四元数偏移线性正则变换的广义测不准原理

超复数信号在空间域和四元数线性正则频域的能量集中

Hypercomplex Signal Energy Concentration in the Spatial and Quaternionic Linear Canonical Frequency Domains

四元数线性正则变换（QLCT）是一类积分变换，它推广了四元数傅里叶变换和四元数分数傅里叶变换.本文将能量集中问题推广到二维超复数信号（特别是四元数信号）。四元数长球体波函数是目前公认的在二维空间域和四元数线性正则频域中能量最集中的信号。研究了QPSWFs的改进定义，给出了QPSWFs的合理性质。本文的目的是了解在二维空间和四元数线性正则频域的能量集中的测量。截断的高斯函数和QPSWFs之间的能量集中比率的示例直观地说明QPSWFs是更能量集中的信号。

四元数偏移线性正则变换的Wigner-Ville分布

Wigner-Ville distribution associated with the quaternion offset linear canonical transforms

Wigner-Ville分布（WVD）和四元数偏移线性正则变换（QOLCT）是信号分析和图像处理中的重要工具。本文的目的是定义Wigner-Ville分布与四元数偏移线性正则变换（WVD-QOLCT）。实际上，该变换结合了WVD和QOLCT两种变换的结果和灵活性。我们得到了这种变换的一些重要性质，如反演和Plancherel公式，我们建立了一个版本的Heisenberg不等式，Lieb定理，我们给出了WVD-QOLCT的Poisson求和公式。

加窗偏移线性正则变换的测不准原理

Uncertainty principles for the windowed offset linear canonical transform

加窗偏移线性正则变换（WOLCT）是加窗线性正则变换（WLCT）的推广。本文概括了WOLCT的几种不同的测不准原理，包括Heisenberg测不准原理、Hardy测不准原理、Beurling测不准原理、Lieb测不准原理、Donoho-Stark测不准原理、Amrein-Berthier-Benedicks测不准原理、Nazarov测不准原理和对数测不准原理。

Uncertainty Principles for Quaternion Windowed Offset Linear Canonical Transform of Two Dimensional Signals

The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical transform for quaternion-valued signals, by introducing a novel time-frequency transform namely the quaternion windowed offset linear canonical transform of 2D quaternion-valued signals. We initiate our investigation by studying some fundamental properties of the proposed transform including inner product relation, energy conservation, and reproducing formula …

Convolution theorems associated with quaternion linear canonical transform and applications

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are consistent once in complex or real space. Various types of convolution formulas are discussed. Consequently, the QLCT of the convolution of two quaternionic functions can be implemented by the product of their QLCTs, or the summation of the products of their QLCTs. As applications, correlation operators and theorems of the QLCT are derived. The proposed convoluti…