# What is the sequence type if ROC is an annulus in the z-plane

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?

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.