The Closed-Form Robust Chinese Remainder Theorem and Its Application in Frequency Estimation with Under sampling

The Chinese remainder theorem is widely used in many fields such an signal processing. 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 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 estimation 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 concise expression.