摘要
中国余数定理在数字信号处理等领域有着非常广泛的应用.但传统的中国余数定理要求待恢复的数及余数都必须为整数,且对噪声极其敏感.为了克服这一缺陷,一种鲁棒的中国余数定理最近被提出,虽然它能在余数含有误差时鲁棒的恢复原来的数.但此算法是基于搜索的,所需运算量非常巨大.提出了中国余数定理的极大似然算法,并对此算法进行了改进.最后,将此方法应用于欠采样下信号频率的估计中.仿真试验的结果表明,在相同信噪比下,所给算法和现有的搜索算法的估计性能一样,但是运算量却大幅的减少,
The Chinese remainder theorem is widely used many in fields such an digital signal processing. But It tells us that an integer can be reconstructed by its corresponding remainders. As we know, it is not robust in the sense that a small error inits remainders may cause a large error in the determined integer by the CRT. In order to overcome this defect, a robust Chinese remainder theorem was proposed recently, although it can when the remainder contains error robust recovery of the original number. But the algorithm is based on the search, the computational complexity is enormous. Chinese remainder theorem is proposed in this paper, maximum likelihood algorithm and this algorithm is improved. Finally, this method was applied to undersampling signal frequency estimation. Simulation test results show that under the same SNR, the algorithm is given and the existing search algorithm estimates the same performance, but the computation is greatly reduced.
作者
牛旭
徐爱英
周宇斌
NIU Xu XU Ai-ying ZHOU Yu-bin(College of Information Engineering, Tarim University, Alar 843300, China College of Mechanical and Electrical ＇Engineering, Tarim University, Alar 843300, China College of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China)
出处
《数学的实践与认识》
北大核心
2016年第24期211-218,共8页
Mathematics in Practice and Theory
基金
塔里木大学自然科学基金(TDZKQN201608)
关键词
中国余数定理
欠采样
频率估计
the Chinese remainder theorem
undersampled
frequency estimation
