分数阶Fourier域上非均匀采样信号的频谱重构研究

Spectral Reconstruction from Nonuniformly Sampled Signals in the Fractional Fourier Domain

本文研究了分数阶Fourier变换域上非均匀采样信号的重构问题.首先得到周期非均匀采样信号经非均匀分数阶Fourier变换后的频谱表达式,研究了该分数阶频谱和信号连续分数阶频谱之间的关系,并基于该关系式提出了一种分数阶Fourier域周期非均匀采样信号的频谱重构算法;其次,讨论了分数阶Fourier变换域上更加一般情况下非均匀采样信号重构问题;最后,给出了周期非均匀采样信号频谱重构的仿真结果.

This paper investigates the problem of signal reconstruction from nonuniformly sampled signals in the fractional Fourier domain.Firstly,the spectral representations of periodic nontmiformly sampled signal in the fractional Fourier domain andthe relationship between the spectral and the nonuniform spectral have been deduced. A spectral reconstruction algorithm is proposed based on the derived relationship. Secondly, the signal reconstruction formula from general nonunfionn samples in the fractional Fourier domain has been proposed. Lastly, the simulation results are obtained for the periodic nonuniform sampling model.