基于有限更新率的非带限信号采样与重建算法  

Sampling and Reconstructing Algorithm for Non-bandlimited Signals Based on Finite Innovation Rate

作　　者：谭雪琴[1] 蒋立平[1] 王建新[1] 刘中[1] 

机构地区：[1]南京理工大学电子工程与光电技术学院,南京210094

出　　处：《数据采集与处理》2010年第2期212-217,共6页Journal of Data Acquisition and Processing

摘　　要：针对Shannon采样定理中要求信号带宽有限的缺陷,提出了一种基于有限更新率的非带限信号采样和重建的方法。该方法借助奇异值分解技术,从空间变换的角度实现了对与狄拉克流有关的一类特殊有限更新率信号的采样与重建。它用采样点的离散傅里叶变换系数构成一个Hankel矩阵,通过对该矩阵进行奇异值分解求得狄拉克流的位置信息,然后再求解范德蒙方程组求取狄拉克流的权信息,重建出原信号。计算机仿真结果表明,只要以不低于信号更新率的速率对信号进行采样,利用该算法就可以准确地重建出原信号,而且具有很好的抗噪性能。According to the Shannon theory limitation of Nyquist rate, a sampling and reconstructing theory of non-bandlimited signals is presented based on the finite innovation rate. The algorithm analyzes the problem from the aspect of the space transform. Based on singular value decomposition （SVD）, it implements the sampling and reconstructing of a special kind of finite innovation rate signal relevant to Diracs stream. Firstly, it finds DFT coefficients of the samples, and constructs a Hankel data matrix. Then, the matrix is decomposed according to SVD technique and the position information of Diracs is obtained. Finally, it computes weight coefficients from the Vandermonde system. Simulation results indicate that the original signal can be reconstructed if the sample rate is more than its innovation rate. The algorithm has good anti-noise performance.

关 键 词：信息处理 采样理论 非带限信号 有限更新率 狄拉克流 

分 类 号：TN911.21[电子电信—通信与信息系统]