Multi-dimensional higher order differential operators derived from the Teager-Kaiser energy-tracking function

Authors:
F. Salzenstein;A. O. Boudraa
Affiliations:
Laboratoire INESS, UMR CNRS 7163 Université Strasbourg 1 (ULP), France;IRENav, Ecole Navale/E3I2 (EA 3876) ENSIETA, Lanvéoc Poulmic, BP600, 29240 Brest-Armées, France
Venue:
Signal Processing
Year:
2009

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Abstract

This paper introduces a new multi-dimensional higher order operator derived from the Teager-Kaiser energy-tracking function. A mathematical model which integrates different existing non-linear operators at any orders is constructed. The proposed non-linear continuous filter is computed using tensors provided by the Kronecker products of higher order derivatives of the signal. In particular, the introduced operator takes into account the diagonal directions through the partial derivatives. We prove that there is a recurrence relationship that allows us to deduce all functions at different orders. To show the effectiveness of the proposed operator, demodulation of noisy multi-dimensional amplitude-modulation (AM)-frequency-modulation (FM) signals are presented and results compared to those of some well-known demodulation approaches.