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Chapter: Signals and Systems - Analysis of Continuous Time Signals

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Properties of ROC of Laplace Transform

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

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)> amax , 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)< amin , where amin 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.

 

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