This dissertation describes research whose the purpose is to remove artefacts from the EEG signals of preterm neonates, thereby facilitating the prediction of carbon dioxide levels dissolved in the blood; this was achieved using key statistics obtained from the EEG. The EEG signals of neonates were recorded over a 24 - 36 hours period using LabVIEW (National Instruments) software and a XLTEK EMU40EX breakout head box with a 7- electrodes configuration. Raw EEG signals of neonates were processed using discrete wavelet transform multiresolution analysis to remove artefacts. A nonlinear energy operator was used to calculate the energy of the artefact-free neonate's EEG signals. Threshold detection was used to find the bursts and the interburst intervals. Spectral power analysis was performed on every burst-interburst interval cycle to calculate the relative powers in the delta (0.5-3.5 Hz), theta (4.0-7.5 Hz), alpha (8-12.5 Hz), and beta (13-30 Hz) frequency bands in each burst-interburst interval cycle of the neonate's EEG signals. A two minute arithmetic average of the interburst intervals, and the burst-interburst interval relative powers were used to develop a linear regression equation for the prediction of the carbon dioxide level. The EEG signals of different gestational age neonates were processed offline. Results were compared with the readings of ABL800 FLEX blood gas analyser (a blood gas machine) with a measuring range of 0.67 - 33.3 kilopascals. For the clean neonate's EEG signals, the absolute prediction error lay between 0 - 1.0 kilopascals.