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

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.