Integral transforms

• Abel transform
  Abel transform
  In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions...
  
  
• Bateman transform
  Bateman transform
  In the mathematical study of partial differential equation, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables...
  
  
• Fourier transform
  Fourier transform
  In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
  
  
  • Short-time Fourier transform
    Short-time Fourier transform
    The short-time Fourier transform , or alternatively short-term Fourier transform, 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....
    
    
• Hankel transform
  Hankel transform
  In mathematics, the Hankel transform expresses any given function f as the weighted sum of an infinite number of Bessel functions of the first kind Jν. The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r-axis...
  
  
• Hartley transform
  Hartley transform
  In mathematics, the Hartley transform is an integral transform closely related to the Fourier transform, but which transforms real-valued functions to real-valued functions. It was proposed as an alternative to the Fourier transform by R. V. L. Hartley in 1942, and is one of many known...
  
  
• Hilbert transform
  Hilbert transform
  In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u, and produces a function, H, with the same domain. The Hilbert transform is named after David Hilbert, who first introduced the operator in order to solve a special case of the...
  
  
  • Hilbert–Schmidt integral operator
• Laplace transform
  • Inverse Laplace transform
  • Two-sided Laplace transform
    Two-sided Laplace transform
    In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform closely related to the Fourier transform, the Mellin transform, and the ordinary or one-sided Laplace transform...
    
    
  • Inverse two-sided Laplace transform
    Mellin inversion theorem
    In mathematics, the Mellin inversion formula tells us conditions underwhich the inverse Mellin transform, or equivalently the inverse two-sided Laplace transform, are defined and recover the transformed function....
    
    
• Laplace–Carson transform
• Laplace–Stieltjes transform
• Linear canonical transform
• Mellin transform
  Mellin transform
  In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform...
  
  
  • Inverse Mellin transform
    Mellin inversion theorem
    In mathematics, the Mellin inversion formula tells us conditions underwhich the inverse Mellin transform, or equivalently the inverse two-sided Laplace transform, are defined and recover the transformed function....
    
    
  • Poisson–Mellin–Newton cycle
• Radon transform
  Radon transform
  thumb|right|Radon transform of the [[indicator function]] of two squares shown in the image below. Lighter regions indicate larger function values. Black indicates zero.thumb|right|Original function is equal to one on the white region and zero on the dark region....
  
  
• Stieltjes transformation
• Sumudu transform
  Sumudu transform
  In mathematics, the Sumudu transform, is an integral transform similar to the Laplace transform, introduced in the early 1990s by Gamage K. Watugala to solve differential equations and control engineering problems. It is equivalent to the Laplace–Carson transform with the substitution...
  
  
• Wavelet transform

Discrete transform

Discrete transform

In signal processing, discrete transforms are mathematical transforms, often linear transforms, of signals between discrete domains, such as between discrete time and discrete frequency....

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• Binomial transform
• Discrete Fourier transform
  Discrete Fourier transform
  In mathematics, the discrete Fourier transform is a specific kind of discrete transform, used in Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function...
  
  , DFT
  • Fast Fourier transform
    Fast Fourier transform
    A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
    
    , a popular implementation of the DFT
• Discrete cosine transform
  Discrete cosine transform
  A discrete cosine transform expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio and images A discrete cosine transform...
  
  
  • Modified discrete cosine transform
    Modified discrete cosine transform
    The modified discrete cosine transform is a Fourier-related transform based on the type-IV discrete cosine transform , with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset,...
    
    
• Discrete Hartley transform
  Discrete Hartley transform
  A discrete Hartley transform is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform , with analogous applications in signal processing and related fields. Its main distinction from the DFT is that it transforms real inputs to real outputs, with no...
  
  
• Discrete sine transform
  Discrete sine transform
  In mathematics, the discrete sine transform is a Fourier-related transform similar to the discrete Fourier transform , but using a purely real matrix...
  
  
• Discrete wavelet transform
  Discrete wavelet transform
  In numerical analysis and functional analysis, a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled...
  
  
  • Fast wavelet transform
    Fast wavelet transform
    The Fast Wavelet Transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets...
    
    
• Hankel transform, the determinant
  Determinant
  In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...
  
   of the Hankel matrix.
• Irrational base discrete weighted transform
  Irrational base discrete weighted transform
  In mathematics, the irrational base discrete weighted transform is a variant of the fast Fourier transform using an irrational base; it was developed by Richard Crandall , Barry Fagin and Joshua Doenias in the early 1990s using Mathematica.The IBDWT is used in the Great Internet Mersenne Prime...
  
  
• Number-theoretic transform
• Stirling transform

Discrete-time transforms

• Discrete-time Fourier transform
  Discrete-time Fourier transform
  In mathematics, the discrete-time Fourier transform is one of the specific forms of Fourier analysis. As such, it transforms one function into another, which is called the frequency domain representation, or simply the "DTFT", of the original function . But the DTFT requires an input function...
  
  
• Z-transform
  Z-transform
  In mathematics and signal processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation....
  
  

Other transforms

• Bäcklund transform
  Bäcklund transform
  In mathematics, Bäcklund transforms or Bäcklund transformations relate partial differential equations and their solutions. They are an important tool in soliton theory and integrable systems...
  
  
• Bilinear transform
  Bilinear transform
  The bilinear transform is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa....
  
  
• Box–Muller transform
• Burrows–Wheeler transform (data compression
  Data compression
  In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....
  
  )
• Wavelet transform
• Chirplet transform
  Chirplet transform
  In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.-Similarity to other transforms:...
  
  
• Distance transform
  Distance transform
  A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another representation, or it is simply endowed with an...
  
  
• Fractal transform
  Fractal transform
  The fractal transform is a technique invented by Michael Barnsley et al. to perform lossy image compression.This first practical fractal compression system for digital images resembles a vector quantization system using the image itself as the codebook....
  
  
• Hadamard transform
  Hadamard transform
  The Hadamard transform is an example of a generalized class of Fourier transforms...
  
  
• Hough transform
  Hough transform
  The Hough transform is a feature extraction technique used in image analysis, computer vision, and digital image processing. The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure...
  
   (digital image processing
  Digital image processing
  Digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing...
  
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• Legendre transform
• Möbius transform
• Perspective transform
  3D projection
  3D projection is any method of mapping three-dimensional points to a two-dimensional plane. As most current methods for displaying graphical data are based on planar two-dimensional media, the use of this type of projection is widespread, especially in computer graphics, engineering and drafting.-...
  
   (computer graphics
  Computer graphics
  Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
  
  )
• Y-delta transform (electrical circuits)

External links

• Tables of Integral Transforms at EqWorld: The World of Mathematical Equations.