• Thumbnail for Fourier transform
    In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function...
    177 KB (20,975 words) - 10:11, 15 October 2024
  • Thumbnail for Fast Fourier transform
    A fast Fourier transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis...
    63 KB (7,379 words) - 17:45, 28 October 2024
  • Thumbnail for Discrete Fourier transform
    In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...
    72 KB (11,265 words) - 18:31, 14 October 2024
  • Thumbnail for Fourier-transform infrared spectroscopy
    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 (4,776 words) - 09:47, 11 October 2024
  • Thumbnail for Fourier analysis
    The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends...
    37 KB (4,733 words) - 23:33, 17 October 2024
  • 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 (3,299 words) - 16:38, 19 October 2024
  • Thumbnail for Short-time Fourier transform
    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 (4,051 words) - 16:46, 1 August 2024
  • other transforms, most notably the Fourier transform and the Mellin transform. Formally, the Laplace transform is converted into a Fourier transform by the...
    75 KB (9,390 words) - 19:27, 12 September 2024
  • Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source,...
    15 KB (1,888 words) - 17:19, 20 March 2023
  • fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to...
    26 KB (3,779 words) - 09:29, 11 October 2024
  • mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively...
    18 KB (3,626 words) - 17:26, 23 July 2024
  • 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...
    42 KB (5,449 words) - 10:29, 25 October 2024
  • Thumbnail for Fourier series
    kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier sine and cosine series Fourier transform Gibbs phenomenon...
    70 KB (10,863 words) - 17:04, 27 October 2024
  • 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) - 15:56, 26 June 2024
  • Thumbnail for Sine and cosine transforms
    In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing...
    18 KB (2,673 words) - 20:15, 14 September 2024
  • arguments, Fourier-related transforms include: Two-sided Laplace transform Mellin transform, another closely related integral transform Laplace transform: the...
    7 KB (1,002 words) - 19:07, 10 September 2024
  • Thumbnail for Hadamard transform
    Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...
    32 KB (4,709 words) - 04:16, 21 September 2024
  • 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) - 00:07, 22 July 2024
  • Laplace transform (the s-domain or s-plane). This similarity is explored in the theory of time-scale calculus. While the continuous-time Fourier transform is...
    43 KB (5,655 words) - 02:40, 28 October 2024
  • the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...
    12 KB (1,855 words) - 19:56, 29 July 2024
  • 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) - 19:46, 11 September 2024
  • Fourier-transform ion cyclotron resonance mass spectrometry is a type of mass analyzer (or mass spectrometer) for determining the mass-to-charge ratio...
    17 KB (2,196 words) - 18:39, 25 March 2024
  • In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...
    19 KB (3,805 words) - 11:16, 3 September 2024
  • the sign of the frequency (see § Relationship with the Fourier transform). The Hilbert transform is important in signal processing, where it is a component...
    59 KB (8,095 words) - 16:30, 29 October 2024
  • Thumbnail for Joseph Fourier
    heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with...
    24 KB (2,296 words) - 08:58, 13 September 2024
  • 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...
    14 KB (2,447 words) - 18:32, 29 August 2024
  • 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
  • Thumbnail for Wavelet transform
    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 (3,943 words) - 18:34, 16 October 2024
  • representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded...
    14 KB (1,634 words) - 20:00, 15 October 2024
  • applied mathematics, a DFT matrix is an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied to a signal...
    11 KB (2,097 words) - 15:00, 24 September 2024