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if:

$|z|>|\alpha|$ is causal and right-sided

and:

$|z|<|\alpha|$ is anti-causal and left-sided

then, what is the annulus/donut-ring ROC?

$|\beta| < |z| < |\alpha|$

non-casual? finite-length? double-sided?

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if the ROC of a Z-transform is a ring on the z-plane, then the associated time domain signal is :

  • two sided infinite length (hence non-causal)

and

  • stable if the ring includes unit-circle or unstable otherwise.
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