Howtosignalprocessing
What is stability in Z domain?
ondition of stability is Z-domain is, [H(Z) < ∞ when evaluated on unit circle. That means the system transfer function should be finite if evaluated on unit circle. (3.7.10) Equation (3.7. 6) gives the condition of stability in Z domain.
What is ROC in Z-plane?
The set of points in z-plane for which the Z-transform of a discrete-time sequence x(n), i.e., X(z) converges is called the region of convergence (ROC) of X(z).
What is the ROC of a stable system?
According to the previous two theorems, we can conclude that for all causal stable systems, R1 < 1 and R2 = ∞. Therefore, the ROC of such systems is includes everything outside the unit circle, including the unit circle.
