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. Thank u in advance, Murty

# Z-Transform - ROC

Started by ●August 29, 2003

Reply by ●August 29, 20032003-08-29

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. > > Thank u in advance, > MurtyThe ROC of the product of the two Z-transform contains the intersection between ROC_x and ROC_y, and not is equal to the intersection. The ROC of the product could be larger than the intersection. If a pole that borders on the region of convergence of one of the z-transform is canceled by a zero of the other, the ROC of the product could be larger. For the example i've to think about it. But i think that in literatury there are a lot of them.