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Volume 32 Issue 8
Sep.  2010
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Liang Hong, Zhang Qi, Yang Chang-Sheng. A Generalized Robust Chinese Remainder Theorem and Its Application to Frequency Estimation with Undersampling[J]. Journal of Electronics & Information Technology, 2010, 32(8): 1802-1805. doi: 10.3724/SP.J.1146.2009.00718
Citation: Liang Hong, Zhang Qi, Yang Chang-Sheng. A Generalized Robust Chinese Remainder Theorem and Its Application to Frequency Estimation with Undersampling[J]. Journal of Electronics & Information Technology, 2010, 32(8): 1802-1805. doi: 10.3724/SP.J.1146.2009.00718

A Generalized Robust Chinese Remainder Theorem and Its Application to Frequency Estimation with Undersampling

doi: 10.3724/SP.J.1146.2009.00718 cstr: 32379.14.SP.J.1146.2009.00718
  • Received Date: 2009-05-12
  • Rev Recd Date: 2010-05-18
  • Publish Date: 2010-08-19
  • The Chinese remainder theorem 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 this paper, a Generalized Robust Chinese Remainder Theorem (GRCRT) is presented when moduli are not pair-wisely co-prime and the remainders have errors. The new theorem is proofed in detail; The formulas of the estimated integer and estimation error upper bound are provided. The RCRT is then applied to determine the frequency when the signal waveforms are undersampled. Simulation results show that new algorithm is robust with considering residue errors and can use to the area of digital signal processing and will have more applications to other areas.
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  • Krishna B, Krishna H C, and Lin K Y. ComputationalNumber Theory and Digital Signal Processing: FastAlgorithms and Error Control Techniques[M]. CRC Press,Boca Raton, FL, USA, 1994: 1-5.[2]Grossschadl J. The Chinese Remainder Theorem and itsapplication in a high-speed RSA crypto chip[C]. 16th AnnualConference on Computer Security Applications, New Orleans,USA, 2000: 384-393.[3]Ding C, Pei D, and Salomaa A. Chinese Remainder Theorem:Applications in Computing, Coding, Cryptography[M].Singapore, World Scientific, 1996: 2-10.[4]Goldreich O, Ron D, and Sudan M. Chinese remainderingwith errors[J].IEEE Transactions on Information Theory.2000, 46(7):1330-1338[5]Guruswami V, Sahai A, and Sudan M. Soft-decisiondecoding of Chinese remainder codes. in Proc[C]. 41st IEEESymp. Foundations Computer Science, Redondo Beach, CA,2000: 159-168.[6]Xia X G and Liu K. A generalized Chinese remaindertheorem for residue sets with errors and its application infrequency determination from multiple sensors with lowsampling rates[J].IEEE Signal Processing Letters.2005,12(11):768-771[7]Xia X G and Wang G. Phase unwrapping and a robustChinese remainder theorem[J].IEEE Signal ProcessingLetters.2007, 14(4):247-250[8]Li G, Xu J, Peng Y N, and Xia X G. An efficientimplementation of robust phase- unwrapping algorithm[J].IEEE Signal Processing Letters.2007, 14(6):393-396[9]Li X and Xia X G. A fast robust Chinese remainder theorembased phased unwrapping algorithm[J].IEEE SignalProcessing Letters.2008, 15(10):665-668
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