卷积型类高斯成形滤波算法研究及应用

Research and application of convolutional quasi-Gaussian pulse shaping filter algorithm

高斯信号具有对称性和完备性,因此高斯滤波方法在核信号处理以及辐射能谱分析时得到大量使用。目前构造实时处理核脉冲信号的真高斯成形滤波器尚有难度,实际常用数字类高斯成形算法主要是基于模拟核电子学中Sallen-Key滤波器和CR-(RC)~n滤波器的电路微分方程推导而得到,其输出的类高斯脉冲信号对称性较差、单级使用时存在下冲等问题。本文提出一种卷积型类高斯成形滤波算法,它以梯形脉冲信号为基础,经过第一次卷积实现双极性脉冲成形,再次卷积进行累加求和从而得到左右对称的类高斯脉冲,利用Z变换方法推导出该算法的数字递推公式。通过仿真模拟研究了算法的有效性和成形参数对幅频特性的影响规律,成形参数n_a和n_c取值增大时,滤波器通频带减小,低频成分幅度相对增加,高频噪声抑制作用增强,但也导致成形脉冲变宽,增加了脉冲堆积概率。最后,利用搭建的X射线荧光测量系统实验平台获取实测核脉冲数据,分别应用类高斯成形算法和梯形成形算法进行离线处理,实验结果表明:该类高斯成形算法具有更好的堆积脉冲分离能力,在相同的X光管管压和管流条件下,设置相同的达峰时间,两者所得能谱的能量分辨率基本相当,但是类高斯成形的能谱具有更高的特征峰面积和总计数。

[Background]Gaussian signals have symmetry and completeness,hence,the Gaussian filtering method is widely used in nuclear signal processing and radiation energy spectrum analysis.The mathematical description of Gaussian signals is relatively complex,which makes it difficult to construct digital Gaussian pulse shaping filters for nuclear pulse signal real-time processing.The commonly used digital quasi-Gaussian shaping algorithm in radiation measurement systems is derived from the differential equations of Sallen-Key and CR-(RC)n filters in analog nuclear electronics.However,its output shaping pulse signals have poor symmetry and problems such as undershoot occur when used in a single stage.[Purpose]This study aims to explore the convolutional quasi-Gaussian pulse shaping filter algorithm and apply it to the processing of X-ray fluorescence measurement system experimental platform to obtain measured nuclear pulse data.[Methods]Firstly,a convolutional quasi-Gaussian pulse shaping algorithm was implemented based on trapezoidal pulse signals,and bipolar pulse shaping was achieved after the initial convolution.Then,the second convolution was accumulated and summed to obtain left and right symmetric quasi-Gaussian shaping pulses.The digital recursive formula of the quasi-Gaussian pulse shaping algorithm was obtained using the Z-transform method,and the effectiveness of the algorithm and the influence of shaping parameters on the amplitude frequency characteristics were studied through simulation.Finally,quasi-gaussian shaping algorithm and trapezoidal shaping algorithm were applied separately to the offline process of measured nuclear pulse data from the X-ray fluorescence measurement system experimental platform.[Results]The quasi-Gaussian pulse shaping filter has better high-frequency noise suppression performance compared to trapezoidal pulse shaping filters.With the increase of the values of shaping parameters na and nc,the filter passband decreases whilst the low-frequency amplitude relatively increases,and the high-frequency noise suppression effect is enhanced.However,this also leads to shaping pulse broadening and increases the probability of pulse pile-up.[Conclusions]The experimental results demonstrate that the quasi-Gaussian pulse shaping algorithm has better pile-up pulse separation ability.Under identical X-ray tube voltage and current conditions and peaking time,the energy resolution of the energy spectra obtained by both algorithms is fundamentally equivalent.However,the energy spectrum with quasi-Gaussian pulse shaping has a higher characteristic peak area.