J Opt Soc Am A Opt Image Sci Vis. 2023 Feb 1;40(2):326-336. doi: 10.1364/JOSAA.476475.
The Wigner distribution function (WDF) is a significant time-frequency analysis tool in, e.g., the theory of optical coherence and signal processing. Recently, various generalizations of the WDF associated with linear canonical transforms have been proposed to improve and broaden its applications. It is useful to identify which of these novel distributions have independent significance for further investigation. We plot these distributions for a test signal using symbolic integration to find which distributions are linear coordinate transforms of the WDF or have unique features. Five distributions are determined to be linear coordinate transforms of the WDF. Two distributions show unique characteristics. We focus on the mathematical interpretation, properties, and possible applications of those two distributions. We demonstrate how one of them can be used in the analysis of partially coherent systems.
维格纳分布函数（WDF）是光学相干和信号处理等理论中的重要时频分析工具。最近，已经提出了与线性正则变换相关的各种 WDF 的广义形式，以改进和拓宽其应用。确定这些新分布中哪些具有独立的意义以供进一步研究是有用的。我们使用符号积分为测试信号绘制这些分布，以找到哪些分布是 WDF 的线性坐标变换或具有独特特征。确定五个分布是 WDF 的线性坐标变换。两个分布显示出独特的特征。我们专注于这两个分布的数学解释、性质和可能的应用。我们演示了如何在部分相干系统的分析中使用其中一个分布。
