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23 septembre 2011
- ISIDORE Id: 10670/1.32c60b...
- hal: hal-00664787
- doi: 10.1080/17459737.2011.608820
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info:eu-repo/semantics/altIdentifier/doi/10.1080/17459737.2011.608820
info:eu-repo/semantics/OpenAccess
Mots-clés
GIS (generalized interval systems) interval vector Patterson function Z-relation homometry phase retrieval spectral units k-deck AMS MSC 05E15, 20H15, 43A20Sujets proches
Results of analysis Analysis results Lebesgue's integral Integration, Lebesgue L-integral Lebesgue-Stieltjes integral Stieltjes integral, Lebesgue- Lebesgue integration Function, Patterson Patterson functions Units Measurement, Units of Groups, Topological Show business Papers Old and new New, The Serious music Musical compositions Art music Musical works Classical music Western music (Western countries) Art music, Western Western art music Products, Manufactured Manufactured goods Products Manufactured products Algebras, Group Case Structures Edifices HallsCiter ce document
John Mandereau et al., « Discrete phase retrieval in musical structures », HAL SHS (Sciences de l’Homme et de la Société), ID : 10.1080/17459737.2011.608820
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Résumé
This paper describes phase-retrieval approaches in music by focusing on the particular case of the cyclic groups (beltway problem). After presenting some old and new results on phase retrieval, we introduce the extended phase retrieval for a generalized musical Z-relation. This concept is accompanied by mathematical definitions and motivations from computer-aided composition. We assume from the reader basic knowledge of groups, topological groups, group algebras, group actions, Lebesgue integration, convolution products, and Fourier transform.
