分数卷积及其光学实现

Fractional Convolution and Its Optical Implementation

将频域中常规卷积的定义推广到分数域中,得到了分数卷积的频域定义,给出了它的空域表达和光学实现装置,进行了计算机模拟实验。结果表明:分数卷积与常规卷积相比较其峰值降低,但对底座的展宽作用没有变化。此结论对完善分数傅里叶的知识体系具有重要的理论意义,同时为滤波器的设计提供一个新的理论指导。

By generalizing the conventional convolution of frequency domain to fractional domain, the fractional convolution is defined, some optical implementations of fractional convolution are suggested and demonstrated with computer simulations. The results show that the fractional convolution declines the peak of convolution and does not affect the width of convolution, compared with conventional convolution. This will improve the theory of fractional Fourier transform and guide the filter design.