有限群的特征标矩阵与离散傅里叶变换  

Character matrix of finite group and discrete Fourier transform

作　　者：刘瑞芹[1] 胡去非[1] 

机构地区：[1]华北科技学院基础部,北京东燕郊101601

出　　处：《大庆石油学院学报》2009年第4期110-111,124,共3页Journal of Daqing Petroleum Institute

基　　金：国家自然科学基金项目(60872062)

摘　　要：在信号的分析处理过程中,需要将信号进行变换处理.对于离散信号,一般进行正交变换,正交变换理论在离散数字信号的分析和处理当中占有非常重要的地位.利用有限Abel群的特征标理论,研究了模N剩余类加群ZN的特征标矩阵的构成.结果表明,有限的模N剩余类加群ZN的特征标矩阵是正交矩阵,其恰好就是N点序列的离散傅里叶反变换的变换矩阵,这可为用代数理论分析和处理离散数字信号提供了一种新的方法和途径.In the process of signal analysis and treatment,signal is processed by transform processing in order to do time-frequency analysis,we usually use the orthogonal transformation for the discrete signal,orthogonal transform theory takes a very important place in the analysis and treatment of discrete digital signal.In this paper,we use the character theory of finite Abel group to analyze the character matrix of residue class additive group Module.The analysis shows that character matrix of residue class additive group Module is orthogonal matrix,just the transformation matrix of the inverse discrete Fourier transforms of point sequence.This provides a new way to analyze and deal with the discrete digital signal by algebra theory.

关 键 词：有限群 特征标 傅里叶变换 矩阵 

分 类 号：O152.1[理学—数学]