# Z-Transform - ROC

Started by August 29, 2003
```Hi friends!

I got a basic doubt in the theoritical dsp. Hope some one can
help me. My actual question is:

Consider a sequence x(n) whose z-transform is X(z) and ROC is
characterized by Rx. Consider another sequence y(n) with z-transform
Y(z) and ROC Ry. Now
suppose that Rx and Ry are mutually exclusive that is their
intersection region is a null-set. Now if I define h(n) as convolution
of x(n) and y(n),

h(n)=x(n)*y(n)
Correspondingly:
H(z)=X(z)Y(z)

Now is it possible for H(z) to hav some region of convergence
eventhough the intersection of ROC's of X(z) and Y(z) is a null set?
If so please give one example to clear my doubt.

Murty
```
```sriram_friendly@yahoo.co.in (Murty) wrote in message news:<d906c40f.0308290030.33ae9fb5@posting.google.com>...
> Hi friends!
>
>      I got a basic doubt in the theoritical dsp. Hope some one can
> help me. My actual question is:
>
>      Consider a sequence x(n) whose z-transform is X(z) and ROC is
> characterized by Rx. Consider another sequence y(n) with z-transform
> Y(z) and ROC Ry. Now
> suppose that Rx and Ry are mutually exclusive that is their
> intersection region is a null-set. Now if I define h(n) as convolution
> of x(n) and y(n),
>
>                           h(n)=x(n)*y(n)
> Correspondingly:
>                           H(z)=X(z)Y(z)
>
> Now is it possible for H(z) to hav some region of convergence
> eventhough the intersection of ROC's of X(z) and Y(z) is a null set?
> If so please give one example to clear my doubt.
>