This study aims 1) To analyse differences in resting-state electroencephalogram (rs-EEG) spectral features of Parkinson's Disease (PD) and healthy subjects (non-PD) using Functional Data Analysis (FDA) and 2) To explore, in four independent cohorts, the external validity and reproducibility of the findings using both epoch-to-epoch FDA and averaged-epochs approach. We included 169 subjects (85 non-PD; 84 PD) from four centres. Rs-EEG signals were preprocessed with a combination of automated pipelines. Sensor-level relative power spectral density (PSD), dominant frequency (DF), and DF variability (DFV) features were extracted. Differences in each feature were compared between PD and non-PD on averaged epochs and using FDA to model the epoch-to-epoch change of each feature. For averaged epochs, significantly higher theta relative PSD in PD was found across all datasets. Also, higher pre-alpha relative PSD was observed in three of four datasets in PD patients. For FDA, similar findings were achieved in theta, but all datasets showed consistently significant posterior pre-alpha differences across multiple epochs. Increased generalised theta, with posterior pre-alpha relative PSD, was the most reproducible finding in PD. Rs-EEG theta and pre-alpha findings are generalisable in PD. FDA constitutes a reliable and powerful tool to analyse epoch-to-epoch the rs-EEG.