An Alternative Approach to Inverse Z-Transform of Rational Functions

MohammadJavad Vaez; Alireza Hosseini; Kamal Jamshidi

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arXiv · 2310.09808

An Alternative Approach to Inverse Z-Transform of Rational Functions

MohammadJavad Vaez·Alireza Hosseini·Kamal Jamshidi

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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.

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MohammadJavad Vaez, Alireza Hosseini, Kamal Jamshidi. 2023-10-15. An Alternative Approach to Inverse Z-Transform of Rational Functions. https://arxiv.org/abs/2310.09808

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