二次相位波包变换
Quadratic phase wave packet transform
摘要：
二次相位傅里叶变换由于在图像和信号处理中的应用，近年来得到了广泛的应用。然而，QPFT是不够的本地化的二次相位谱，这是在某些应用中所需要的。本文在波包变换WPT和QPFT的基础上，提出了二次相位波包变换QP WPT。首先，我们提出了QP小波变换的定义，并给出了它与加窗傅里叶变换小波变换的关系。其次，给出了新定义的QP WPT的几个重要不等式和重要性质，如有界性、重构公式、Moyals公式、再生核等。最后，我们给出了几类测不准不等式，如Leibs测不准原理、对数测不准不等式和Heisenberg测不准不等式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
