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Next generation PET scanners should fulfill very high requirements in terms of spatial, energy and timing resolution. Modern scanner performances are inherently limited by the use of standard photomultiplier tubes. The use of Silicon Photomultiplier (SiPM) matrices is proposed for the construction of a 4D PET module based on LYSO continuous crystals, which is envisaged to replace the standard PET block detector. The module will provide a submillimetric spatial resolution on the photon hit position, performing at the same time, the Depth Of Interaction (DOI) calculation and the Time Of Flight (TOF) measurement. The use of large area multi-pixel Silicon Photomultiplier (SiPM) detectors requires the development of a multichannel Digital Acquisition system (DAQ) as well as of a dedicated front-end in order not to degrade the intrinsic detector capabilities. At the University of Pisa and INFN Pisa we have developed a flexible and modular DAQ system for the read-out of 2 module in time coincidence for Positron Emission Tomography (PET) applications. Here we describe the acquisition system architecture and its characterization measurements.