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Hilbert transform

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 another function of a real variable H(u)(t). The Hilbert transform is given by the Cauchy principal value of the convolution with the function 1 / ( π t ) {\displaystyle 1/(\pi t)} (see § Definition). The…

History, Properties & Hilbert transform in signal processing

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Overview

Definition

History

Relationship with the Fourier transform

Table of selected Hilbert transforms

Domain of definition

Properties

Extending the domain of definition

Conjugate functions

Hilbert transform on the circle

Hilbert transform in signal processing

Discrete Hilbert transform

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Hilbert transform

Nodes100
Edges99
Triples127
Avg. degree1.98
Density0.02
Components1

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Hilbert transform

Top relations

related to history · 19
Hilbert transform → Alberto Calderón, Antoni Zygmund, Discrete Hilbert Transform, Göttingen, Hermann Weyl, Hilbert, Hilbert's, In, L2, Lp, Marcel Riesz, Riemann, Schur, Some, The, The Hilbert, Their, These, Various
related to External links · 10
Hilbert transform → Archived, Contains, Derivation, Eric, GS256 Lecture, Hilbert, Hilbert Transformation, MathWorld, PDF, Titchmarsh
is a · 9
Hilbert transform → anti-involution, anti-self adjoint operator relative to the duality pairing between L p, bounded operator from L1 to L1, bounded operator on L p, extension of the discrete Hilbert transform to integers modulo an appropriate prime number, Hilbert transform of the derivative, multiplier operator, only bounded operator on L2 with these properties.In fact there is a wider set of operators that commute with the Hilbert transform, specific singular integral that takes a function
related to Complex structure · 9
Hilbert transform → Banach, Because H2, H2, Hardy, Hilbert, In, Paley, The, Wiener
related to Hilbert transform of bounded functions · 8
Hilbert transform → Banach, BMO, For, Hilbert, Interpreted, Properly, The Hilbert, To
related to Hilbert transform of distributions · 7
Hilbert transform → Chapter, Hilbert, It, Lp, Pandey, Since, Sobolev
related to Titchmarsh's theorem · 7
Hilbert transform → H2, Hardy, Hilbert, It, The, Titchmarsh, Titchmarsh's
related to Conjugate functions · 6
Hilbert transform → Hilbert, Poisson, Suppose, The Hilbert, Then, Under
related to Definition · 6
Hilbert transform → Because, Cauchy, Explicitly, Hilbert, Instead, The Hilbert
related to Notation · 6
Hilbert transform → Fourier, Furthermore, Hilbert, However, In, Occasionally

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Important terminology

displaystyle transform hilbert function operatorname mathbb convolution functions frac pi frequency real infty integral analytic fourier left right theorem signal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hilbert transformis aspecific singular integral that takes a function0.90text
Hilbert transformis abounded operator on L p0.90text
Hilbert transformis amultiplier operator0.90text
Hilbert transformis abounded operator from L1 to L10.90text
Hilbert transformis aanti-self adjoint operator relative to the duality pairing between L p0.90text
Hilbert transformis aanti-involution0.90text
Hilbert transformis aHilbert transform of the derivative0.90text
Hilbert transformis aonly bounded operator on L2 with these properties.In fact there is a wider set of operators that commute with the Hilbert transform0.90text
Hilbert transformis aextension of the discrete Hilbert transform to integers modulo an appropriate prime number0.90text
Hilbert transformrelated to Anti-self adjointnessThe Hilbert0.60section
Hilbert transformrelated to Anti-self adjointnessHölder0.60section
Hilbert transformrelated to Anti-self adjointnessSymbolically0.60section

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