Editing Fourier (section)

==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