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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==