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１９４６年，Ｇａｂｏｒ提出一种将信号分解为一组离散的高斯型基元信号的分析方法。由于高斯函数不能直接构成正交完备系，因而直到８０年代初随着双正交函数的引入，Ｇａｂｏｒ展开的存在性及唯一性问题才得以妥善解决。这一方法随之在信号分析及电磁口径辐射等问题中得以应用。在波场分析中，这一方法介于口径场辐射的空间波源积分表示与平面波谱积分表示之间，每个基元波束在几何光学近似下则能进一步简化为单根复射线场，这给实际问题的分析带来极大的方便。本文旨在对上述内容加以系统的归纳和总结。
In 1946, Gabor proposed an analysis method that decomposes a signal into a set of discrete Gaussian-type primitive signals. Since the Gaussian function can not directly form the orthogonal complete system, until the early 80s with the introduction of biorthogonal function, the existence and uniqueness problem of Gabor expansion can be properly solved. This method is followed by signal analysis and electromagnetic caliber radiation and other issues to be applied. In the wavefield analysis, this method is between the spatial wave source integral representation of the caliber field radiation and the integral representation of the plane spectrum, and each elementary beam can be further simplified into a single complex ray field under geometric optical approximation, which gives The analysis of practical problems brings great convenience. This article aims to systematically summarize the above content.