A new class of multi-dimensional Teager Kaiser and higher order operators based on directional derivatives
| hal.structure.identifier | Institut d'Électronique du Solide et des Systèmes de Strasbourg [InESS] | |
| dc.contributor.author | SALZENSTEIN, Fabien | |
| hal.structure.identifier | Institut de Recherche de l'Ecole Navale [IRENAV] | |
| dc.contributor.author | BOUDRAA, Abdel-Ouahab | |
| hal.structure.identifier | Lab-STICC_TB_CID_TOMS | |
| hal.structure.identifier | Département Signal et Communications [SC] | |
| dc.contributor.author | CHONAVEL, Thierry | |
| dc.date.accessioned | 2021-05-14T10:04:39Z | |
| dc.date.available | 2021-05-14T10:04:39Z | |
| dc.date.issued | 2013-09 | |
| dc.identifier.issn | 0923-6082 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/78504 | |
| dc.description | This work aims at introducing some energy operators linked to Teager-Kaiser energy operator and its associated higher order versions and expand them to multidimensional signals. These operators are very useful for analyzing oscillatory signals with time-varying amplitude and frequency (AM-FM). We prove that gradient tensors combined with Kronecker powers allow to express these operators by directional derivatives along any n-D vector. In particular, we show that the construction of a large class of non linear operators for AM-FM multidimensional signal demodulation is possible. Also, a new scalar function using the directional derivative along a vector giving the ”sign” of the frequency components is introduced. An application of this model to local n-D AM-FM signal is presented and related demodulation error rates estimates. To show the effectiveness and the robustness of our method in term of envelope and frequency components extraction, results obtained on synthetic and real data are compared to multi-dimensional energy separation algorithm and to our recently introduced n-D operator. | |
| dc.description.abstractEn | This work aims at introducing some energy operators linked to Teager-Kaiser energy operator (TKEO) (Kaiser, 1990), its associated higher order versions and expanding them to multi-dimensional signals. These operators are very useful for analysing oscillatory signals with time-varying amplitude and frequency (AMFM). We first propose a new mathematical expression of these operators using directional derivatives along any n-D vector and Kronecker powers (proposition 1, section 3). This mathematical formulation allows us to extend to n-D case some properties of the classical TKEO such as tracking of AM envelope and instantaneous frequency of a multi-dimensional AM-FM signal. In addition, we have introduced a new scalar function using the directional derivative along a vector to recover the "sign" of the frequency components . Applications of this model to a local n-D AM-FM signal and the related demodulation errors are presented. To show the effectiveness and the robustness of the new class of operators in term of envelope and frequency tracking, results obtained on synthetic and real data are compared to multi-dimensional energy separation algorithm (Maragos and Bovik, 1995) and to our previously developed method (Salzenstein and Boudraa, 2009). Finally, the performances of these methods are investigated in the presence of an additive noise. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.publisher | Springer Verlag | |
| dc.title.en | A new class of multi-dimensional Teager Kaiser and higher order operators based on directional derivatives | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s11045-012-0179-2 | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Traitement du signal et de l'image | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| bordeaux.journal | Multidimensional Systems and Signal Processing | |
| bordeaux.page | 543-572 | |
| bordeaux.volume | 24 | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00704168 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00704168v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Multidimensional%20Systems%20and%20Signal%20Processing&rft.date=2013-09&rft.volume=24&rft.issue=3&rft.spage=543-572&rft.epage=543-572&rft.eissn=0923-6082&rft.issn=0923-6082&rft.au=SALZENSTEIN,%20Fabien&BOUDRAA,%20Abdel-Ouahab&CHONAVEL,%20Thierry&rft.genre=article |
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