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基于Gabor框架的窄脉冲信号采样及重构效果已经得到验证,其解决了有限新息率(finite rate of innovation,FRI)采样方法无法在波形未知的情况下重构出脉冲波形的问题.但是目前的Gabor框架采样系统的窗函数构造复杂且难以物理实现.本文将指数再生窗函数引入Gabor框架,将窗函数序列调制部分简化为一阶巴特沃斯模拟滤波器,构造了Gabor系数重构所需要的压缩感知(compressed sensing,CS)测量矩阵.为了使得测量矩阵满足信号精确重构所需的约束等距特性(restricted isometry property,RIP),根据高阶指数样条函数能量聚集特性,选择了最优的窗函数支撑宽度,推导了信号重构所需的约束条件,还对其鲁棒性进行了分析.本文通过仿真实验对上述分析进行了有效验证,该系统可应用于测试仪器、状态监测、雷达及通信领域等多种背景下的窄脉冲信号采样与重构.
The sampling and reconstruction of narrow pulse signals based on Gabor framework has been verified, which solves the problem that the finite rate of innovation (FRI) sampling method can not reconstruct the pulse waveform when the waveform is unknown. However, The window function of Gabor frame sampling system is complex and difficult to be implemented physically.In this paper, the exponential regeneration window function is introduced into Gabor framework, and the modulation of window function sequence is simplified as first-order Butterworth filter. The Gabor coefficient reconstruction In order to make the measurement matrix satisfy the constraint isometric property (RIP) required for accurate signal reconstruction, according to the energy aggregation characteristics of the high-order exponential spline function, The optimal width of the window function support is deduced and the necessary constraints of the signal reconstruction are derived and the robustness of the window function is also analyzed.This paper validates the above analysis through the simulation experiment.The system can be applied to the test equipment, , Radar and communications and other areas of narrow pulse signal sampling and reconstruction.