# Category: Transforms

Choi–Williams distribution function
Choi–Williams distribution function is one of the members of Cohen's class distribution function. It was first proposed by Hyung-Ill Choi and William J. Williams in 1989. This distribution function ad
Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representat
Zak transform
In mathematics, the Zak transform (also known as the Gelfand mapping) is a certain operation which takes as input a function of one variable and produces as output a function of two variables. The out
Box–Muller transform
The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, is a random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation,
Identity transform
The identity transform is a data transformation that copies the source data into the destination data without change. The identity transformation is considered an essential process in creating a reusa
Wigner distribution function
The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis. The WDF was first proposed in physics to account for quantum corrections to classical sta
In mathematics and signal processing, the advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time. It takes the form where * T
Starred transform
In applied mathematics, the starred transform, or star transform, is a discrete-time variation of the Laplace transform, so-named because of the asterisk or "star" in the customary notation of the sam
Fourier–Bros–Iagolnitzer transform
In mathematics, the FBI transform or Fourier–Bros–Iagolnitzer transform is a generalization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer
Bäcklund transform
In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential equations and their solutions. They are an im
In statistics, the Khmaladze transformation is a mathematical tool used in constructing convenient goodness of fit tests for hypothetical distribution functions. More precisely, suppose are i.i.d., po
Star-mesh transform
The star-mesh transform, or star-polygon transform, is a mathematical circuit analysis technique to transform a resistive network into an equivalent network with one less node. The equivalence follows
The pseudo-Hadamard transform is a reversible transformation of a bit string that provides cryptographic diffusion. See Hadamard transform. The bit string must be of even length so that it can be spli
Reassignment method
The method of reassignment is a technique forsharpening a time-frequency representation by mappingthe data to time-frequency coordinates that are nearer tothe true region of support of theanalyzed sig
Finite 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., (pp. 52–53) describes the finite Fourier tra
Quantum Fourier transform
In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a
Move-to-front transform
The move-to-front (MTF) transform is an encoding of data (typically a stream of bytes) designed to improve the performance of entropy encoding techniques of compression. When efficiently implemented,
In mathematics and Fourier analysis, a rectangular mask short-time Fourier transform (rec-STFT) has the simple form of short-time Fourier transform. Other types of the STFT may require more computatio
Fisher transformation
In statistics, the Fisher transformation (or Fisher z-transformation) of a Pearson correlation coefficient is its inverse hyperbolic tangent (artanh). When the sample correlation coefficient r is near
Kelvin transform
The Kelvin transform is a device used in classical potential theory to extend the concept of a harmonic function, by allowing the definition of a function which is 'harmonic at infinity'. This techniq
Non-uniform discrete Fourier transform
In applied mathematics, the nonuniform 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
Overlap–save method
In signal processing, overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal and a finite impulse response (FIR) filter : where h[m]
Burrows–Wheeler transform
The Burrows–Wheeler transform (BWT, also called block-sorting compression) rearranges a character string into runs of similar characters. This is useful for compression, since it tends to be easy to c
Stirling transform
In combinatorial mathematics, the Stirling transform of a sequence { an : n = 1, 2, 3, ... } of numbers is the sequence { bn : n = 1, 2, 3, ... } given by where is the Stirling number of the second ki
Chirplet transform
In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Similar to the wavelet transform, chirplets are usually gener
Hubbard–Stratonovich transformation
The Hubbard–Stratonovich (HS) transformation is an exact mathematical transformation invented by Russian physicist Ruslan L. Stratonovich and popularized by British physicist John Hubbard. It is used
Esscher transform
In actuarial science, the Esscher transform is a transform that takes a probability density f(x) and transforms it to a new probability density f(x; h) with a parameter h. It was introduced by F. Essc
Modified Wigner distribution function
A Modified Wigner distribution function is a variation of the Wigner distribution function (WD) with reduced or removed cross-terms. The Wigner distribution (WD) was first proposed for corrections to
Discrete-time Fourier transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function.
List of transforms
This is a list of transforms in mathematics.
In signal processing, the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal with a finite impulse response (FIR) filter : where h[m] = 0 for m outside t
Harmonic wavelet transform
In the mathematics of signal processing, the harmonic wavelet transform, introduced by in 1993, is a wavelet-based linear transformation of a given function into a time-frequency representation. It co
Inverse Laplace transform
In mathematics, the inverse Laplace transform of a function F(s) is the piecewise-continuous and exponentially-restricted real function f(t) which has the property: where denotes the Laplace transform
Convex conjugate
In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–
Canonical transformation
In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p, t) → (Q, P, t) that preserves the form of Hamilton's equations. This is sometimes known as form invaria
Boustrophedon transform
In mathematics, the boustrophedon transform is a procedure which maps one sequence to another. The transformed sequence is computed by an "addition" operation, implemented as if filling a triangular a
Bilinear transform
The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to
Hankel matrix
In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.: More generally,
Legendre transformation
In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physica
List of common coordinate transformations
This is a list of some of the most commonly used coordinate transformations.
Spectrum continuation analysis
Spectrum continuation analysis (SCA) is a generalization of the concept of Fourier series to non-periodic functions of which only a fragment has been sampled in the time domain. Recall that a Fourier
Scale factor
No description available.
Binomial transform
In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely related to the Euler transform, which is th
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 of a signal as it changes over time. In practice,
Schwartz kernel theorem
In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized func
Transform theory
In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice
Zero bias transform
The zero-bias transform is a transform from one probability distribution to another. The transform arises in applications of Stein's method in probability and statistics.
Inverse scattering transform
In mathematics, the inverse scattering transform is a method for solving some non-linear partial differential equations. The method is a non-linear analogue, and in some sense generalization, of the F
Discrete Chebyshev transform
In applied mathematics, the discrete Chebyshev transform (DCT), named after Pafnuty Chebyshev, is either of two main varieties of DCTs: the discrete Chebyshev transform on the 'roots' grid of the Cheb
Cayley transform
In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by , the Cayley transform is a mapping between skew-symmetric matrices a