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In mathematics, the K transform (also called the Single-Pixel X-ray Transform) is an integral transform introduced by R. Scott Kemp and Ruaridh Macdonald
K-transform
Integral transform in mathematics
In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional)
Radon_transform
Mathematical transform that expresses a function of time as a function of frequency
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent
Fourier_transform
Function in discrete mathematics
{\displaystyle {\tilde {X}}_{k}=\Delta t\cdot X_{k}} . The corresponding inverse transform then becomes: x n = Δ f ∑ k = 0 N − 1 X ~ k ⋅ e i 2 π k N n {\displaystyle
Discrete_Fourier_transform
Mathematical operation
Hankel transform of order ν {\displaystyle \nu } of a function f(r) is given by F ν ( k ) = ∫ 0 ∞ f ( r ) J ν ( k r ) r d r , {\displaystyle F_{\nu }(k)=\int
Hankel_transform
Linear transform from the time domain to the frequency domain
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
Z-transform
Mapping involving integration between function spaces
function K {\displaystyle K} of two variables, that is called the kernel or nucleus of the transform. Some kernels have an associated inverse kernel K − 1
Integral_transform
Involutive change of basis in linear algebra
Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an
Hadamard_transform
Technique used in signal processing and data compression
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies
Discrete_cosine_transform
Integral transform useful in probability theory, physics, and engineering
For example, through the Laplace transform, the equation of the simple harmonic oscillator (Hooke's law) x ″ ( t ) + k x ( t ) = 0 {\displaystyle x''(t)+kx(t)=0}
Laplace_transform
Short-time Fourier transform with variable resolution
the k-th filter, fmin is the central frequency of the lowest filter, and n is the number of filters per octave. The short-time Fourier transform of x[n]
Constant-Q_transform
Transformation of a mathematical sequence
binomial transform, T, of a sequence, {an}, is the sequence {sn} defined by s n = ∑ k = 0 n ( − 1 ) k ( n k ) a k . {\displaystyle s_{n}=\sum _{k=0}^{n}(-1)^{k}{\binom
Binomial_transform
Mathematical algorithm
transform calculates the Z transform at a finite number of points zk along a logarithmic spiral contour, defined as: X k = ∑ n = 0 N − 1 x ( n ) z k −
Chirp_Z-transform
Integral transform and linear operator
In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces
Hilbert_transform
Mathematical technique used in data compression and analysis
mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function ψ ∈ L 2 ( R ) {\displaystyle \psi \,\in \,L^{2}(\mathbb {R}
Wavelet_transform
Branch of mathematics
coefficients. The inverse transform, also known as a discrete Fourier series, is given by: s N [ n ] = 1 N ∑ k S [ k ] ⋅ e i 2 π n N k , {\displaystyle s_{_{N}}[n]={\frac
Fourier_analysis
Fourier analysis technique applied to sequences
Fourier transform: Poisson summation The components of the periodic summation are centered at integer values (denoted by k {\displaystyle k} ) of a normalized
Discrete-time Fourier transform
Discrete-time_Fourier_transform
Mathematical operation
on eigenfunction expansions. The transform was rediscovered independently by Joshua Zak in 1967 who called it the "k-q representation". There seems to
Zak_transform
Change of basis applied in quantum computing
quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier
Quantum_Fourier_transform
Mathematical operation
Laplace transform of f {\displaystyle f} , then the inverse Laplace transform of F {\displaystyle F} is given by f ( t ) = L − 1 { F } ( t ) = lim k → ∞
Inverse_Laplace_transform
Signal processing operation
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
Bilinear_transform
Special case of the short-time Fourier transform
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency
Gabor_transform
Integral transform
geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integrating
Funk_transform
Type of singular integral operator
asserts that the Riesz transform is equivariant with respect to these two actions; that is, ρ ∗ R j [ ( ρ − 1 ) ∗ f ] = ∑ k = 1 d ρ j k R k f . {\displaystyle
Riesz_transform
Discrete Fourier transform algorithm
Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform converts
Fast_Fourier_transform
Mathematical operation
Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the
Fractional_Fourier_transform
Mathematical operation
Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by Cayley (1846), the Cayley transform is a
Cayley_transform
all the properties of the z-transform hold for the advanced z-transform. Z { ∑ k = 1 n c k f k ( t ) } = ∑ k = 1 n c k F k ( z , m ) . {\displaystyle {\mathcal
Advanced_z-transform
Concept in applied mathematics
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, but
Non-uniform discrete Fourier transform
Non-uniform_discrete_Fourier_transform
