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 1


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.

  • $\begingroup$ Hi could you tell me why ROC is outside the pole with maximum magnitude for causal systems? $\endgroup$
    – Austin
    Sep 20, 2016 at 2:27
  • 1
    $\begingroup$ @Jake: Take a look at this answer. $\endgroup$
    – Matt L.
    Sep 20, 2016 at 5:08

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