In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function...

A fast Fourier transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis...

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

Fourier-transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas...

the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum...

The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends...

The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections...

other transforms, most notably the Fourier transform and the Mellin transform. Formally, the Laplace transform is converted into a Fourier transform by the...

Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source,...

fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to...

mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively...

kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier sine and cosine series Fourier transform Gibbs phenomenon...

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...

classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph Fourier transform is...

In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing...

arguments, Fourier-related transforms include: Two-sided Laplace transform Mellin transform, another closely related integral transform Laplace transform: the...

Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...

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...

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...

the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...

formula for the inverse Laplace transform, called the Mellin's inverse formula, the Bromwich integral, or the Fourier–Mellin integral, is given by the...

In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...

Fourier-transform ion cyclotron resonance mass spectrometry is a type of mass analyzer (or mass spectrometer) for determining the mass-to-charge ratio...

the sign of the frequency (see § Relationship with the Fourier transform). The Hilbert transform is important in signal processing, where it is a component...

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...

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...

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...

in time resolution at ascending frequencies for the Fourier transform and the wavelet transform is shown below. Note however, that the frequency resolution...

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...

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...