Howtosignalprocessing
- What is convergence of Laplace transform?
- What is ROC of Z-transform and Laplace transform?
- What is the region of convergence?
What is convergence of Laplace transform?
If the Laplace transform converges (conditionally) at s = s0, then it automatically converges for all s with Re(s) > Re(s0). Therefore, the region of convergence is a half-plane of the form Re(s) > a, possibly including some points of the boundary line Re(s) = a.
What is ROC of Z-transform and Laplace transform?
Region of Convergence (ROC) of Z-Transform
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 region of convergence?
The Region of Convergence is the area in the pole/zero plot of the transfer function in which the function exists. For purposes of useful filter design, we prefer to work with rational functions, which can be described by two polynomials, one each for determining the poles and the zeros, respectively.
