A Residue Calculus of Isolated Singular Zero Point and Its Application in Z Transform

The residue theorem is a powerful tool in mathematics and signal processing, such as it is usually employed for the inverse Laplace transform and the inverse Z transform. With respect to the most commonly rational functional form in the Z transform, a theorem and a new formula for residue calculus based on the singular zero point is introduced. Then two consequences are proposed. Finally, based on the derived theorems, a new convenient algorithm for computing the inverse Z transform is presented. Applications with satisfying results indicate convenience and workability of the proposed method.

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