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.

Statistical properties of real-valued symmetric -stable noise after short-time Fourier transformation are derived. Circularity, stationarity and dependence between the real and imaginary components are studied as a function of the STFT parameters and the stability index.

This paper addresses the maximizing network lifetime problem in wireless sensor networks (WSNs) taking into account the total Symbol Error rate (SER) at destination. Therefore, efficient power management is needed for extend network lifetime. Our approach consists to provide the optimal transmission power using the orthogonal multiple access channels between each sensor. In order to deeply study the properties of our approach, firstly, the simple case is considered; the information sensed by the source node passes by a single relay before reaching the destination node. Secondly, global case is studied; the information passes by several relays. We consider, in the previous both cases, that the batteries are nonrechargeable. Thirdly, we spread our work the case where the batteries are rechargeable with unlimited storage capacity. In all three cases, we suppose that Maximum Ratio Combining (MRC) is used as a detector, and Amplify and Forward (AF) as a relaying strategy. Simulation results show the viability of our approach which the network lifetime is extended of more than 70.72%when the batteries are non rechargeable and 100.51% when the batteries are rechargeable in comparison with other traditional method.

Statistical model of sea clutter is approximated as the product of speckle and texture characterized respectively by a short and long decorrelation times. This paper introduces two approaches for the estimation of such texture. The first approach exploits the physical properties of the correlation time and the energy of texture and speckle. To identify the texture range profile from one pulse radar frequency to another, we combine the AR estimation of sea clutter auto-covariance with the Empirical Orthogonal Functions. The second approach employs a mixed l2-l1 norm minimization criterion to account for the sparse harmonic structure of the texture.