Region of convergence of derivative of Z transform

Abstract

A well-known property of the Z transform is the differentiation in z-domain property, which states that if X(z) Z{x[n]} is the Z transform of a sequence x[n] then the Z transform of the sequence nx[n] is Z{nx[n]}=-z(dX (z)/dz). It is generally believed that the regions of convergence (ROC) for the two Z transforms are the same. It is shown that this is not true in the general case where X(z) is not rational and an example, in which the ROC is different for X(z) and Z{nx[n]}, is given. © The Institution of Engineering and Technology 2016.