基于分数阶Gabor变换的LFM回波信号压缩采样方法

针对现有的压缩采样系统在线性调频(linear frequency modulated, LFM)回波信号压缩采样重构过程中存在的重构效果不佳的问题, 提出一种基于分数阶Gabor变换的回波信号压缩采样方法。首先, 利用不同目标回波信号在时延上的差异性, 给出基于分数阶Gabor变换的LFM回波信号稀疏表示方法, 并分析了分数阶Gabor变换的完备性条件。然后, 根据分数阶Gabor变换低通滤波的实现方式, 设计了LFM回波信号压缩采样系统, 建立了信号重构模型。最后, 通过仿真实验与应用实例分析, 验证了所提压缩采样系统的有效性。实验结果表明, 与现有压缩采样系统相比, 所提压缩采样系统的重构误差更低、重构效果更好。

Compressive sampling method based on fractional Gabor transform for LFM echo signals

In order to overcome the poor reconstruction performance of current compressive sampling methods, a novel compressive sampling method based on the fractional Gabor transform is proposed for linear frequency modulated (LFM) echo signals. Firstly, utilizing the difference in time delay of different echoes, the fractional Gabor transform is introduced to achieve the sparse representation for LFM echo signals, and the corresponding completeness condition is analyzed. Then, according to the low-pass filter implementation of fractional Gabor transform, compressive sampling system is designed for LFM echo signals. And the signal reconstruction model is also established. Finally, the effectiveness of the proposed method is verified by simulation and application examples. Experimental results show that compared with the existing compressive sampling methods, the proposed method has lower reconstruction error and better reconstruction performance.