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Relationships between Psi_B energy operator and some time-frequency representations

hal.structure.identifierInstitut de Recherche de l'Ecole Navale [IRENAV]
dc.contributor.authorBOUDRAA, Abdel-Ouahab
dc.date.accessioned2021-05-14T09:58:53Z
dc.date.available2021-05-14T09:58:53Z
dc.date.issued2010-06
dc.identifier.issn1070-9908
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/77985
dc.descriptionPsi_B operator is an energy operator that measures the interactions between two complex signals. In this letter, new properties of Psi_B operator are presented. Connections between Psi_B operator and some time-frequency representations (cross ambiguity function, short-time Fourier transform, Zak transform, and Gabor coefficients) are established. Link between Psi_B operator of two input signals and their cross-spectrum is also derived. For two equal input signals, we find that Fourier transform of Psi_B operator is proportional to the second derivative of the ambiguity function. The established links show the ability of Psi_B operator to analyze non stationary signals. A numerical example is provided for illustrating how to estimate the second order moment, of a FM signal, using Psi_B operator. We compare the result to the moment given by the Wigner-Ville distribution
dc.description.abstractEnPsi_B operator is an energy operator that measures the interactions between two complex signals. In this letter, new properties of Psi_B operator are presented. Connections between Psi_B operator and some time-frequency representations (cross ambiguity function, short-time Fourier transform, Zak transform, and Gabor coefficients) are established. Link between Psi_B operator of two input signals and their cross-spectrum is also derived. For two equal input signals, we find that Fourier transform of Psi_B operator is proportional to the second derivative of the ambiguity function. The established links show the ability of Psi_B operator to analyze non stationary signals. A numerical example is provided for illustrating how to estimate the second order moment, of a FM signal, using Psi_B operator. We compare the result to the moment given by the Wigner-Ville distribution
dc.language.isoen
dc.publisherIEEE
dc.publisherInstitute of Electrical and Electronics Engineers
dc.subjectGabor coefficients
dc.subjectFourier transform
dc.subjectShort-time
dc.subjectCross-ambiguity function
dc.subjectPsi_B energy operator
dc.subjectCross-spectrum
dc.subjectOpérateur d'énergie Psi_B
dc.subjectfonctiond'Ambiguïté croisée
dc.subjectTransformée de Fourier à Court terme
dc.subjectcoefficients de Gabor
dc.subjectspectre croisé
dc.title.enRelationships between Psi_B energy operator and some time-frequency representations
dc.typeArticle de revue
dc.identifier.doi10.1109/LSP.2010.2045548
dc.subject.halSciences de l'ingénieur [physics]/Traitement du signal et de l'image
bordeaux.journalIEEE Signal Processing Letters
bordeaux.page527-530
bordeaux.volume17
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue6
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01083621
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01083621v1
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