基于傅立叶分析的非均匀采样信号内插重构方法

Signal recovering based on fourier analysis from nonuniform samples

针对实际采样过程中出现的采样非均匀性,从随机过程的角度研究非均匀采样信号的谱特性,提出频域均匀抽样傅立叶逆变换的非均匀时域采样信号重构方法。将非均匀采样信号描述为不均匀采样时刻冲激函数代数和的形式,利用傅立叶变换得到非均匀采样信号的频谱曲线,由采样时刻随机均匀分布的特点,得到反应原信号频谱特性的非均匀采样信号频谱数学期望,再由频域抽样理论重构原信号。MATLAB仿真实验验证了这种非均匀采样信号分析与重构方法的正确性,将这一研究成果应用到机械抖动激光陀螺输出信号处理中,得到了可靠的符合实际的机械正弦抖动幅频曲线并重构出激光陀螺正弦抖动机构的输出信号。

This paper describes a new approach that can process nonuniformly sampled signals efficiently,in the sense the digital spectrum and signal recovering from nonuniformly sampled signal can be derived precisely.The results of research on estimation spectra of signals whose samples were taken at randomly distributed sampling instants are presented.The paper determines the conditions under which a discrete Fourier transformation spectrum estimator provides an unbiased approximation of the spectrum of the original continuous-time signal in an unlimited range of frequencies.In the research non-uniformly sampled signals is represented as the algebraic addition of impulse function.Based on the random theory,the expected value is obtained.The signal is recovered by the inverse Fourier transformation.The validity of this method has been verified by simulation experiments.This developed technique can be applied in the processing of laser gyroscope output signal for the spectrum analysis and signal recovering.