@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr: a skos:ConceptScheme .
psr:-RPTVHBSM-9
  skos:inScheme psr: ;
  skos:broader psr:-ZSN127JX-M ;
  skos:altLabel "transformation de Hilbert"@fr ;
  a skos:Concept ;
  skos:prefLabel "Hilbert transform"@en, "transformée de Hilbert"@fr ;
  skos:definition """In mathematics and signal processing, the <b>Hilbert transform</b> is a specific singular integral that takes a function, <span class="texhtml"><i>u</i>(<i>t</i>)</span> of a real variable and produces another function of a real variable <span class="texhtml">H(<i>u</i>)(<i>t</i>)</span>. The Hilbert transform is given by the Cauchy principal value of the convolution with the function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle 1/(\\\\pi t)}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mn>1</mn>
         <mrow class="MJX-TeXAtom-ORD">
         <mo>/</mo>
         </mrow>
         <mo stretchy="false">(</mo>
         <mi>π<!-- π --></mi>
         <mi>t</mi>
         <mo stretchy="false">)</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle 1/(\\\\pi t)}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5346b721e36c4a1e6d237e4020e71845e3ae70e2" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.306ex; height:2.843ex;" alt="{\\\\displaystyle 1/(\\\\pi t)}"></span>. The Hilbert transform has a particularly simple representation in the frequency domain: It imparts a phase shift of ±90° (<span class="texhtml mvar" style="font-style:italic;">π</span>/2 radians) to every frequency component of a function, the sign of the shift depending on the sign of the frequency. The Hilbert transform is important in signal processing, where it is a component of the analytic representation of a real-valued signal <span class="texhtml"><i>u</i>(<i>t</i>)</span>. The Hilbert transform was first introduced by David Hilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Hilbert_transform">https://en.wikipedia.org/wiki/Hilbert_transform</a>)"""@en, """En mathématiques et en traitement du signal, la transformation de Hilbert, ici notée <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\\\mathcal {H}}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mrow class="MJX-TeXAtom-ORD">
         <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi>
         </mrow>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle {\\\\mathcal {H}}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\\\\mathcal {H}}"></span>, d'une fonction de la variable réelle est une transformation linéaire qui permet d'étendre un signal réel dans le domaine complexe, de sorte qu'il vérifie les équations de Cauchy-Riemann. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Transformation_de_Hilbert">https://fr.wikipedia.org/wiki/Transformation_de_Hilbert</a>)"""@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Hilbert_transform>, <https://fr.wikipedia.org/wiki/Transformation_de_Hilbert> .

psr:-ZSN127JX-M
  skos:prefLabel "opérateur intégral"@fr, "integral transform"@en ;
  a skos:Concept ;
  skos:narrower psr:-RPTVHBSM-9 .