Since the value of Z-transform tends to infinity at poles, poles can not be a part of ROC. So ROC either starts from a pole or end in a pole.
- Why the ROC of z-transform can not contain any pole?
- Does ROC have both poles and zeros?
- What is the ROC of the z-transform of the signal?
- What are poles in z-transform?
Why the ROC of z-transform can not contain any pole?
The ROC cannot contain any poles.
By definition a pole is a where X(z) is infinite. Since X(z) must be finite for all z for convergence, there cannot be a pole in the ROC.
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.
What is the ROC of the z-transform of the signal?
The ROC of the Z-transform is a ring or disc in the z-plane centred at the origin. The ROC of the Z-transform cannot contain any poles. The ROC of Z-transform of an LTI stable system contains the unit circle.
What are poles in z-transform?
Introduction to Poles and Zeros of the Z-Transform
The two polynomials, P(z) and Q(z), allow us to find the poles and zeros of the Z-Transform. The value(s) for z where P(z)=0. The complex frequencies that make the overall gain of the filter transfer function zero.