Characteristics and comparison of two digital quasi-Gauss filters for gamma spectroscopy

Abstract

This paper presents two digital quasi-Gauss filters, the first of which is a digital CR-RCm filter with the function of pole-zero cancellation (digital CRPZC-RCm filter) and the second a digital Sallen-Key filter (digital S-K filter). The digital filters are established according to the differential equations of an analog CRPZC-RCm circuit and an analog S-K circuit, respectively. Characteristics including frequency response, noise suppression and stability for both digital filters are discussed and improved algorithm cascade structures are obtained to reduce the resources consumption of field programmable gate arrays (FPGAs). To compare the two digital filters, the energy resolution (@Cs-137, 662 keV) for LaBr3(Ce) and NaI(Tl) detectors is calculated for the digital spectroscopy system and the analog spectroscopy system from CANBERRA. The results prove that the two digital filters exhibit similar performance in frequency response, noise suppression and energy resolution improvement. Further, the optimum energy resolution (@Cs-137, 662 keV) for both digital filters is slightly superior to that of CANBERRA. The digital S-K filter consumes fewer FPGA resources compared to the digital CRPZC-RCm filter due to its simpler algorithm cascade structure, though the digital S-K filter becomes unstable when its gain (K) exceeds a certain threshold.