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Prior to birth, fetus health can be monitored by the variety and scale of its movements. In addition, at birth, EEG signals are recorded from at-risk newborns. Studies have shown that both fetal movements and newborn EEGs are non-stationary signals. This paper aims to represent both newborn EEG and fetal movement signals in a time-frequency domain using a specifically designed time-frequency distribution (TFD) that is well adapted to these types of data for the purpose of analysis, detection and classification. The approach to design the quadratic TFDS is based on relating separable-kernel TFDS to DSP spectral window and digital filter design. To reach this goal, we compared recently proposed TFDs such as the Modified B distribution, a separable Gaussian distribution and the B distribution. Then, an extension of the modified B distribution (MBD) is proposed, referred to as the extended separable-kernel MBD. This new TFD uses a separable kernel based on an extension of the modified B kernel in both time and frequency domain with different windows for each domain. Simulation results are provided to compare the proposed Method with different TFDs and to assess its performance. The new TFD is then first applied to real fetal movement data recorded using accelerometers.