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In this paper, a frequency synchronization technique for the equalization digital on-channel repeater (EDOCR) in ATSC system is proposed and the proposed algorithm is verified by mathematical analysis. The proposed algorithm uses the frequency offset information that comes from carrier and symbol timing recovery in the receiving part of EDOCR when the demodulated symbol is re-modulated in transmitting part. Therefore, the algorithm makes it possible for the EDOCR output signal to synchronize with input signal in frequency without additional reference source. Also, the synchronized EDOCR output does not degrade the reception performance of legacy receivers.