基于Gabor空间的未知调频率LFM信号压缩采样与重构

针对现有压缩采样系统在宽带线性调频信号压缩采样过程中存的采样系统不适用、调制信息依赖等问题，提出了一种基于Gabor空间的线性调频信号压缩采样与重构方法，在未知调频率的条件下，实现了线性调频信号的压缩采样与有效重构。首先，结合压缩感知以及平移不变空间理论，设计了基于Gabor空间的压缩采样系统，分析了压缩采样系统组成部分以及工作原理。然后，利用信号在Gabor空间的稀疏性，建立了Gabor系数的压缩重构模型，并在充分考虑噪声、失配的条件下，分析了原始信号重构误差上界。最后，通过数值仿真实验，验证了所提方法的有效性，实验结果表明，基于Gabor空间的压缩采样系统具有采样频率低，采样点数少，以及工作稳定性高等优点。 

Compressive Sampling and Reconstruction for LFM Signals with Unknown Modulating Rate Based on Gabor Space

In order to solve the problems existing in the current compressive sampling systems， such as the inapplicability of sampling system and the dependence for modulation information， a compressive sampling and reconstruction method based on Gabor space is proposed to realize the compressive sampling and effective reconstruction for LFM signals under the condition of unknown modulation rate. Firstly， combined with compressive sensing theory and translation invariant space theory， the compressive sampling system based on Gabor space is designed. The components and working principle of the compressive sampling system are analyzed. Then， utilizing the sparsity of signals in Gabor space， the compressive and reconstruction models of Gabor coefficients are established. The upper bound of the reconstruction error is also analyzed with full considerations of noises and mismatch. Finally， the effectiveness of the proposed method is verified by numerical simulation. The results show that the compressive sampling system based on Gabor space has the advantages of low sampling rate， low sample number and high working robustness.