I want to try to summarize some relationships between z transform, ROC and causality. But I am getting confused between left/right sided sequences, the ROC and causal.
If you need stability then the ROC must contain the unit circle. I can understand that.
If you need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. I am fine with that too.
If you need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence. Yes that's fine.
If you need both, stability and causality, all the poles of the system function must be inside the unit circle.
But #4, doesn't it violate number 2 because we don't include infinity?
Got it from here: http://en.wikipedia.org/wiki/Z-transform#Example_2_.28causal_ROC.29