几种离散时间系统的移不变性证明

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。

Proofs of shift-invariant property for several discrete-time systems

The analysis of linear shift-invariant (LSI) system is the key content in digital signal processing course, and shift-invariance 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, e.g., 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.