Optimal parameter choice of CR–RCm digital filter in nuclear pulse processing

CR–RC\(^m\) filters are widely used in nuclear energy spectrum measurement systems. The choice of parameters of a CR–RC\(^m\) digital filter directly affects its performance in terms of energy resolution and pulse count rate in digital nuclear spectrometer systems. A numerical recursive model of a CR differential circuit and RC integration circuit is derived, which shows that the shaping result of CR–RC\(^m\) is determined by the adjustment parameter (k, it determines the shaping time of the shaper) and the integral number (m). Furthermore, the amplitude–frequency response of CR–RC\(^m\) is analyzed, which shows that it is a bandpass filter; the larger the shaping parameters (k and m), the narrower is the frequency band. CR–RC\(^m\) digital Gaussian shaping is performed on the actual sampled nuclear pulse signal under different shaping parameters. The energy spectrum of \(^{137}\)Cs is measured based on the LaBr\(_3\)(Ce) detector under different parameters. The results show that the larger the shaping parameters (m and k), the closer the shaping result is to Gaussian shape, the wider is the shaped pulse, the higher is the energy resolution, and the lower is the pulse count rate. For the same batch of pulse signals, the energy resolution is increased from 3.8 to 3.5%, and the full energy peak area is reduced from 7815 to 6503. Thus, the optimal shaping parameters are \(m=3\) and \(k=0.95\). These research results can provide a design reference for the development of digital nuclear spectrometer measurement systems.