An Alternative Approach to Inverse Z-Transform of Rational Functions

Abstract: 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.