Howtosignalprocessing
- What is the region of convergence?
- What is ROC and its significance?
- What are the properties of region of convergence?
- What is region of convergence in s-plane?
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.
What is ROC and its significance?
Significance of ROC: ROC gives an idea about values of z for which Z-transform can be calculated. ROC can be used to determine causality of the system. ROC can be used to determine stability of the system.
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.
What is region of convergence in s-plane?
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.
