In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent...
177 KB (21,313 words) - 19:14, 8 July 2025
Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts...
67 KB (7,809 words) - 05:39, 1 July 2025
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...
76 KB (12,338 words) - 20:01, 27 June 2025
the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum...
20 KB (3,302 words) - 15:43, 25 February 2025
The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends...
38 KB (4,788 words) - 15:31, 27 April 2025
fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to...
27 KB (3,937 words) - 02:28, 16 June 2025
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT...
40 KB (5,076 words) - 15:50, 30 May 2025
Fourier transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas...
37 KB (4,802 words) - 00:54, 11 July 2025
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections...
22 KB (4,046 words) - 13:46, 21 July 2025
arguments, Fourier-related transforms include: Two-sided Laplace transform Mellin transform, another closely related integral transform Laplace transform: the...
7 KB (1,001 words) - 15:55, 27 May 2025
other transforms, most notably the Fourier transform and the Mellin transform. Formally, the Laplace transform is converted into a Fourier transform by the...
76 KB (9,635 words) - 14:49, 12 July 2025
mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively...
17 KB (2,744 words) - 01:27, 23 June 2025
Fourier-transform spectroscopy (FTS) is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source...
15 KB (1,889 words) - 05:20, 25 May 2025
Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier inversion theorem Fourier sine and cosine series Fourier transform Gibbs...
72 KB (11,152 words) - 14:33, 14 July 2025
Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...
32 KB (4,745 words) - 16:18, 5 July 2025
In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing...
18 KB (2,693 words) - 17:39, 18 July 2025
In mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g...
2 KB (298 words) - 14:04, 23 July 2023
In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...
20 KB (3,992 words) - 20:05, 19 June 2025
classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph Fourier transform is...
12 KB (1,845 words) - 20:01, 8 November 2024
mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions...
10 KB (1,340 words) - 00:07, 18 June 2025
The Radon transform is closely related to the Fourier transform. We define the univariate Fourier transform here as: f ^ ( ω ) = ∫ − ∞ ∞ f ( x ) e − 2 π...
24 KB (3,500 words) - 01:31, 17 July 2025
The sparse Fourier transform (SFT) is a kind of discrete Fourier transform (DFT) for handling big data signals. Specifically, it is used in GPS synchronization...
12 KB (1,624 words) - 00:16, 18 February 2025
the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...
13 KB (2,052 words) - 20:50, 6 July 2025
Fourier-transform ion cyclotron resonance mass spectrometry is a type of mass analyzer (or mass spectrometer) for determining the mass-to-charge ratio...
18 KB (2,264 words) - 06:36, 2 June 2025
is also known as the Fourier–Bessel transform. Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval...
26 KB (4,204 words) - 21:10, 3 February 2025
Frequency domain (redirect from Fourier domain)
domains with a pair of mathematical operators called transforms. An example is the Fourier transform, which converts a time function into a complex valued...
10 KB (1,193 words) - 21:38, 1 June 2025
Hann function (section Fourier transform)
⟷ Fourier transform sinc ( L f ) ≜ sin ( π L f ) π L f . {\displaystyle {\tfrac {1}{L}}\operatorname {rect} (x/L)\quad {\stackrel {\text{Fourier...
10 KB (1,674 words) - 02:56, 23 May 2025
in time resolution at ascending frequencies for the Fourier transform and the wavelet transform is shown below. Note however, that the frequency resolution...
28 KB (3,993 words) - 15:23, 21 July 2025
discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform...
15 KB (2,481 words) - 15:53, 18 June 2025
formula for the inverse Laplace transform, called the Mellin's inverse formula, the Bromwich integral, or the Fourier–Mellin integral, is given by the...
8 KB (1,012 words) - 13:27, 30 June 2025