How do I find the ROC of a system if it has no poles

1. Why ROC does not contain any pole?
2. How do you find the ROC of a system?
3. Does ROC have poles?
4. Does ROC have both poles and zeros?

Why ROC does not contain any pole?

The ROC cannot contain any poles.

Since X(z) must be finite for all z for convergence, there cannot be a pole in the ROC. If x[n] is a finite-duration sequence, then the ROC is the entire z-plane, except possibly z=0 or |z|=∞. A finite-duration sequence is a sequence that is nonzero in a finite interval n1≤n≤n2.

How do you find the ROC of a system?

If x(t) is absolutely integral and it is of finite duration, then ROC is entire s-plane. If x(t) is a right sided sequence then ROC : Res > σ_o. If x(t) is a left sided sequence then ROC : Res < σ_o. If x(t) is a two sided sequence then ROC is the combination of two regions.

Does ROC have poles?

The region of convergence (ROC) for a given DT transfer function is a disk or annulus which contains no poles.

Does ROC have both poles and zeros?

The ROC cannot contain a Pole, since at a pole H(z) is infinite by definition and hence does not converge. For a causal system (impulse response h(n) is zero for n< 0), the ROC is the exterior of a circle, including ¥. Further, for a system to be stable, its impulse response must be absolutely summable.