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The most common method for time pick-off from signals coming from SiPMs coupled to scintillator crystals in PET applications is the Leading Edge Triggering. In this work we propose a new filtering scheme to be applied before the discriminator. It implements a type of baseline compensation aimed at the reduction of the time jitter due to the dark counts of the detector and is based on a simple analog filter, which is well suited for an ASIC implementation. We describe a circuit, built with discrete components, that implements the filter. Finally we report on the Coincidence Resolving Time measurements performed coupling the circuit to the real detector, composed of a SiPM built at FBK and a LYSO crystal, for the detection of 511 keV photons. The results obtained are promising, showing that the method is quite effective in reducing the impact of the detector noise on the timing performance of the system.