# Region of Convergence for pole at z=-1 ?

I am caught up in a following question:

I have a mixed (causal + anti-causal) input to a system whose output is causal, with system having transfer function with pole at z=-1 and zero at z=1. What is the ROC for the system (if any) ?

Thanks a bunch.

## 1 Answer

If the system is causal then the ROC is outside the pole with maximum magnitude. Since there is only one pole at $z=-1$, the ROC is $|z|>1$. Note that the system is not stable since the ROC does not include the unit circle.

• Hi could you tell me why ROC is outside the pole with maximum magnitude for causal systems? – Austin Sep 20 '16 at 2:27
• @Jake: Take a look at this answer. – Matt L. Sep 20 '16 at 5:08