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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 413431, 6 pages
Research Article

Computationally Efficient Robust Chinese Remainder Theorem for Frequency Estimation from Undersampled Waveforms

MOE Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Received 28 April 2013; Revised 26 October 2013; Accepted 13 November 2013

Academic Editor: Alexei Mailybaev

Copyright © 2013 Xiaoping Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an efficient algorithm based on the robust Chinese remainder theorem (CRT) to perform single frequency determination from multiple undersampled waveforms. The optimal estimate of common remainder in robust CRT, which plays an important role in the final frequency estimation, is first discussed. To avoid the exhausted searching in the optimal estimation, we then provide an improved algorithm with the same performance but less computation. Besides, the sufficient and necessary condition of the robust estimation was proposed. Numerical examples are also provided to verify the effectiveness of the proposed algorithm and related conclusions.