基于等效采样的高速啁啾信号恢复

High-speed Chirp Signal Recovery Based on Equivalent Sampling

在压缩感知原理的基础上,利用分数阶傅里叶变换和等效时间采样构造观测矩阵,对观测过程进行稀疏表达,建立符合压缩感知原理的高频观测方程,并对其进行求解,最终实现对原始信号的重建。利用比奈奎斯特取样速率更短的特定时间取样,可以实现对线性调频信号的高精度重构;而当取样采用不等间隔取样,在时频范围内,取样的时频范围不再是固定的,但会因原信号中的非零点出现能量泄漏而造成大量无关扰动。等效时间采样使得频谱不再是规律性搬移,而是一小部分胡乱地搬移,频率泄漏均匀地分布在整个频域,因而数值都比较小,使恢复过程误差更小。仿真实验结果表明,所提方法在采样点个数为17时,重构成功率高达99.62%。

This project proposes to construct an observation matrix based on the principle of compressive sensing,using fractional Fourier transform and equivalent time sampling to perform a sparse representation of the observation process,to establish a high frequency observation equation in accordance with the principle of compressive sensing,and to solve it,and finally to realise the reconstruction of the original signal.High-precision reconstruction of linear FM signals can be achieved using time-specific sampling at shorter rates than Nyquist sampling.When sampling is done at unequal intervals,the time-frequency range sampled is no longer fixed in the time-frequency range,but results in a large amount of extraneous perturbation due to energy leakage from non-zero points in the original signal.Equivalent time sampling makes the spectrum no longer move regularly,but a small part of it moves haphazardly,and the frequency leakage is uniformly distributed throughout the frequency domain,thus the leakage values are all smaller,making the recovery process less errorprone.The simulation experiment results show that the proposed method achieves a reconstructed power of 99.62%at 17 sampling points.