Impulse Shaping Method Based on Bayesian Deconvolution

A novel impulse shaping method based on Bayesian deconvolution as a means of enhancing the energy range of the energy spectrum was proposed. The initial step of this method entailed expressing the measured pulse signal as the convolution of the current impulse pulse signal and the detection system response function. Then, the measured signal was expressed in the continuous time domain and decomposed into the form of an impulse signal and a double exponential kernel convolution by derivation. Subsequently, Bayesian deconvolution should be performed on the measured signal, after which the expression of the impulse signal can be solved. It is important to note that due to the limitations of the double exponential kernel in terms of length, the Z-transform was employed as a substitute for the convolution process in Bayesian deconvolution. The simulation experiment was conducted to examine the nuclear pulse signal, utilizing the MATLAB software. The results demonstrate that the Bayesian deconvolution pulse shaping method is an effective approach for resolving the impulse signal embedded within a double exponential signal. And this method enables precise characterization of the amplitude, occurrence time, and number of pulses present in the original nuclear signal. A comparison with alternative impulse shaping methods, including inverse system cascade impulse shaping and Z-transform impulse shaping, demonstrates that the Bayesian deconvolution impulse shaping method is capable of effectively suppressing noise in a double exponential signal with a signal-to-noise ratio of 40 dB, thereby enabling the complete solution of the impulse signal. The experimental test was conducted using a CIT-3000MD X-ray fluorescence spectrometer measurement system, which was based on a FAST-SDD detector produced by Amptek Inc. This system was equipped with a thermoelectrically cooled solid-state detector and a preamplifier. The light source was a silver target X-ray tube, which was designed by Shanghai KeyWay Electronic Technology Co., Ltd. The results show that, in comparison with the Z-transform pulse shaping method and the inverse system cascade pulse shaping method, the Bayesian deconvolution pulse shaping method is capable of extracting low-amplitude pulses, preserving their peak values, and generating low-energy spectra. In conclusion, the Bayesian deconvolution pulse shaping method proposed in this paper does not necessitate consideration of the size of the convolution kernel and exhibits reduced sensitivity to pulse noise. In comparison with traditional inverse Z-transform and inverse system pulse shaping, the Bayesian deconvolution method is capable of suppressing noise and retaining a greater proportion of low-amplitude pulses. This is advantageous for the measurement and analysis of low-energy spectra.