Since X(z) is a infinite power series, it is defined only at few values of z. The set of all values of z where X(z) converges to a finite value is called as Radius of Convergence(ROC).

We know that, for a given signal x(n) the z-transform is defined as X(z)=\\(\\sum_{n=-\\infty}^{\\infty} x(n)z^{-n}\\)

We know that, the z-transform of a signal x(n) is X(z)=\\(\\sum_{n=-\\infty}^{\\infty} x(n)z^{-n}\\)

Let us an example of anti causal sequence whose z-transform will be in the form X(z)=1+z+z2 which has a finite value at all values of ‘z’ except at z=∞. So, ROC of an anti-causal sequence is entire z-plane except at z=∞.

Let us plot the graph of z-transform of any two sided sequence which looks as follows.

For a given signal x(n), its z-transform X(z)=\\(\\sum_{n=-\\infty}^{\\infty} x(n)z^{-n}\\)

We know that,

The z-transform of a real discrete time sequence x(n) is defined as a power of ‘z’ which is equal to X(z)=\\(\\sum_{n=-{\\infty}}^{\\infty} x(n)z^{-n}\\), where ‘z’ is a complex variable.