Mathematical method for optimal digitization and discrimination of scintillation detectors' pulses

The crystal identification and particle identification require applying pulse shape discrimination (PSD) methods to differentiate between two or more types of scintillation pulses according to their decay times. The sampling rate and the number of used samples of scintillation pulses significantly affect the performance and the complexity of the PSD. Despite their importance, there is no method in the literature, to the best of our knowledge, regarding how to optimally select these parameters. This paper introduces a mathematical analysis of the frequency spectra to determine the most discriminated frequency band of any two different pulse-types. The proposed analysis showed that the most discriminated frequency band depends on the two decay times of the pulse-types. Based on this analysis, a digitization criterion is proposed to determine the optimum sampling rate, number of used samples and the cutoff frequency of the anti-aliasing filter. Furthermore, determining the most discriminated frequency band reduces the number of needed frequency components and provides the highest discrimination performance with the lowest number of required computations. The proposed digitization criterion is applied on two pulse-types with different decay times (20 ns and 40 ns) and shows that the most discriminated frequency is8MHz. It also recommends using 32 MHz sampling rate, 8 samples and an anti-aliasing filter with 10 MHz cutoff frequency for these two pulse-types.