几种离散时间系统的移不变性证明  

Proofs of Shift-invariant Property for Several Discrete-time Systems

作　　者：贾彬彬 张爱华[1] 黄玲[1] JIA Binbin;ZHANG Aihua;HUANG Ling(College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学电气工程与信息工程学院,兰州730050

出　　处：《电气电子教学学报》2024年第2期134-137,共4页Journal of Electrical and Electronic Education

基　　金：教育部新工科研究与实践项目(E-DZYQ20201402);兰州理工大学研究生课程思政建设项目(KCSZ-YB-202242013)。

摘　　要：线性移不变系统的分析是“数字信号处理”课程的重点内容,而移不变性是线性移不变系统必须满足的性质之一。当系统输入与输出关系涉及时间折叠、抽取与内插等关于时间变量的复合运算时,系统移不变性的分析将会变得十分抽象。证明了几种典型的涉及时间变量复合运算的离散时间系统是否满足移不变性质,并给出了相应的例子以便于理解。最后总结了此类系统关于移不变性的一般规律。The analysis of linear shift-invariant(LSI)system is the key content in Digital Signal Processing course,and shiftinvariance is one of the properties that LSI system must satisfy.When the relationship between input and output of system involves composite operation w.r.t.time variable,such as time-folding,decimation and interpolation,the analysis of shift-invariance will become very abstract.In this paper,it is proved whether some typical discrete-time systems involving composite operation of time variable satisfy shift-invariant property,and corresponding examples are also given for easy understanding.Finally,the general law of the shift-invariant property w.r.t.such kind of systems is summarized.

关 键 词：数字信号处理 离散时间系统 移不变性质 

分 类 号：TN911.72[电子电信—通信与信息系统]