连续Gabor四元数线性正则变换的测不准原理
Uncertainty Principles For the continuous Gabor quaternion linear canonical transform
摘要：
Gabor变换是时频信号分析的常用工具之一。本文的主要目的是将Gabor傅里叶变换推广到四元数线性正则变换。实际上，这种变换为我们研究与四元数线性正则变换相关的非平稳和局部信号提供了更大的灵活性。导出了一些有用的性质，如Plancherel和反演公式。证明了一些测不准原理：包括Heisenberg不等式、Lieb不等式和对数不等式。最后，我们用浓度和本尼迪克型定理的类似物来结束。
英文摘要：
Gabor transform is one of the performed tools for time-frequency signal analysis. The principal aim of this paper is to generalize the Gabor Fourier transform to the quaternion linear canonical transform. Actually, this transform gives us more flexibility to studied nonstationary and local signals associated with the quaternion linear canonical transform. Some useful properties are derived, such as Plancherel and inversion formulas. And we prove some uncertainty principles: those including Heisenberg's, Lieb's and logarithmic inequalities. We finish by analogs of concentration and Benedick's type theorems.
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