he octonion offset linear canonical transform can be defined as a time shifted and frequency modulated version of the octonion linear canonical transform, a more general framework of most existing signal processing tools. In this paper, we first define the and provide its closed-form representation. Based on this fact, we study some fundamental properties of proposed transform including inversion formula, norm split and energy conservation. The crux of the paper lies in the generalization of several well known uncertainty relations for the that include Pitts inequality, logarithmic uncertainty inequality, Hausdorff Young inequality and local uncertainty inequalities.
翻译:octonion 抵消线性罐体变异可定义为时间转移和频率调控版的八溴二苯醚线性变异,这是大多数现有信号处理工具的更一般的框架。我们首先在本文中定义并提供其封闭式代表形式。基于这一事实,我们研究了拟议变异的一些基本特性,包括反向公式、规范分解和节能。文件的要点在于对包括Pitts不平等、对数不确定性不平等、Hausdorf Young不平等和地方不确定性不平等在内的若干众所周知的不确定性关系的概括化。