In this paper, we propose a new technique for positron emission tomography (PET) pulse processing that has the potential to overcome design limitations in PET arising from the need to use fast, high-cost analog-to-digital converters (ADCs). In this technique, we consider the voltage pulse derived from the charge pulse generated by a scintillator/photomultiplier tube (PMT) detector upon a detection event and model the voltage pulse by a fast, linearly rising edge followed by a slower exponential decay. Based on this model, we show that the basic parameters of the voltage pulse that are relevant for PET event detection can be determined from a trigger time and four time intervals measured on the pulse. We also discuss an electronic implementation in which the required measurements can be obtained by using clocks, comparators, and registers, thereby eliminating the use of ADCs and constant fraction discriminators in PET front-end electronics. We conduct computer simulation studies to evaluate the performance of the proposed technique and our results are promising. When used with Cerium Doped Lutetium Oxyorthosilicate (LSO)/PMT, the proposed technique can generate accurate results for the photon energy, the event time, and the decay-time constant. In addition, it can support an energy resolution of about 30% and a coincidence window of about 10 ns. On the other hand, in its present form the proposed technique is not suitable for use with BGO/PMT due to its low light yield.