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A New class of multi-dimensional Teager Kaiser and higher order operators based on directional derivatives

Une nouvelle classe d'opérateurs de Teager-Kaiser multidimensionnels basée sur les dérivées directionnelles d'ordre supérieur

Article dans une revue avec comité de lecture
Author
SALZENSTEIN, Fabien
3211 Institut d'Electronique du Solide et des Systèmes [InESS]
ccBOUDRAA, Abdel-Ouahab
13094 Institut de Recherche de l'Ecole Navale [IRENAV]
CHONAVEL, Thierry
98040 Département Signal et Communications [SC]

URI
http://hdl.handle.net/10985/8857
DOI
10.1007/s11045-012-0179-2
Date
2013
Journal
Multidimensional Systems and Signal Processing

Abstract

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.

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