论文标题
四元素线性典型小波变换和相应的不确定性不平等现象
Quaternion Linear Canonical Wavelet Transform and The Corresponding Uncertainty Inequalities
论文作者
论文摘要
线性规范小波变换已被证明是用于光学和信号处理的有价值且强大的时频分析工具。在本文中，我们提出了一种称为Quaternion线性典型小波变换的新型变换，该变换旨在在不同的尺度，位置和方向上代表二维四维Quaternion值信号。所提出的变换不仅继承了四元小波变换的特征，而且还具有四个线性规范域中信号表示的能力。我们研究了四元素线性典型小波变换的基本特性，包括parseval的公式，能源保护，反转公式以及使用Quaternion线性规范变换的机械和卷积的机械来对其范围进行表征。我们通过得出经典的海森堡 - 波利 - - 韦尔 - 韦尔 - - 韦尔的不平等不平等以及相关的对数和局部版本的类似物来结束调查，以实现Quaternion线性规范小波变换的相关对数和局部版本。
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet transform which is designed to represent two dimensional quaternion-valued signals at different scales, locations and orientations. The proposed transform not only inherits the features of quaternion wavelet transform but also has the capability of signal representation in quaternion linear canonical domain. We investigate the fundamental properties of quaternion linear canonical wavelet transform including Parseval's formula, energy conservation, inversion formula, and characterization of its range using the machinery of quaternion linear canonical transform and its convolution. We conclude our investigation by deriving an analogue of the classical Heisenberg-Pauli-Weyl uncertainty inequality and the associated logarithmic and local versions for the quaternion linear canonical wavelet transform.
