Howtosignalprocessing
- What is the region of convergence ROC for the Laplace transform?
- How do you find the region of convergence of Z-transform?
- How do you find the region of convergence in Laplace?
What is the region of convergence ROC for the Laplace transform?
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.
How do you find the region of convergence of Z-transform?
For x(n)=δ(n), i.e., impulse sequence is the only sequence whose ROC of Z-transform is the entire z-plane. If x(n) is an infinite duration causal sequence, then its ROC is |z|>a, i.e., it is the exterior of a circle of the radius equal to a.
How do you find the region of convergence in Laplace?
Perhaps the best way to look at the region of convergence is to view it in the s-plane. What we observe is that for a single pole, the region of convergence lies to the right of it for causal signals and to the left for anti-causal signals.
