Gaussian shaper for nuclear pulses based on multilevel cascade convolution

For nuclear measurements, it is necessary to obtain accurate information from nuclear pulses, which should be obtained by first shaping the pulses outputted by the detectors. However, commonly used pulse-shaping algorithms have certain problems. For example, certain pulse-shaping algorithms have long dead-times in high-counting-rate environments or are difficult to achieve in digital systems. Gaussian signals are widely used in analog nuclear instruments owing to their symmetry and completeness. A Gaussian signal is usually implemented by using a multilevel S–K filter in series or in parallel. It is difficult to construct a real-time digital Gaussian filter for the complex Gaussian filtering algorithm. Based on the multilevel cascade convolution, a pulse-shaping algorithm for double exponential signals is proposed in this study, which, in addition to double exponential signals, allows more complex output signal models to be used in the new algorithm. The proposed algorithm can be used in high-counting-rate environments and has been implemented in an FPGA with fewer multipliers than those required in other traditional Gaussian pulse-shaping algorithms. The offline processing results indicated that the average peak base width of the output-shaped pulses obtained using the proposed algorithm was reduced compared with that obtained using the traditional Gaussian pulse-shaping algorithm. Experimental results also demonstrated that signal-to-noise ratios and energy resolutions were improved, particularly for pulses with a low energy. The energy resolution was improved by 0.1–0.2% while improving the counting rate.