Biquaternion Z Transform

TL;DR

This paper introduces the biquaternion Z transform, extending the complex Z transform to solve biquaternion recurrence relations, with analysis of convergence and properties demonstrated through examples.

Contribution

It proposes a novel biquaternion Z transform method, including convergence analysis and properties, for solving biquaternion recurrence relations.

Findings

Effective solution of biquaternion recurrence relations

Analysis of convergence region using special norm

Illustrative examples demonstrating method effectiveness

Abstract

In this work, the biquaternion Z transformation method is proposed to solve a class of biquaternion recurrence relations. Biqueternion Z transform is an natural extension of the complex Z transform. In the design process, special norm presentation is employed to analyze the region of convergence of the biquaternion geometry sequence. In addition, some useful properties have been given. It is shown that the proposed properties is helpful to understand the biquaternion Z transform. Finally, several examples have been given to illustrate the effectiveness of the proposed design method.