Properties of the region of convergence for Z-transform
A number of properties are listed in the oppenheim willsky textbook. These properties state the insights of the z-transforms region of convergence.
Property 1: The ROC of X(z) consists of a ring in the z-plane centered about the origin.
Property 2: The ROC does not contain any poles.
Property 3: If x[n] is of finite duration then the ROC is the entire z-plane except possibly z=0 and z=$ \inf $
