本文定义了随机信号的分数阶功率谱和分数阶相关函数,得到了分数阶功率谱和分数阶相关函数的关系.在此基础上,推导出分数阶Fourier域滤波器的输入输出分数阶功率谱的关系.仿真结果表明,分数阶功率谱估计可以用于chirp信号的检测和估计,以及分数阶系统辨识.

The definition of the fractional power spectrum and the fractional correlation for random signals are proposed,and the expression of the fractional power spectral density in terms of the fractional correlation function is described.Then,the fractional power spectral relations for the fractional Fourier filter are derived.Finally,the theory obtained is verified by simulations,and indicate the potential applications in chirp signals detection and fractional system identification.