最小二乘法重构r重平移不变子空间采样的研究

Studying on Reconstruction Sampling in Shift-Invariant Subspace with Multiplicity r from Least Squares Method

该文根据r重平移不变子空间采样模型,提出了一种基于最小二乘法的r重平移不变子空间采样重构方法,并且获得了重构滤波器的频域表达式;同时利用Hilbert空间投影理论分析了重构误差;最后,以调幅信号为例,验证了最小二乘法重构r重平移不变子空间采样的可行性。

According to the model of sampling in shift-invariant subspace with multiplicity r,this paper proposes a reconstruction method of sampling in shift-invariant subspace with multiplicity r based on least squares method,moreover,obtains the reconstruction filter＇s frequency expression.And the reconstruction error is analyzed from the projection theory of Hilbert space.Finally,with amplitude modulation signal as example,the reconstruction method of sampling in shift-invariant subspace with multiplicity r based on least squares method is proved by simulation,the results show that the reconstruction algorithm is effective.