Howtosignalprocessing
How do you determine stability from ROC?
For a system to be causal, all poles of its transfer function must be right half of s-plane. A system is said to be stable when all poles of its transfer function lay on the left half of s-plane. A system is said to be unstable when at least one pole of its transfer function is shifted to the right half of s-plane.
What is ROC and its properties?
The region of convergence (ROC) of Z-transform has the following properties − 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 is ROC signals?
Region of Convergence (ROC) is defined as the set of points in s-plane for which the Laplace transform of a function x(t) converges. In other words, the range of Re(s) (i.e.,σ) for which the function X(s) converges is called the region of convergence.
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