ROC of Laplace Transform
It is the range of Complex variable ‘s’ in s-plane for which the Laplace Transform is finite of convergent.
The Laplace transform of a continuous-time signal or system x(t) is given by:
X(s)=\int_{0}^{\infty}x(t).e^{-st}dt
The ROC for the Laplace transform is the set of complex values s for which this integral converges absolutely. In other words, it’s the set of values of s for which the integral is finite.
Types of Region of Convergence of the Z-Transform for Causal, Anti-causal and Non-causal signals
Given below are the ROC of Causal, Anti-causal and Non-causal signals
ROC for z-Transform of Causal Signals is given below
ROC of Z- transform for an Anti-Causal signal is given below
ROC of Z-Transform for a Non-Causal Signal is given below
Properties of Region of Convergence (ROC) of the Z-Transform
The Z-transform is a mathematical tool used primarily in digital signal processing and discrete-time systems analysis. Our basic introduction for the properties of the region of convergence (ROC) of the Z-Transform starts with the basic question, what do we exactly mean by Region of Convergence. In this article we will be going through the properties of the region of convergence in the Z transform in brief.
Table of Content
- What is Z-Transform?
- What is Region of Convergence (ROC)signal-processing?
- ROC of Laplace Transform
- Properties of Region of Convergence of Z- Transform
- Advantages of ROC of Z-Transform
- Disadvantages of ROC of Z-Transform
- Applications of ROC of Z-Transform