基于多测量向量模式的周期非均匀采样研究

Multiple Measurement Vectors for Periodic Non-uniform Sampling

为了实现稀疏信号的有效采样与完整重构,结合多测量向量模式,提出了一种针对稀疏信号的周期非均匀采样与重构方法。根据周期非均匀采样需要多个采样通道的特点,利用联合子空间理论将采样与重构转换为矩阵向量运算。利用多测量向量确定非零行向量的位置参数并分析了多测量向量模式在周期非均匀采样系统中的完整重构条件并通过插值器实现信号完整重构,使其能在数字系统中应用。最后,分别从可完整重构概率和系统整体验证两个方面证明了该方法能够实现稀疏信号的采样与重构。

Based on multiple measurement vectors,a method was proposed to realize the sampling and reconstruction of the sparse signals.According to the feature of periodic non-uniform sampling that needs multiple channels,the sampling and reconstruction of signals were transformed into matrix and vector operations by using the theory of union of subspaces.The necessary condition of reconstruction was analyzed and the complete reconstruction of sparse signal was achieved in the virtue of interpolations,which could insure that the signals could be applied in digital system.Finally,it was proved that the method can achieve the sampling and reconstruction of sparse signals from recovery successful rate and integer of system.