序列运算理论的伪逆运算研究  

Analysis of pseudo-converse operation in the sequence operation theory

作　　者：徐玮[1] 康重庆[1] 夏清[1] 

机构地区：[1]清华大学电机工程与应用电子技术系,电力系统国家重点实验室,北京100084

出　　处：《清华大学学报（自然科学版）》2010年第10期1623-1630,共8页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(50777031);新世纪优秀人才支持计划资助(NCET-07-0484)

摘　　要：针对序列运算的逆运算问题,提出了利用伪序列的概念实现序列运算逆运算的新思路。首先给出了伪序列与伪逆运算的定义,并以卷差运算为例,分别探讨了求解被卷差序列、长度已知与未知主卷差序列三种情况下卷差逆运算的有解条件,研究了卷差逆运算的计算方法。同时,还给出了伪序列与原序列之间关系,进而分析了利用伪序列代替原序列进行序列运算的误差。最后,利用算例对所提出方法与结论加以检验,算例结果表明以伪序列代替原序列进行卷差运算时,所得卷差序列与原卷差序列之间的平均相对误差为2.47%,并且两序列之间关系符合本文中结论,证明了该文工作的正确性。This paper presents a method using the concept of pseudo sequence to implement the converse operation in sequence operation,with the definition of pseudo sequence and pseudo-converse operation given first.Subtraction-type-convolution（STC） operation was taken as an example to deduce the solvability conditions of solving subordinate STC sequence and primary STC sequence with certain and unknown lengths separately,and to analyze the detailed calculating method for the STC converse operation.This paper also expounded the relationship between the pseudo sequence and practical sequence,analyzing the error of basic sequence operations using pseudo sequences.Case study shows that the mean relative error between the original subtraction-type-convolution sequence and the result sequence obtained by substituting pseudo sequence for original sequence in subtraction-type-convolution is 2.47%,with the relationship of the sequences satisfying the conclusions in the paper.

关 键 词：序列运算理论 伪序列 伪逆运算 

分 类 号：O211.9[理学—概率论与数理统计] TM744[理学—数学]