Signal-to-Noise Analysis in Count Rate Dependent Adaptive Digital Pulse Processing for Gamma-Ray Spectroscopy

An optimum filter to achieve best signal to noise ratio is a primary prerequisite in high resolution gamma spectroscopy systems. Digital techniques for nuclear spectroscopy are increasingly implemented in modern radiation detection systems, which allow consideration of the attributes of the generated signal on a pulse-by-pulse basis. In this work, the limits of the count rate dependent signal-to-noise ratio (SNR) are established for time invariant (fixed) and time variant (adaptive) digital filters. The calculated results illustrate that the adaptive filter provides improved SNR for a given pulse throughput rate as compared to a fixed filter. Further analysis shows that the detector with a low input capacitance is a preferable choice to achieve better SNR and improved performance at high count rates. A 14-bit adaptor module with sampling rate of 250 MS/s is used for digitizing a high purity germanium (HPGe) detector's pre-amplifier pulses. Fixed and adaptive digital trapezoid shaping algorithms with timing filter, baseline restorer, and pile-up rejecter are implemented using field programmable gate array (FPGA) for real-time signal processing. The experimental results using the coaxial HPGe with fixed and adaptive shaping show reasonable agreement with the theoretical calculations. At input count rate of 400 kcps with 50% throughput rate after pile- up rejection, the improvement in measured SNR is 30% with adaptive trapezoid filter in comparison to the fixed filter.