To plan a rapid response and minimize operational costs, passive optical network operators require to automatically detect and identify faults that may occur in the optical distribution network. In this work, we present DSP-Enhanced OTDR, a novel methodology for remote fault analysis based on conventional optical time-domain reflectometry complemented with reference traces and DSP-based techniques. We first obtain the optimal decision thresholds to detect deviations in the noisy OTDR measurement. In order to quantify and characterize the fault, the detection stage is followed by one of estimation where its return loss and insertion loss are determined. We experimentally demonstrate that this approach allows to detect and characterize faults with an accuracy higher than that found in conventional OTDR trace analysis. In our experiments, we achieved detection sensitivities higher than 0.2 dB in a 1:16 split-ratio PON, and higher than 1 dB in a 1:64 split-ratio PON, achieving estimation errors that can be as low as 0.01 dB. We also verified how the optical network terminal's reflectivity can improve the detection capabilities.