Howtosignalprocessing
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 of z-transform state its properties?
- What is the importance of ROC of z-transform?
- What is ROC and its properties?
- How do you find the region of convergence of a transfer function?
What is ROC of z-transform state its properties?
Properties of ROC of Z-Transforms
If x(n) is a finite duration causal sequence or right sided sequence, then the ROC is entire z-plane except at z = 0. If x(n) is a finite duration anti-causal sequence or left sided sequence, then the ROC is entire z-plane except at z = ∞.
What is the importance of ROC of z-transform?
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 is ROC and its properties?
Properties of ROC of Laplace Transform
ROC contains strip lines parallel to jω axis in s-plane. If x(t) is absolutely integral and it is of finite duration, then ROC is entire s-plane. If x(t) is a right sided sequence then ROC : Res > σo. If x(t) is a left sided sequence then ROC : Res < σo.
How do you find the region of convergence of a transfer 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.
