fourier analysis
• Fourier (crater)
• Fourier (company), a Chinese robotics company
• Fourier Island, small rocky island near Cape Mousse, Antarctica

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