This 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, the proposed method allows for the direct computation of the inverse \(\mathcal {Z}\) -transform without such division. Furthermore, this method expands the rational functions over real numbers instead of complex numbers. Hence, it does not 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.
