In this paper, the offset linear canonical transform associated with biquaternion is defined, which is called the biquaternion offset linear canonical transforms (BiQOLCT). Then, the inverse transform and Plancherel formula of the BiQOLCT are obtained. Next, Heisenberg uncertainty principle and Donoho-Stark’s uncertainty principle for the BiQOLCT are established. Finally, as an application, we study signal recovery by using Donoho-Stark’s uncertainty principle associated with the BiQOLCT.

中文翻译：

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双四元数偏移线性正则变换的不确定性原理

本文定义了与双四元数相关的偏移线性正则变换，称为双四元数偏移线性正则变换（BiQOLCT）。然后，得到BiQOLCT的逆变换和Plancherel公式。接下来，建立了BiQOLCT的海森堡不确定性原理和Donoho-Stark不确定性原理。最后，作为一个应用，我们通过使用与 BiQOLCT 相关的 Donoho-Stark 不确定性原理来研究信号恢复。