Timing of pulses of any shape with arbitrary constraints and noises: optimum filters synthesis method

In this paper the optimum filtering for the precise measurement of the occurrence time of any kind of time-limited signal is dealt with. We find the time-limited optimum weighting function (WF) in the presence of any kind of uncorrelated, stationary, additional noises and we allow the introduction of arbitrary assigned time domain constraints in the WF. The method can be easily translated into computer programs and it can be used as a tool for optimising a digital signal processing spectroscopy set-up in its digital filter section. An application of the method to signals at the output of large volume HPGe γ-ray detectors is finally presented.