Comments on “Fair and Square Computation of Inverse $\cal Z$-Transforms of Rational Functions”

In the recent paper “Fair and Square Computation of Inverse
$\cal Z$
-Transforms of Rational Functions” (IEEE Trans. Educ., vol. 55, no. 2, pp. 285–290, May 2012), Moreira and Basilio present methods for finding the inverse
$\cal Z$
-transform of a rational function
$X(z)$
, which has: 1) poles at the origin of the
$z$
-plane, and 2) multiple poles anywhere in the
$z$
-plane. Compared to their methods, it is shown here that the partial fraction expansion method for inversion of
$\cal Z$
-transforms can be used to take care of both the cases in a simpler manner. For the case of multiple poles, some easier alternatives to the laborious multiple differentiation formula, as prescribed in textbooks, are presented. These have been applied in courses taught by the author and have proved to be student-friendly .