Fetal movements are clinically correlated to fetal wellbeing. Ultrasounds are the most accurate measurements of the fetal movement but expensive and intrusive. To avoid these constraints, Fetal activity is captured through data acquired using low cost and nonintrusive accelerometer . Time-frequency distributions (TFDs) are often used to represent the energy, temporal and spectral characteristics of non-stationary signals in the time and frequency plane.

Many quadratic TFDs were proposed in the literature such as Wigner-Ville distribution, Spectrogram, B-Distribution, Choi-Williams , etc. The drawbacks of the majority of these techniques is that only a few parameters can be modified in the kernel, generally the lag and Doppler parameters, so that they cannot be easily adapted to the data.

This work aims at designing a new kernel with several parameters that leads to a higher resolution time frequency representation (TFR) of the signal, therefore improving the characteristic of the fetal movement.

The proposed TFD can be considered as an extension of the Gaussian TFD (also called Choi-Williams distribution). The kernel function of the proposed kernel is given by the sum of the weighted derivative Gaussian TFD (refer to the equation).

The weighted parameters in the above formula can be estimated by maximizing the concentration of the instantaneous frequency. The resulting TFD is compared with other methods and applied to the analysis and classification of the fetal movement data recorded by the accelerometers. The results obtained indicate that the proposed time-frequency methodology allows the detection of fetal movement data recorded by accelerometers.


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