Properties of ROC of Laplace Transform

Properties of ROC of Laplace Transform:

1.           The ROC of X(s) consists of strips parallel to the jω axis in the s-plane.

2.           The ROC does not contain any poles.

3.           If x(t) is of finite duration and is absolutely integrable, then the ROC is the entire s-plane.

4.           It x(t) is a right sided signal, that is x(t) = 0 for t<t₀<∞ then the ROC is of the form Re(s)> a_max , where a _max equals the maximum real part of any of the poles of X(s).

5.           If x(t) is a left sided, that is x(t) = 0 for t>t₁> -∞, then the ROC is of the form Re(s)< a_min , where a_min equals the minimum real part of any of the poles of X(s).

6.           If x(t) is a two sided signal, than the ROC is of the form a₁<Re(s)< a₂.