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The single-ion Penning trap (SIPT) at the Low-Energy Beam Ion Trapping Facility has been developed to perform precision Penning trap mass measurements of single ions, ideal for the study of exotic nuclei available only at low rates at the Facility for Rare Isotope Beams (FRIB). Single-ion signals are very weak—especially if the ion is singly charged—and the few meaningful ion signals must be disentangled from an often larger noise background. A useful approach for simulating Fourier transform ion cyclotron resonance signals is outlined and shown to be equivalent to the established yet computationally intense method. Applications of supervised machine learning algorithms for classifying background signals are discussed, and their accuracies are shown to be ≈65% for the weakest signals of interest to SIPT. Additionally, a deep neural network capable of accurately predicting important characteristics of the ions observed by their image charge signal is discussed. Signal classification on an experimental noise dataset was shown to have a false-positive classification rate of 10.5%, and 3.5% following additional filtering. The application of the deep neural network to an experimental 85Rb+ dataset is presented, suggesting that SIPT is sensitive to single-ion signals. Lastly, the implications for future experiments are discussed.