Region of convergence Z-transform

[MikeSv]

Hello everyone.

Iam just learning the z-transform for discrete signals and I can't get my head around the Region of covergence (ROC).
As far as I have understood describes the ROC if the z-transform excists or not ?

But how to I actually calculate it? Is there any kind of formula?

I all examples I found they never show howto actually get to the solution.

Thanks in advance,

kind regards,

Mike

 

[PhysicoRaj]

http://fourier.eng.hmc.edu/e102/lectures/Z_Transform/node3.html
http://pilot.cnxproject.org/content/collection/col10064/latest/module/m10622/latest
If you are familiar with the Laplace transform and the s-plane, the straight lines parallel to your imaginary axis in the s-plane is transformed to concentric circles centred about the origin in the z-plane.

 

[MikeSv]

Thank you very much for your reply.
Does that mean its just finding out the poles of the z transform to find the ROC?

Regards,
Michael

 

[PhysicoRaj]

If you have checked those links, there are a few examples and explanation on how to arrive at the ROC.
Here are a few ways to arrive at it. Given the discrete time signal you analyze the convergence of the summation in the definition of z transform, which gives you the roots as well as the condition for which the summation converges (i.e., transform exists) thus giving the ROC.
Suppose you are given the roots but no time domain sequence, you need the knowledge of whether the signal is finite in duration, or is causal (positive time, negative time or both) with which you can decide the ROC.
If you have the z-domain transform right away, then you have the roots.