  Our paper introduces a novel method for calculating the inverse
$\mathcal{Z}$-transform of rational functions. Unlike some existing approaches
that rely on partial fraction expansion and involve dividing by $z$, our method
allows for the direct computation of the inverse $\mathcal{Z}$-transform
without such division. Furthermore, our method expands the rational functions
over real numbers instead of complex numbers. Hence, it doesn't need algebraic
manipulations to obtain a real-valued answer. Furthermore, it aligns our method
more closely with established techniques used in integral, Laplace, and Fourier
transforms. In addition, it can lead to fewer calculations in some cases.
