中文摘要：

分数阶傅里叶变换是传统傅里叶变换的一种扩展形式,它能够在介于时域和频域之间的分数域内分析和处理信号。由于分数阶傅里叶变换的一些独特的性质,已经被广泛应用于解微分方程、量子力学、图像处理和信号处理当中。本文介绍分数阶傅里叶变换,综述其在滤波器、神经网络、图像处理和无线通信等领域的应用;结合本课题组近年来的工作成果,重点介绍了其在光通信领域中的典型应用;展望了分数阶傅里叶变换在光通信中的发展趋势。

英文摘要：

Fraelional Fourier transformatinn （FrFF） is an extension form of the Fourier transfnrmation （FT）. It can analyze the fi＇actinnal signal between lime and frequency domains. Thanks to its unique properlies, the FrFT has fouud muhiple applications such as solving differential equations, quantum mechanics, optical image processing and signal processing. This paper gives a brief introduction to FrFT and reviews the current research progress of FrFT in several fields such as filtering, neural network, image processing and wireless communication. In addition, some typical applications in optical communication are depicted in detail. Some research directions of FrFT in optical communication field are suggested.