Design for a Symmetrical Gaussian Shaping Algorithm Based on Fourier Transform for Handling Digital Pulse

With the emergence of high-speed analog-to-digital converters, shaping algorithms for handling digital pulses was applied broadly in nuclear instruments. Trapezoidal shaper and Gaussian shaper are the common shaping algorithms. The former can increase the pulse passing rate due to its narrowed output pulse. The latter can make better energy resolution of nuclear instruments because of its attractive signal-to-noise ratio (SNR). The output gaussian shaper pulse has to narrow to add the discernment ability to piled-up pulses. The recurrence formula of the symmetrical gaussian shaping algorithm (SGSA) is deduced based on Fourier transform in the assumption that the shape of the output pulse obeys the gaussian function and its amplitude is equal to the corresponding input pulse. Moreover, its recurrence formula is composed of only multiplier and adder, which are easily implemented in field programmable gate arrays. After dealing with ideal pulses with SGSA, the result shows that the discernment ability to piled-up pulses is weaker along with the bigger g (standard deviation) of its output pulse. Compare the shape of the output pulse of the trapezoidal shaper at the smallest rise and flat-top time with this method under sigma=3T(s). This proves this method has a better discernment ability to piled-up pulses. After dealing 180 000 simulating pulses under different SNR with SGSA, the result reflects that the average extractive amplitude increases at SNR<55 dB, and then maintain stability. Meanwhile, the output pulse is smoother after the bigger value of g. Their frequency spectrums also prove it. The cutofffrequency decreases, and the denoising effect rises when sigma increases. It can increase the energy resolution of nuclear instruments. Applying the total-reflection X-ray fluorescence spectrometer shows that the energy resolution increases 5. 42 %a and total count rate decreases 13. 02% when sigma increases. The experiments further strengthen the above-simulating conclusion. Those results proved that SGSA improves the discernment ability to piled-up pulses and can be implemented high-speed real-time processing for a pulse on a multi-channel analyzer.