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=$ \infty $
Property 4: If x[n] is a right sided sequence and if the cirlce |z| = ro is in the ROC then all finite values of z for which |z| >ro will also be in the ROC.
Property 5: If x[n] is a left sided
