Howtosignalprocessing
What is Region of Convergence? 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.
- What is the region of convergence?
- How do you find the region of convergence of a function?
- What are the properties of region of convergence?
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.
How do you find the region of convergence of a function?
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.
What are the properties of region of convergence?
Properties of ROC of Z-Transform
The ROC of the Z-transform cannot contain any poles. The ROC of Z-transform of an LTI stable system contains the unit circle. The ROC of Z-transform must be connected region. When the Ztransform X(z) is a rational, then its ROC is bounded by poles or extends up to infinity.
