Optimum zero-area filter for nuclear signal sequences

A zero-area optimum filter for the processing of nuclear signal sequences is discussed in this paper. In contrast to known optimum filters (e.g. 'finite cusp' and Deighton filters), in which the weight function is entirely constrained to the finite time span available between three subsequent δ-pulses, we suggest that the filter weight function may be built along a larger packet of these time intervals. The proposed filter is basically the combination of an optimum filter for pulse-area estimation (finite cusp like) and an optimum multi-lobe filter for baseline subtraction. The left- and right-handed parts of the cusp-like filter, as each lobe of the baseline filter, are constrained to single inter-pulse time spans, but the overall filter has a time width which exceeds that between three subsequent pulses: the larger the number of lobes, the longer the overall filter duration. We show that the noise performance of the new filter tends to that of the finite-cusp filter as the number of lobes is increased: with a eight lobe weight function the signal-to-noise ratio is in typical situations 76-97% that of the finite cusp; whereas the low-frequency-disturbance rejection is by far better. The synthetized filter is to be regarded as a trade-off between the finite cusp filter (optimum signal-to-noise performance but no low-frequency-rejection capability) and the Deighton filter (excellent low-frequency rejection but relatively poor signal-to-noise performance).