We propose a new electronic design to overcome design limitations in PET that arise from the need to use high-cost fast analog-to-digital converters (ADCs). Our design may completely remove the use of ADCs in PET, and possibly the constant fraction discriminator (CFD) as well. In our approach, we model the eletric pulse generated upon an event detection by a fast linearly rising edge followed by a slower exponential decay. Based on this modeling, basic properties of the pulse that are relevant for PET event detection, including the decay constant, the peak value and the peak time, can be determined from simple time interval measurements of the pulse. In this work, we will present methods for determining these pulse properties and propose eletronic implementations of these methods. We will employ computer simulations to conduct sensitivity analysis of the proposed new event processing methods to modeling errors, noise and clock rate.