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List of Fourier-related transforms; Fourier transform on finite groups; Fractional Fourier transform; Continuous Fourier transform; Fourier operator; Fourier inversion theorem; Sine and cosine transforms; Parseval's theorem; Paley–Wiener theorem; Projection-slice theorem; Frequency spectrum
The equation of a 1-D Gabor wavelet is a Gaussian modulated by a complex exponential, described as follows: [3] = / ()As opposed to other functions commonly used as bases in Fourier Transforms such as and , Gabor wavelets have the property that they are localized, meaning that as the distance from the center increases, the value of the function becomes exponentially suppressed.
The Bailey's FFT (also known as a 4-step FFT) is a high-performance algorithm for computing the fast Fourier transform (FFT). This variation of the Cooley–Tukey FFT algorithm was originally designed for systems with hierarchical memory common in modern computers (and was the first FFT algorithm in this so called "out of core" class).
An example FFT algorithm structure, using a decomposition into half-size FFTs A discrete Fourier analysis of a sum of cosine waves at 10, 20, 30, 40, and 50 Hz. A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT).
Finite Fourier transform; Fourier integral operator; Fourier operator; Fourier optics; Fourier transform; Fourier transform on finite groups; Fourier–Bros–Iagolnitzer transform; Fourier-transform infrared spectroscopy; Fourier-transform spectroscopy; Fractional Fourier transform; Fractional wavelet transform; Fraunhofer diffraction equation
The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N 1 N 2 as a two-dimensional N 1 ×N 2 DFT, but only for the case where N 1 and N 2 are relatively prime.
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform.It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency.