Automated analysis of the neonatal EEG has the potential to assist clinical decision making for neonates with hypoxic-ischaemic encephalopathy. This paper proposes a method of automatically grading the degree of abnormality in an hour long epoch of neonatal EEG. The automated grading system (AGS) was based on a multi-class linear classifier grading of short-term epochs of EEG which were converted into a long-term grading of EEG using a majority vote operation. The features used in the AGS were summary measurements of two sub-signals extracted from a quadratic time-frequency distribution: the amplitude modulation and instantaneous frequency. These sub-signals were based on a model of EEG as a multiplication of a coloured random process with a slowly varying pseudo-periodic waveform and may be related to macroscopic neurophysiological function. The 4 grade AGS had a classification accuracy of 83% compared to human annotation of the EEG (level of agreement, κ = 0.76). Features estimated on the developed sub-signals proved more effective at grading the EEG than measures based solely on the EEG and the incorporation of additional sub-grades based on EEG states into the AGS also improved performance.