论文标题
循环卷积和产品定理，用于仿射离散分数傅立叶变换
Circular Convolution and Product Theorem for Affine Discrete Fractional Fourier Transform
论文作者
论文摘要
分数傅立叶变换是基础科学和应用科学中普遍存在的信号处理工具。分数傅立叶变换概括了傅立叶变换的每个属性和应用。尽管离散的分数傅立叶变换具有实际的重要性，但其在数字通信中的应用仍然难以捉摸。离散傅立叶变换的卷积属性在设计多载波调制系统中起着至关重要的作用。在这里，我们报告了封闭形式的仿射离散分数傅立叶变换，并为其显示了圆形卷积属性。所提出的方法是多功能的，并概括了离散的傅立叶变换，并且可以在基于傅立叶的信号处理工具中找到应用程序。
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of the discrete fractional Fourier transform, its applications in digital communications have been elusive. The convolution property of the discrete Fourier transform plays a vital role in designing multi-carrier modulation systems. Here we report a closed-form affine discrete fractional Fourier transform and we show the circular convolution property for it. The proposed approach is versatile and generalizes the discrete Fourier transform and can find applications in Fourier based signal processing tools.
