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