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Property 2: The ROC does not contain any poles. | Property 2: The ROC does not contain any poles. | ||
| − | Property 3: If x[n] is of finite duration then the ROC is the entire z-plane except possibly z=0 and z=<math> \ | + | Property 3: If x[n] is of finite duration then the ROC is the entire z-plane except possibly z=0 and z=<math> \infty </math> |
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| + | Property 4: If x[n] is a right sided sequence and if the cirlce |z| = ro is in the ROC then all finite values of z for which |z| >ro will also be in the ROC. | ||
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| + | Property 5: If x[n] is a left sided | ||
Revision as of 15:00, 30 November 2008
Properties of the region of convergence for Z-transform
A number of properties are listed in the oppenheim willsky textbook. These properties state the insights of the z-transforms region of convergence.
Property 1: The ROC of X(z) consists of a ring in the z-plane centered about the origin.
Property 2: The ROC does not contain any poles.
Property 3: If x[n] is of finite duration then the ROC is the entire z-plane except possibly z=0 and z=$ \infty $
Property 4: If x[n] is a right sided sequence and if the cirlce |z| = ro is in the ROC then all finite values of z for which |z| >ro will also be in the ROC.
Property 5: If x[n] is a left sided
