Background: In order to monitor the health of new borns , high performance sensors are placed on the body to record information from different organs: nervous system (EEG signals), heartbeat and fetal movement (accelerometer signals). As the received data are non-stationary signals, Quadratic Time-frequency distributions (QTFDs) are often used to represent the energy, temporal and spectral characteristics of these signals. The suitable QTFD should conserve a high resolution and removes the cross-terms artifacts given by inner- and outer- terms. The inner-terms artifacts are observed in mono-component signals. Due to the Quadratic form of the QTFD, outer-terms are added to inner-terms if the signal contains more than one component. Recent QTFDs such as Wigner-Ville distribution, Spectrogram, B distribution, Modified B-Distribution, Choi-Williams, focus on the elimination of outer-terms whereas few works dealt with the inner-terms artifacts. Objectives: This work aims at designing a new kernel that takes into account the presence of both inner-terms and outer-terms artifacts. The proposed QTFD should remove these artifacts while maintaining a high resolution. Methods: A theoretical analysis of the localization of the inner-terms is given. Based on this analysis, we propose first a new kernel that removes the inner-terms for mono-component signal. Multicomponent signals are also considered, in which case we extend the proposed kernel in order to take into account the presence of the outer-terms. Results and conclusion: The resulting TFDs are compared with other methods using several examples of mono-component and multi-component signals. Some real data representing EEG signals and fetal movement are also used. The different simulations indicate that the proposed TFDs are more efficient to the existing ones, leading to potential significant improvement in newborn health outcomes. This work is supported by Qatar National Research Fund, NPRP project No 09-626-2-243


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