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中文摘要：
中国余数定理在数字信号处理等领域有着广泛的应用。传统的中国余数定理要求待恢复的数及余数都为整数，且对噪声极其敏感。为了在余数含有误差时鲁棒的恢复原来的数，一种鲁棒的中国余数定理最近被提出。但是现有的算法都是基于搜索的，因此所需的运算量极大。为了克服这一缺陷，本文提出了鲁棒的闭式中国余数定理，在此基础上给出了重建原来数的算法。最后，将该方法应用于欠采样下信号频率的估计中。仿真的结果表明，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的，但是所给出的算法所需的运算量大幅的减少，且解的形式更为简洁。
英文摘要：
The Chinese remainder theorem is widely used in many fields such an signal processing. It tells us that an in- teger can be reconstructed by its corresponding remainders. As we know, it is not robust in the sense that a small error in its remainders may cause a large error in the determined integer by the CRT. In order to resist the error sensitivity, a robust CRT was proposed recently. However, all of the methods in the literatures were searching based which required a heavy computational load. In this paper, a Closed-form robust Chinese Remainder Theorem is presented to solve the robust esti- mation problem. Furthermore, we give the algorithm to reconstruct the original number. In order to verify the effectiveness of the method, we applied it to the frequency determination when the signal waveforms are undersampled. Simulation results show that the proposed algorithm has the same performance but less computational complexity. Moreover, it has a more con- clse expression
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Computationally efficient robust Chinese remainder theorem for frequency estimation from undersample
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