论文标题
二次相波数据包转换
Quadratic phase wave packet transform
论文作者
论文摘要
近年来，由于其在图像和信号处理中的应用，二次傅立叶变换已广受欢迎。但是，QPFT不足以定位某些应用中需要的二次相光谱。在本文中，提出了二次波数据包转换QP WPT，以根据波数据包转换WPT和QPFT来解决此问题。首先，我们提出了QP WPT的定义，并与窗户的傅立叶变换WFT给出了关系。其次，得出了新定义的QP WPT的几种显着不平等和重要特性，例如有界，重建公式，Moyals公式，复制核。最后，我们制定了几类不确定性不平等的类别，例如Leibs不确定性原理，对数不确定性不平等和Heisenberg的不确定性不平等。
The quadratic phase Fourier transform has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic phase spectrum which is required in some applications. In this paper, the quadratic phase wave packet transform QP WPT is proposed to address this problem, based on the wave packet transform WPT and QPFT. Firstly, we propose the definition of the QP WPT and gave its relation with windowed Fourier transform WFT. Secondly, several notable inequalities and important properties of newly defined QP WPT, such as boundedness, reconstruction formula, Moyals formula, Reproducing kernel are derived. Finally, we formulate several classes of uncertainty inequalities such as Leibs uncertainty principle, logarithmic uncertainty inequality and the Heisenberg uncertainty inequality.
