On the time invariance of linear systems

In this paper we revise the concept of time invariance of a system, using exclusively a time domain approach. To this aim, we adopt a group theoretical formulation which let us recognize that the concept of time invariance is truly confined to a few possible cases. This depends on the fact that, for a general multirate linear system, the shift invariance property depends not only on the kernel, but also on the input and output domains. We illustrate the concept with an example of application in one dimensional domains, indicating that our definition has a useful impact in the analysis and synthesis of multirate linear systems. Furthermore, the proposed approach permits to extend the concept of system invariance to multidimensional domains.