Open AccessRegion of convergence of derivative of Z transform
Author(s) -
Forouzan A.R.
Publication year - 2016
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
ISSN - 1350-911X
DOI - 10.1049/el.2016.0189
Subject(s) - sequence (biology) , z transform , convergence (economics) , mathematics , domain (mathematical analysis) , derivative (finance) , combinatorics , algorithm , discrete mathematics , mathematical analysis , fractional fourier transform , fourier transform , fourier analysis , chemistry , finance , biochemistry , economics , economic growth
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 (d X ( 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.