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%。
Abstract
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 error-prone.The simulation experiment results show that the proposed method achieves a reconstructed power of 99.62% at 17 sampling points.
关键词
分数阶傅里叶变换 /
等效时间采样 /
压缩感知 /
啁啾信号
Key words
fractional Fourier transform /
equivalent time sampling /
compressive sensing /
chirp signal
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