Generalisation of Fourier transform to any ring
discrete Fourier transform (2), we obtain: f k = v 0 + v 1 α k + v 2 α 2 k + ⋯ + v n − 1 α ( n − 1 ) k . {\displaystyle f_{k}=v_{0}+v_{1}\alpha ^{k}+v_{2}\alpha
Discrete Fourier transform over a ring
Discrete_Fourier_transform_over_a_ring
Transform in numerical harmonic analysis
discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage
Discrete_wavelet_transform
Mathematical analysis of frequency content of signals
more dimensions. One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation
Multidimensional_transform
Transform in mathematics
mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real
Discrete_sine_transform
Plate boundary where the motion is predominantly horizontal
A transform fault or transform boundary, is a fault along a plate boundary where the motion is predominantly horizontal. It ends abruptly where it connects
Transform_fault
Measure preserving automorphism
{\displaystyle T} is called a K-automorphism, K-transform or K-shift, if there exists a sub-sigma algebra K ⊂ B {\displaystyle {\mathcal {K}}\subset {\mathcal {B}}}
Kolmogorov_automorphism
"Smoothing" integral transform
In mathematics, the Weierstrass transform of a function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } , named after Karl Weierstrass, is a
Weierstrass_transform
Generalization of the discrete Fourier transform
Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform of a
Fourier transform on finite groups
Fourier_transform_on_finite_groups
Programming idiom for efficiently sorting a list by a computed key
In computer programming, the Schwartzian transform is a technique used to improve the efficiency of sorting a list of items. This idiom is appropriate
Schwartzian_transform
Mathematical transformation on sequences
In mathematics, the boustrophedon transform is a procedure which maps one sequence to another. The transformed sequence is computed by an "addition" operation
Boustrophedon_transform
Method for solving certain nonlinear partial differential equations
In mathematics, the inverse scattering transform (or nonlinear Fourier transform) is a method that solves the initial value problem for a nonlinear partial
Inverse_scattering_transform
Integral transform generalizing both Laplace and Sumudu transforms
mathematics, the Shehu transform is an integral transform which generalizes both the Laplace transform and the Sumudu transform. It was introduced by Shehu
Shehu_transform
Integral transform introduced in 1990
The Sumudu transform is an integral transform introduced in 1990 by G K Watagala. It is defined over the set of functions A={f(t):∋M,p,q>0,|f(t)|≤Mexp(1/u)}
Sumudu_transform
Fourier-related mathematical transform
are given by: Z k = [ X k ( Y k + Y N − k ) + X N − k ( Y k − Y N − k ) ] / 2 Z N − k = [ X N − k ( Y k + Y N − k ) − X k ( Y k − Y N − k ) ] / 2 {\displaystyle
Discrete_Hartley_transform
sections of O ( k ) {\displaystyle {\mathcal {O}}(k)} . The Penrose–Ward transform is a nonlinear modification of the Penrose transform, introduced by
Penrose_transform
applied mathematics, the starred transform, or star transform, is a discrete-time variation of the Laplace transform, so-named because of the asterisk
Starred_transform
Fourier transform is a type of fast Fourier transform algorithm over finite fields. This algorithm first decomposes a discrete Fourier transform into several
Cyclotomic fast Fourier transform
Cyclotomic_fast_Fourier_transform
Time-frequency transform in geophysics
S transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the
S_transform
Mathematical transform using in signal processing
The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being
Modified discrete cosine transform
Modified_discrete_cosine_transform
projection X×Y→Y. Then the Fourier-Mukai transform ΦK is a functor Db(X)→Db(Y) given by F ↦ R p ∗ ( q ∗ F ⊗ L K ) {\displaystyle {\mathcal {F}}\mapsto \mathrm
Fourier–Mukai_transform
Stirling transform of a sequence { an : n = 1, 2, 3, ... } of numbers is the sequence { bn : n = 1, 2, 3, ... } given by b n = ∑ k = 1 n { n k } a k {\displaystyle
Stirling_transform
P_{n}(x)} as kernels of the transform. Legendre transform is a special case of Jacobi transform. The Legendre transform of a function f ( x ) {\displaystyle
Legendre transform (integral transform)
Legendre_transform_(integral_transform)
Discrete Fourier transform algorithm
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
Sparse_Fourier_transform
Mapping between functions in the quantum phase space
In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions
Wigner–Weyl_transform
. Then the point process ζ = ∑ k δ τ k {\displaystyle \zeta =\sum _{k}\delta _{\tau _{k}}} is called the ν-transform of the measure μ {\displaystyle
Nu-transform
Indian-American electrical engineer (1931 - 2021)
(UT Arlington). Academically known as K. R. Rao, he is credited with the co-invention of discrete cosine transform (DCT), along with Nasir Ahmed and T.
