| dbo:abstract |
The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional function when it corresponds to the Fourier transform of one-dimensional functions. It is complex-valued and has a constant (typically unity) magnitude everywhere. When depicted, e.g. for teaching purposes, it may be visualized by its separate real and imaginary parts, or as a colour image using a colour wheel to denote phase. It is usually denoted by a capital letter "F" in script font, e.g. the Fourier transform of a function would be written using the operator as . It may be thought of as a limiting case for when the size of the discrete Fourier transform increases without bound while its spatial resolution also increases without bound, so as to become both continuous and not necessarily periodic. (en) |
| dbo:thumbnail |
wiki-commons:Special:FilePath/Fourieropr.png?width=300 |
| dbo:wikiPageID |
1091252 (xsd:integer) |
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3787 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1113840335 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbc:Fourier_analysis dbr:DFT_matrix dbr:Limiting_case_(mathematics) dbr:Chirplet_transform dbr:Least-squares_spectral_analysis dbr:Fractional_Fourier_transform dbc:Unitary_operators dbc:Integral_transforms dbr:Discrete_Fourier_transform dbr:Fredholm_integral_equation dbr:Integral_kernel dbr:Continuous_Fourier_transform dbr:File:Fourieroperator_equation_visualization.png |
| dbp:caption |
Imaginary part (en) Real part (en) |
| dbp:footer |
A plot of the Fourier operator (en) |
| dbp:image |
Fourieropi.png (en) Fourieropr.png (en) |
| dbp:width |
160 (xsd:integer) |
| dbp:wikiPageUsesTemplate |
dbt:Multiple_image dbt:Reflist |
| dcterms:subject |
dbc:Fourier_analysis dbc:Unitary_operators dbc:Integral_transforms |
| gold:hypernym |
dbr:Kernel |
| rdf:type |
dbo:Software yago:WikicatUnitaryOperators yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Operator113786413 yago:Relation100031921 |
| rdfs:comment |
The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional function when it corresponds to the Fourier transform of one-dimensional functions. It is complex-valued and has a constant (typically unity) magnitude everywhere. When depicted, e.g. for teaching purposes, it may be visualized by its separate real and imaginary parts, or as a colour image using a colour wheel to denote phase. (en) |
| rdfs:label |
Fourier operator (en) |
| owl:sameAs |
freebase:Fourier operator yago-res:Fourier operator wikidata:Fourier operator https://global.dbpedia.org/id/4jMbY |
| prov:wasDerivedFrom |
wikipedia-en:Fourier_operator?oldid=1113840335&ns=0 |
| foaf:depiction |
wiki-commons:Special:FilePath/Fourieroperator_equation_visualization.png wiki-commons:Special:FilePath/Fourieropi.png wiki-commons:Special:FilePath/Fourieropr.png |
| foaf:isPrimaryTopicOf |
wikipedia-en:Fourier_operator |
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dbr:Fourier |
| is dbo:wikiPageWikiLink of |
dbr:DFT_matrix dbr:Unitary_operator dbr:Parametric_array dbr:Fourier dbr:List_of_Fourier_analysis_topics |
| is foaf:primaryTopic of |
wikipedia-en:Fourier_operator |
