In signal processing, the adjoint filter mask of a filter mask is reversed in time and the elements are complex conjugated.[1][2][3]
Its name is derived from the fact that the convolution with the adjoint filter is the adjoint operator of the original filter, with respect to the Hilbert space of the sequences in which the inner product is the Euclidean norm.
The autocorrelation of a signal can be written as .
^Broughton, S. Allen; Bryan, Kurt M. (2011-10-13). Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing. John Wiley & Sons. p. 141. ISBN 9781118211007.
^Koornwinder, Tom H. (1993-06-24). Wavelets: An Elementary Treatment of Theory and Applications. World Scientific. p. 70. ISBN 9789814590976.
^Andrews, Travis D.; Balan, Radu; Benedetto, John J.; Czaja, Wojciech; Okoudjou, Kasso A. (2013-01-04). Excursions in Harmonic Analysis, Volume 2: The February Fourier Talks at the Norbert Wiener Center. Springer Science & Business Media. p. 174. ISBN 9780817683795.
In signal processing, the adjointfilter mask h ∗ {\displaystyle h^{*}} of a filter mask h {\displaystyle h} is reversed in time and the elements are...
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements...
Laurent-polynomial a ∗ ( z ) {\displaystyle a^{*}(z)} denotes the adjointfilter, it has time-reversed adjoint coefficients, a ∗ ( z ) = ∑ n = − N N a − n ∗ z − n {\displaystyle...
{R}}f(\alpha ,s)e^{-2\pi isr}\,ds.} The dual Radon transform is a kind of adjoint to the Radon transform. Beginning with a function g on the space Σ n {\displaystyle...
applications include image processing, where it is known as the Laplace filter, and in machine learning for clustering and semi-supervised learning on...
y\iff x\leq g(y)} where f is called the lower adjoint and g is called the upper adjoint. By the adjoint functor theorem, a monotone map between any pair...
'local' theory. The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry...
T Γ {\displaystyle A^{*}A+\Gamma ^{\mathsf {T}}\Gamma } is then a self-adjoint bounded invertible operator. With Γ = α I {\displaystyle \Gamma =\alpha...
contains no "cycles": equivalently, its transitive closure is antisymmetric. Adjoint. See Galois connection. Alexandrov topology. For a preordered set P, any...
{H}}^{\dagger }.} Operators like this that are equal to their adjoints are called Hermitian or self-adjoint. The infinitesimal transition of the polarization state...
and addition, respectively. Both of these functors have left adjoints. The left adjoint of A is the functor which assigns to every abelian group X (thought...
field. They also represent the interaction states of two polarization filters for horizontal / vertical polarization, 45 degree polarization (right/left)...
Categorically, the group ring construction is left adjoint to "group of units"; the following functors are an adjoint pair: R [ − ] : G r p → R - A l g {\displaystyle...
{\displaystyle L^{p}(\mathbb {R} )} . The Hilbert transform is an anti-self adjoint operator relative to the duality pairing between L p ( R ) {\displaystyle...
set lattices is equivalent to finding a functor from Frm to Top which is adjoint to Ω. The goal of this section is to define a functor pt from Frm to Top...
theory, which asserts that the composition of two left adjoint functors is also a left adjoint functor. Here, the forgetful functor from commutative algebras...
are then the axiomatization of prederivators which come equipped with adjoint functors f ? ⊣ f ! ⊣ f ∗ ⊣ f ∗ ⊣ f ! {\displaystyle f^{?}\dashv f_{!}\dashv...
in the space of the input (hence the 'local' in the name of the class). Adjoint modelling and Automated Differentiation are methods which allow to compute...
satisfying some conservation laws and the construction of the ocean model adjoint. Meteorological reanalysis Carton, J.A., and A. Santorelli, 2008: Global...
( ⇒: H × H → H {\displaystyle \Rightarrow :H\times H\to H} ) is right adjoint to meet ( ∧ : H × H → H {\displaystyle \wedge :H\times H\to H} ). This...
derivatives. The calculus has applications in, for example, stochastic filtering. Malliavin introduced Malliavin calculus to provide a stochastic proof...
was based in turn on the theory of projection-valued measures for self-adjoint operators which had been recently developed (by von Neumann and independently...
. For complex-valued functions, the cross-correlation operator is the adjoint of the convolution operator. Convolution has applications that include...
under the proper conditions it may be expected to result from a self-adjoint generator N {\displaystyle N} via F [ ψ ] = e − i t N ψ . {\displaystyle...
missions include: police and security in civilian airfields and airports; filtering access to aircraft, counter-terrorism and counter-narcotic activities...
is a generalization of the fiber product. Exponentiation is the right adjoint of the Cartesian product; thus any category with a Cartesian product (and...
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