Hong Jiaying, Zhou Xi, Xin Nian, Chen Zhengyu, He Bin, Hu Zhangwei, Zhang Ning, Li Qin, Xue Ping, Zhang Xiao
Opt Express. 2021 Nov 22;29(24):40106-40115. doi: 10.1364/OE.443223.
Fractional Fourier transform (FRFT) is the generalization of Fourier transform. It provides many significant advantages, such as fractional order as the new degree of freedom and high efficiency and great performance for non-stationary signal analysis/processing, that other operations including Fourier transform cannot. Here, we report a hybrid optical system for computation of arbitrary-order FRFT of temporal signals. In experiment, the fractional-domain information of input temporal signals could be directly acquired by detector. In addition, the optical computing results are in good agreement with numerical results. Then we apply the optical computing engine to demodulation of chirp spread spectrum signals. Using sub-Nyquist sampling, the proposed technology could greatly save the number of measurements in demodulation. The compression ratio could be as low as 0.4%, because of the high compression performance of chirp signals in FRFT domain. As a result, the proposed technology has unique advantages in analysis and information extraction for non-stationary signals, especially for chirp-like signals, and may become a powerful optical time-frequency analysis tool for temporal signals.
分数阶傅里叶变换（FRFT）是傅里叶变换的推广。它具有许多显著优势，例如分数阶作为新的自由度，以及在非平稳信号分析/处理方面具有高效率和出色性能，而包括傅里叶变换在内的其他运算则无法做到。在此，我们报道一种用于计算时间信号任意阶FRFT的混合光学系统。在实验中，输入时间信号的分数域信息可由探测器直接获取。此外，光学计算结果与数值结果吻合良好。然后我们将该光学计算引擎应用于线性调频扩频信号的解调。利用亚奈奎斯特采样，所提出的技术可在解调中大幅减少测量次数。由于线性调频信号在FRFT域具有高压缩性能，压缩比可低至0.4%。结果表明，所提出的技术在非平稳信号的分析和信息提取方面具有独特优势，尤其是对于类线性调频信号，并且可能成为一种强大的用于时间信号的光学时频分析工具。