K._R._Rao
wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT)
Stationary_wavelet_transform
Mathematical algorithm
its Z-transform, which is simply a Laurent series, to the sequence of the coefficients with even indices, ( ↓ 2 ) ( c ( z ) ) = ∑ k ∈ Z c 2 k z − k {\displaystyle
Fast_wavelet_transform
Family of functions to transform data
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions. It is a data transformation
Power_transform
Mathematical operation
Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is
Mellin_transform
is a list of Laplace transforms for many common functions of a single variable. The Laplace transform is an integral transform that takes a function
List_of_Laplace_transforms
Fourier-related transform for signals that change over time
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections
Short-time_Fourier_transform
K.B. Wolf, "Integral Transforms in Science and Engineering", New York, Plenum Press, 1979. Almeida, Luís B. (1994). "The fractional Fourier transform
Transform_theory
Mathematical transform
In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors
Graph_Fourier_transform
Theorem in mathematics
suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution
Convolution_theorem
Theory of stochastic processes
∑ k = 1 N p k ≥ ∑ k = 1 N q k {\displaystyle \sum _{k=1}^{N}p_{k}\geq \sum _{k=1}^{N}q_{k}} This implies that: − ∑ k = 1 ∞ p k log ( p k ) ≤ − ∑ k =
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Mathematical identity in queueing theory
relationship between the queue length and service time distribution Laplace transforms for an M/G/1 queue (where jobs arrive according to a Poisson process and
Pollaczek–Khinchine_formula
Theorem in complex analysis
which the inverse Mellin transform, or equivalently the inverse two-sided Laplace transform, are defined and recover the transformed function. If φ ( s )
Mellin_inversion_theorem
First known wavelet basis
transform, whose matrix is composed of +1 and −1. Input and output length are the same. However, the length should be a power of 2, i.e. N = 2 k , k ∈
Haar_wavelet
Mathematical theorem about functions
Fourier transform § On Lp spaces). For example, putting g k ( ξ ) := ∫ { y ∈ R n : | y | ≤ k } e − 2 π i y ⋅ ξ f ( y ) d y , k ∈ N , {\displaystyle g_{k}(\xi
Fourier_inversion_theorem
Mathematical integral transform
{2}{\pi ^{2}x}}\int _{0}^{\infty }g(y)K_{iy}(x)\sinh(\pi y)y\,dy.} Laguerre previously studied a similar transform regarding Laguerre function as: g ( y
Kontorovich–Lebedev_transform
Theorem in mathematics
mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function
Parseval's_theorem
given function f(r), the Y-transform of order ν is given by F ( k ) = ∫ 0 ∞ f ( r ) Y ν ( k r ) k r d r {\displaystyle F(k)=\int _{0}^{\infty }f(r)Y_{\nu
Y_and_H_transforms
Transform in signal processing
chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Similar to the wavelet transform, chirplets
Chirplet_transform
Data compression
Transform coding is a type of data compression for "natural" data like audio signals or photographic images. The transformation is typically lossless
Transform_coding
Integral transform
transform is used to describe electromagnetic wave propagation in free space: U0(x,y)=−jλejkzz∫−∞∞∫−∞∞ejk2z[(x−xi)2+(y−yi)2]Ui(xi,yi)dxidyi, where k=2π/λ
Linear canonical transformation
Linear_canonical_transformation
Function for integral Fourier-like transform
= ∑ k c j 0 , k ϕ j 0 , k + ∑ j ≤ j 0 ∑ k d j , k ψ j , k {\displaystyle S=\sum _{k}c_{j_{0},k}\phi _{j_{0},k}+\sum _{j\leq j_{0}}\sum _{k}d_{j,k}\psi
Wavelet
Recursive algorithm in applied mathematics
windows differ by only one sample, so the transform for the new window can be obtained by updating the transform of the previous window rather than recomputing
Sliding_DFT
actuarial science, the Esscher transform (Gerber & Shiu 1994) is a transform that takes a probability density f(x) and transforms it to a new probability density
Esscher_transform
Reversible data-stream 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
Move-to-front_transform
