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Electroencephalography (EEG) is a well-established tool to assess the neonatal brain health. However, the EEG recordings are usually contaminated by eye blinks and movement artifacts, muscle noise, cardiac signals and powerline interference. In this paper, we are exploiting the linearization property of Finite Impulse Response (FIR) filter to remove these artifacts. Moreover, the 50Hz powerline noise is filtered out by band pass filter with the frequency range of 0-40 Hz. Power spectral density (PSD), kurtosis and skewness was used to evaluate the EEG signal after filtering. The results demonstrate that the proposed approach can remove artifacts efficiently.