Can I assume that the R.O.C. from a Z-Transform will always start from or end in a pole or 0/infinity?
Using an example:
$$H(z)=\frac{(z+1)(z-1)(z+j)(z-j)}{z^4}\space,\space\space j=\sqrt{(-1)}$$
So we have 4 zeros in the unit circle equally spaced by a $\frac{\pi}{2}$ angle and 4 poles in the origin ($z=0$). If not specified, can I assume the the ROC wil necessarily start from exclusive zero and go towards infinity? Or maybe possible to exist a ROC which is a ring in the Z-plane (which will not start/end in a pole)?