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
摘要：
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。
英文摘要：
Quaternionic Linear Canonical Transforms (QLCTs) are a family of integral transforms, which generalized the quaternionic Fourier transform and quaternionic fractional Fourier transform. In this paper, we extend the energy concentration problem for 2D hypercomplex signals (especially quaternionic signals). The most energy concentrated signals both in 2D spatial and quaternionic linear canonical frequency domains simultaneously are recently recognized to be the quaternionic prolate spheroidal wave functions (QPSWFs). The improved definitions of QPSWFs are studied which gave reasonable properties. The purpose of this paper is to understand the measurements of energy concentration in the 2D spatial and quaternionic linear canonical frequency domains. Examples of energy concentrated ratios between the truncated Gaussian function and QPSWFs intuitively illustrate that QPSWFs are more energy concentrated signals.
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