About: Number theoretic Hilbert transform

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

The number theoretic Hilbert transform is an extension of the discrete Hilbert transform to integers modulo a prime . The transformation operator is a circulant matrix. The number theoretic transform is meaningful in the ring , when the modulus is not prime, provided a principal root of order n exists. The NHT matrix, where , has the form The rows are the cyclic permutations of the first row, or the columns may be seen as the cyclic permutations of the first column. The NHT is its own inverse: where I is the identity matrix.

Property Value
dbo:abstract
  • The number theoretic Hilbert transform is an extension of the discrete Hilbert transform to integers modulo a prime . The transformation operator is a circulant matrix. The number theoretic transform is meaningful in the ring , when the modulus is not prime, provided a principal root of order n exists. The NHT matrix, where , has the form The rows are the cyclic permutations of the first row, or the columns may be seen as the cyclic permutations of the first column. The NHT is its own inverse: where I is the identity matrix. The number theoretic Hilbert transform can be used to generate sets of orthogonal discrete sequences that have applications in signal processing, wireless systems, and cryptography. Other ways to generate constrained orthogonal sequences also exist. (en)
dbo:wikiPageID
  • 44982289 (xsd:integer)
dbo:wikiPageLength
  • 2253 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1056871653 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • The number theoretic Hilbert transform is an extension of the discrete Hilbert transform to integers modulo a prime . The transformation operator is a circulant matrix. The number theoretic transform is meaningful in the ring , when the modulus is not prime, provided a principal root of order n exists. The NHT matrix, where , has the form The rows are the cyclic permutations of the first row, or the columns may be seen as the cyclic permutations of the first column. The NHT is its own inverse: where I is the identity matrix. (en)
rdfs:label
  • Number theoretic Hilbert transform (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageDisambiguates of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License