An alternative approach to inverse Z-transform of rational functions

Abstract

This paper introduces a novel method for calculating the inverse 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 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. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.