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Digital positron emission tomography (PET) systems enable us to implement sophisticated algorithms for real time signal processing. Usually, energy and position are encoded on the amplitude of the digitized signals. Although a lot of work has been made for spectroscopy applications, digital pulse height estimation in PET detectors presents important challenges mainly due to the fast response of state-of-the-art detectors. In this paper we propose a digital filtering technique for improving amplitude estimation in order to achieve high spatial and energy resolution with moderated conversion rates (<80 MSPS). Our approach is based on the trapezoidal shaping of the incoming pulses by using adaptive filtering based on least-mean-squares (LMS) algorithm for modelling detector and front-end electronics response. Thus, the filtered signals are well suited both for pile-up recovery and accurate pulse height computation. The filter can be easily implemented on programmable devices and integrated on the data acquisition chain for real-time applications.