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- Hilbert_transform abstract "In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u(t), and produces a function, H(u)(t), 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 Riemann–Hilbert problem for holomorphic functions. It is a basic tool in Fourier analysis, and provides a concrete means for realizing the harmonic conjugate of a given function or Fourier series. Furthermore, in harmonic analysis, it is an example of a singular integral operator, and of a Fourier multiplier. The Hilbert transform is also important in the field of signal processing where it is used to derive the analytic representation of a signal u(t).The Hilbert transform was originally defined for periodic functions, or equivalently for functions on the circle, in which case it is given by convolution with the Hilbert kernel. More commonly, however, the Hilbert transform refers to a convolution with the Cauchy kernel, for functions defined on the real line R (the boundary of the upper half-plane). The Hilbert transform is closely related to the Paley–Wiener theorem, another result relating holomorphic functions in the upper half-plane and Fourier transforms of functions on the real line.".
- Hilbert_transform thumbnail Hilbert_transform.svg?width=300.
- Hilbert_transform wikiPageExternalLink 0909.1426.
- Hilbert_transform wikiPageExternalLink Analytic_Signals_Hilbert_Transform.html.
- Hilbert_transform wikiPageExternalLink HilbertTransform.html.
- Hilbert_transform wikiPageExternalLink mj_ex.pdf.
- Hilbert_transform wikiPageExternalLink GS256_Lecture3.pdf.
- Hilbert_transform wikiPageExternalLink hilbert.html;jsessionid=67ed4e69e9729363548abed31054.
- Hilbert_transform wikiPageExternalLink RM3439.pdf.
- Hilbert_transform wikiPageExternalLink mj_ex.pdf.
- Hilbert_transform wikiPageExternalLink GS256_Lecture3.pdf.
- Hilbert_transform wikiPageID "574024".
- Hilbert_transform wikiPageRevisionID "601551154".
- Hilbert_transform first "A.V.".
- Hilbert_transform first "B.V.".
- Hilbert_transform hasPhotoCollection Hilbert_transform.
- Hilbert_transform id "H/h047430".
- Hilbert_transform id "b/b017400".
- Hilbert_transform last "Bitsadze".
- Hilbert_transform last "Khvedelidze".
- Hilbert_transform title "Boundary value problems of analytic function theory".
- Hilbert_transform title "Hilbert transform".
- Hilbert_transform title "Titchmarsh theorem".
- Hilbert_transform urlname "TitchmarshTheorem".
- Hilbert_transform year "2001".
- Hilbert_transform subject Category:Harmonic_functions.
- Hilbert_transform subject Category:Integral_transforms.
- Hilbert_transform subject Category:Signal_processing.
- Hilbert_transform subject Category:Singular_integrals.
- Hilbert_transform type Abstraction100002137.
- Hilbert_transform type Calculation105802185.
- Hilbert_transform type Cognition100023271.
- Hilbert_transform type Function113783816.
- Hilbert_transform type HarmonicFunctions.
- Hilbert_transform type HigherCognitiveProcess105770664.
- Hilbert_transform type Integral106015505.
- Hilbert_transform type MathematicalRelation113783581.
- Hilbert_transform type ProblemSolving105796750.
- Hilbert_transform type Process105701363.
- Hilbert_transform type PsychologicalFeature100023100.
- Hilbert_transform type Relation100031921.
- Hilbert_transform type SingularIntegrals.
- Hilbert_transform type Thinking105770926.
- Hilbert_transform comment "In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u(t), and produces a function, H(u)(t), 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 Riemann–Hilbert problem for holomorphic functions. It is a basic tool in Fourier analysis, and provides a concrete means for realizing the harmonic conjugate of a given function or Fourier series.".
- Hilbert_transform label "Hilbert transform".
- Hilbert_transform label "Hilbert-Transformation".
- Hilbert_transform label "Transformada de Hilbert".
- Hilbert_transform label "Transformada de Hilbert".
- Hilbert_transform label "Transformata Hilberta".
- Hilbert_transform label "Transformée de Hilbert".
- Hilbert_transform label "Trasformata di Hilbert".
- Hilbert_transform label "Преобразование Гильберта".
- Hilbert_transform label "تحويل هيلبرت".
- Hilbert_transform label "希爾伯特轉換".
- Hilbert_transform sameAs Hilbert-Transformation.
- Hilbert_transform sameAs Transformada_de_Hilbert.
- Hilbert_transform sameAs Transformée_de_Hilbert.
- Hilbert_transform sameAs Trasformata_di_Hilbert.
- Hilbert_transform sameAs Transformata_Hilberta.
- Hilbert_transform sameAs Transformada_de_Hilbert.
- Hilbert_transform sameAs m.02rhxt.
- Hilbert_transform sameAs Q685437.
- Hilbert_transform sameAs Q685437.
- Hilbert_transform sameAs Hilbert_transform.
- Hilbert_transform wasDerivedFrom Hilbert_transform?oldid=601551154.
- Hilbert_transform depiction Hilbert_transform.svg.
- Hilbert_transform isPrimaryTopicOf Hilbert_transform.