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In this research, two different approaches for detecting seizure patterns in newborns' Electroencephalogram (EEG) signals are compared. The first proposed approach is a time-frequency (TF) based method, in which, the discrimination between seizure and non-seizure states is based on the TF distance between the consequent segments in the EEG signal. Three different TF measures and three different reduced time-frequency distributions (TFD) are used in this study. The second proposed approach is a discrete wavelet transform (DWT) based method, in which, the detection scheme is based on observing the changing behavior of few statistical quantities of the wavelet coefficients (WCs) of the EEGs at various scales. These statistics form a feature set which is fed into an artificial neural network (ANN) classifier to organize the EEG signals into seizure and non-seizure activities. The proposed methods are tested on the EEG data acquired from three neonates with ages under two weeks. The empirical results validate the suitability of the two proposed methods in automated newborns' seizure detection. The results present an average seizure detection rate (SDR) of 96% and false alarm rate (FAR) of 5% using Kullback-Leibler measure which outperforms the other two distance measures and the DWT based method.