BIBO Stability in Z-domain

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I'd really appreciate it if someone could please explain to me the condition for a LTI system to be BIBO stable, in z-domain.

I have a background in control, and in linear control for example, if we have the transfer function, we simply look at the poles. But in digital signal processing, sometime we look at the poles - they should be inside the unit circle in order to have BIBO stability - and soemtimes the professor says it depends on the ROC - ROC should include the unit circle -.

I am really confused. Could someone please explain to me the difference?