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Coincidence timing resolution in Positron Emission Tomography (PET) can be improved by replacing fast analog pulse shaping and Constant Fraction Discriminator (CFD) with fully digital signal processing. This can be achieved by digitizing the signal from individual detectors using 100-MHz, 8-bit Analog-to-Digital converters (ADC) and by processing the data on-the-fly in Field Programmable Gate Arrays (FPGA). Various digital filters and baseline restorers were implemented and combined with numerical least mean square fit to the data to extract the time of interaction and the energy deposited in BGO-APD detectors. An intrinsic time resolution of 7.2 ns was obtained with digital techniques. However, it is shown that bias in the timestamp estimation can be introduced by digital time discrimination techniques, which could affect the ability of digital methods to accurately estimate random event rates by the delayed time window method. Accordingly, the coincidence FWHM metric should not be the only figure of merit when comparing digital and analog time discrimination strategies.