基于Z变换的C-R逆算子分析及其应用研究  

Analysis and application of inverse C-R transform based on Z transform

作　　者：金幼贤 周建斌[1,3] 马英杰 岳爱忠[2] 洪旭 刘易[1] 王敏 JIN Youxian;ZHOU Jianbin;MA Yingjie;YUE Aizhong;HONG Xu;LIU Yi;WANG Min(College of Nuclear Technology and Automation Engineer,Chengdu University of Technology,Chengdu 610059,China;China Petroleum Logging Co.,Ltd,Xi'an 710032,China;Sichuan Xinxianda Measurement and Control Technology Co.,Ltd,Chengdu 610052,China)

机构地区：[1]成都理工大学核技术与自动化工程学院,成都610059 [2]中石油测井公司,西安710032 [3]四川新先达测控技术有限公司,成都610052

出　　处：《核技术》2021年第7期39-45,共7页Nuclear Techniques

基　　金：国家自然科学基金-面上项目(No.11975060、No.12075038、No.12005026);四川省科技计划(No.2021JDRC0028)资助。

摘　　要：本文首先基于拉式变换以及Z变换,对C-R系统进行分析,得到了相应的时域连续解与离散解,考虑到指数运算在现场可编程门阵列(Field-Programmable Gate Array,FPGA)中难以实现,结合泰勒级数展开了指数项,得到了改进的离散解,然后结合数值解对这三个离散解进行了仿真对比;结合Z变换解,对其做相应的处理得到C-R逆系统的时域数字解,并且给出了基于FPGA的C-R逆算子的电路系统结构实现框图。在构建的C-R逆算子算法基础上,针对单指数脉冲信号通过C-R系统后产生的反冲拖尾现象进行了初步应用研究,得到了无反冲的更窄的脉冲信号,实现了数字极零相消的功能。最后通过模拟实验发现了数字基线漂移的问题,分析了原因,并提出了改进方法,得到改进的C-R逆算子算法,并通过模拟实验验证了可行性。[Background]In nuclear radiation measurement,nuclear pulse signal can only process the analog circuit system in sequence,generally,signal distortion appeared.[Purpose]This paper proposed inverse C-R algorithm aims at obtaining narrow nuclear pulse signal,implementing baseline elimination,and realizing better precision and high-resolution energy spectrum measurement under high counting rate.[Method]This paper makes detail study in C-R circuit system with Laplace transform and Z-transform,and corresponding continuous and discrete solutions to step signal and minus exponential signal of C-R circuit are presented,besides,considering the difficulty in algorithm deployment in FPGA(Field-Programmable Gate Array)with exponential parameter,Taylor expansion is applied to simplify the discrete response,which an modified discrete solution is also presented,besides,numerical solution of C-R system is also considered,the comparison of the three discrete solutions are simulated with MATLAB.And with suitable transform of C-R numerical solution,inverse C-R numerical solution is obtained,as appropriate choice of parameter,inverse C-R numerical solution can not only eliminate the undershoot in nuclear signal,but also realize the narrowing of the signal.[Results&Conclusions]Simulation results presents that the three methods are in consistence in nuclear signal processing,and with suitable parameter setting,inverse C-R system can eliminate the undershoot and narrow the signal,and with accurate baseline estimation,baseline restoration can be realized with modified inverse C-R baseline eliminating algorithm.

关 键 词：Z变换 C-R逆算子 时域数值分析 基线恢复 

分 类 号：TL99[核科学技术—核技术及应用]