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Partial discharge (PD) monitoring is an established method for insulation health monitoring in high-voltage plant. A number of different approaches to PD defect diagnosis have been developed to extract defect-specific information from PD pulse data in both the time and frequency domains. Frequency-based PD pulse analysis has previously been demonstrated to offer a low-power approach to PD defect identification, where a mixture of passive and active analog electronics can be used to generate diagnostic features in a low-power device suited to wireless sensor network operation. This paper examines approaches to implementing diagnostic methods for frequency-based PD pulse diagnosis targeted at compositional frequency spectrum features in a computationally efficient manner. Dirichlet and Gaussian distributions are used to demonstrate the complex probabilistic form of fault class decision surfaces, which motivates the proposed application of the log ratio transform to frequency composition data. The results demonstrate that PD defects can be differentiated using these frequency-based methods and that employing the log ratio transform to the compositional frequency content data yields increases in classification accuracy without necessarily resorting to more complex classifiers.