论文标题
朝向四个二次相傅立叶变换
Towards Quaternion Quadratic Phase Fourier Transform
论文作者
论文摘要
二次相傅立叶变换QPFT是对傅立叶变换类别的新添加，并体现了各种信号处理工具，包括傅立叶，分数傅立叶，线性规范和特殊的仿射傅立叶变换。在本文中，我们将二次相傅立叶变换概括为四基因估值信号，即被称为QPFT QQPFT。我们通过研究2D Quaternionic信号的QPFT来启动研究，然后介绍2D Quaternionic信号的QQPFT。利用QQPFT和四元基因傅立叶变换QFT之间的基本关系，我们得出了与QQPFT相关的逆变换和parseval和Plancherel公式。还研究了一些其他属性，包括线性，偏移和QQPFT的调制。最后，我们为QQPFT制定了几类的不确定性原则，其中包括海森伯格（Heisenberg type），对数UP，Hardys Up，Beurlings up和Donohon Stark up up。可以将其视为QQPFT在现实世界中应用程序中的第一步。
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier transform. In this paper, we generalize the quadratic phase Fourier transform to quaternion valued signals, known as the quaternion QPFT QQPFT. We initiate our investigation by studying the QPFT of 2D quaternionic signals, then we introduce the QQPFT of 2D quaternionic signals. Using the fundamental relationship between the QQPFT and quaternion Fourier transform QFT, we derive the inverse transform and Parseval and Plancherel formulas associated with the QQPFT. Some other properties including linearity, shift and modulation of the QQPFT are also studied. Finally, we formulate several classes of uncertainty principles UPs for the QQPFT, which including Heisenberg type UP, logarithmic UP, Hardys UP, Beurlings UP and Donohon Starks UP. It can be regarded as the first step in the applications of the QQPFT in the real world.