Fractional wavelet transform (FRWT) is a generalization of the classical wavelet transform (WT). This transform is proposed in order to rectify the limitations
Fractional_wavelet_transform
Decomposition of periodic functions
k th {\displaystyle k^{\text{th}}} power of | n | {\displaystyle |n|} . One of the interesting properties of the Fourier transform which we have mentioned
Fourier_series
Statistical concept
statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson
Anscombe_transform
Theorem bounding the growth rate of analytic functions
or may not be of exponential type, and the kernel K ( u ) {\displaystyle K(u)} has a Mellin transform. The solution can be obtained using Nachbin summation
Nachbin's_theorem
Function used in signal processing
terms of its real-valued discrete Fourier transform, W0[k]: W0(k)=TN(βcos(πkN+1))TN(β)=TN(βcos(πkN+1))10α, 0≤k≤N. Tn(x) is the n-th Chebyshev polynomial
Window_function
Mathematical model which is both linear and time-invariant
is the Laplace transform or Z-transform of the system's impulse response, respectively. As a result of the properties of these transforms, the output of
Linear_time-invariant_system
British author (born 1965)
Duggan, Jennifer (28 March 2021). "Transformative readings: Harry Potter fan fiction, trans/queer reader response, and J. K. Rowling". Children's Literature
J._K._Rowling
Concept in probability theory and statistics
two-sided Laplace transform of its probability density function fX(x) holds: MX(t)=ℒ{fX}(−t), since the PDF's two-sided Laplace transform is given as
Moment_generating_function
Fast Fourier Transform algorithm
Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size N
Cooley–Tukey_FFT_algorithm
In mathematics, the Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P n
Jacobi_transform
Filter conversion technique
is transformed into the digital transfer function H ( z ) = k d ∏ i = 1 M ( 1 − e ξ i T z − 1 ) ∏ i = 1 N ( 1 − e p i T z − 1 ) {\displaystyle H(z)=k_{\mathrm
Matched_Z-transform_method
Mathematical operator acting on sequences
{\displaystyle T_{n}} of k n + 1 {\displaystyle k_{n}+1} variables for each n . {\displaystyle n.} See for instance the binomial transform and Aitken's delta-squared
Sequence_transformation
Theorem in mathematics
function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function
Projection-slice_theorem
Topics referred to by the same term
K-space or k-space can refer to: Another name for the spatial frequency domain of a spatial Fourier transform Reciprocal space, containing the reciprocal
K-space
South Korean popular music genre
K-pop (Korean: 케이팝; RR: Keipap; an abbreviation of "Korean popular music") is a form of popular music originating in South Korea. The music genre that
K-pop
K~(u)⋅L~(u)⋅ei2πNun (5) where u is the discrete frequency, K~(u) is the phase filter, L~(u) is the amplitude filter and FFT is fast Fourier transform
Phase_stretch_transform
Indian-American electrical engineer (1946–1988)
adaptive image estimation and image data compression", including work on transform coding for image compression and block-based motion compensation for video
Anil K. Jain (electrical engineer, born 1946)
Anil_K._Jain_(electrical_engineer,_born_1946)
mathematics, a discrete Chebyshev transform (abbreviated DCT, DChT, or DTT) is an analog of the discrete Fourier transform for a function of a real interval
Discrete_Chebyshev_transform
Square matrix in which each ascending skew-diagonal from left to right is constant
if one writes c n = ∑ k = 0 n ( n k ) b k {\displaystyle c_{n}=\sum _{k=0}^{n}{n \choose k}b_{k}} as the binomial transform of the sequence b n {\displaystyle
Hankel_matrix
) . {\displaystyle x(t)=\sum _{k}L_{x}(k)P_{k}(t).} The fLT should not be confused with the Legendre transform or Legendre transformation used in thermodynamics
Finite_Legendre_transform
fast Fourier transform algorithm. The transform uses a family of "harmonic" wavelets indexed by two integers j (the "level" or "order") and k (the "translation")
Harmonic_wavelet_transform
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K TRANSFORM
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