A robust Chinese remainder theorem with its applications in frequency estimation from undersampled waveforms

Authors:
Xiaowei Li;Hong Liang;Xiang-Gen Xia
Affiliations:
Department of Electrical and Computer Engineering, University of Delaware, Newark, DE;Department of Electrical and Computer Engineering, University of Delaware, Newark, DE and College of Marine, Northwestern Polytechnical University, Xi'an, China;Department of Electrical and Computer Engineering, University of Delaware, Newark, DE
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 4
Cited 1

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Abstract

The Chinese remainder theorem (CRT) allows to reconstruct a large integer from its remainders modulo several moduli. In this paper, we propose a robust reconstruction algorithm called robust CRT when the remainders have errors. We show that, using the proposed robust CRT, the reconstruction error is upper bounded by the maximal remainder error range named remainder error bound, if the remainder error bound is less than one quarter of the greatest common divisor (gcd) of all the moduli.We then apply the robust CRT to estimate frequencies when the signal waveforms are undersampled multiple times. It shows that with the robust CRT, the sampling frequencies can be significantly reduced.