分数阶Fourier级数展开及相关性质研究

介绍了一种从分数阶Fourier变换（FRFT）思想导出的分数阶Fourier级数（FRFS）展开方法，可以看作为Fourier级数的进一步推广，在研究非平稳信号中有着重要的应用。分数阶Fourier级数以一组有限时域内的正交Chirp信号为基函数来逼近分析信号，与Fourier级数相比，在分析非平稳信号中具有更大的灵活性。文中给出了Chirp信号FRFS分解的解析表示，分析了FRFS展开系数的振荡特性；同时对不同参数下的FRFS收敛速度进行了研究和计算机仿真，对于工程实际中的计算具有较好的参考价值。

FRFS Expansion and Its Characters Analysis

A fractional Fourier series(FRFS) derived from fractional Fourier transform(FRFT) is presented in this paper.FRFS can be regarded as an extension of conventional Fourier series(FS).It finds a number of important applications in non-stationary signals.Based on a set of orthogonal chirp functions in finite time,arbitrary function in finite time can be decomposed into the sum of orthogonal chirp functions using FRFS,which shows more advantages than FS when analyzing non-stationary signals.This paper gives its ...