Confusion About Convolution z-Transform ROC

  • Thread starter ckutlu
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Homework Statement


I need to find a transfer function using the given functions which i have no problem with. But i don't know how to exactly define the Region Of Convergence of the resulting transfer function.

I have h1[n] and h2[n] as to be convoluted to find the transfer function.


Homework Equations


[tex]h_{1}[n]\ast h_{2}[n]\stackrel{Z}{\rightarrow}H_{1}(z) H_{2}(z) = H(z)[/tex]


The Attempt at a Solution


I looked into Wikipedia page :
http://en.wikipedia.org/wiki/Z-transform#Example_1_.28no_ROC.29"
Under the properties section, this is written for the ROC of the convolution z-Transform:
Mr. Wikipedia said:
At least the intersection of ROC1 and ROC2"

My confusion starts here, why "at least"? What more can then be? I think since we are multiplying the transforms, "only" the intersection of the ROC's should define the transfer function's ROC. Am i wrong?
 
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