On the optimum area-balanced filters for nuclear spectroscopy

The minimum noise Area-Balanced (A-B) filters for nuclear spectroscopy are disentangled in the sum of two optimized individual filters. The former is the unipolar finite cusp filter, used for pulse amplitude estimation but affected by baseline shift errors, the latter is a specific filter used for baseline estimation. Each of them is optimized so as to give the minimum noise in the estimation of the pulse amplitude or of its baseline level. It is shown that double optimisation produces an overall optimum filter exhibiting a total noise Vn2 equal to the sum of the noises Vn12 and Vn22 exhibited by each filter individually. This is a consequence of the orthogonality of the individual filter weight-functions in a function space where the norm is defined as V2n.