The aim is to describe new geometric approaches to define the statistics of spatio-temporal and polarimetric measurements of the states of an electromagnetic wave, using the works of Maurice Fr{\'e}chet, Jean-Louis Koszul and Jean-Marie Souriau, with in particular the notion of 'average' state of this digital measurement as a Fr{\'e}chet barycentre in a metric space and a model derived from statistical mechanics to define and calculate a maximum density of entropy (extension of the notion of Gaussian) to describe the fluctuations of the electromagnetic wave. The article will illustrate these new tools with examples of radar application for Doppler, spatio-temporal and polarimetric measurement of the electromagnetic wave by introducing a distance on the covariance matrices of the electromagnetic digital signal, based on Fisher's metric from Information Geometry.

中文翻译：

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电磁数字信息的基本几何结构：雷达电磁波空间多普勒和极化涨落数字测量的统计表征

目的是使用 Maurice Fr{\'e}chet、Jean-Louis Koszul 和 Jean-Marie Souriau 的作品，描述定义电磁波状态的时空和极化测量统计的新几何方法，特别是这个数字测量的“平均”状态的概念作为度量空间中的 Fr{\'e}chet 重心和从统计力学派生的模型来定义和计算最大熵密度（概念的扩展Gaussian）来描述电磁波的波动。本文将通过在电磁数字信号的协方差矩阵上引入距离来说明这些新工具，并举例说明多普勒雷达应用、电磁波的时空测量和极化测量，基于 Fisher 的