Fast least mean squares method for time determination and pileup rejection in high resolution spectroscopy

A method for reducing the mathematical complexity of least mean squares algorithms used for deriving energy and arrival time of detected events has been derived. It is based on exploiting the quasi-orthogonality of the amplitude and time estimates. A suitable digital filter, insensitive to the event arrival time, determines directly the event energy. This information is provided to the least mean squares routine, which times the event roughly five times faster. A by-product of the procedure is the chi-square value of the fit, which is very sensitive to pileupped low energy events, and can thus be employed for pileup rejection. By further refining the least mean squares method, additional savings in computation times can be achieved. This yields an easier path towards the implementation of the method in a real time digital processing setup.