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A 1-Tb/s single-channel coherent optical OFDM (CO-OFDM) signal consisting of continuous 4104 spectrally-overlapped subcarriers is generated using a recirculating frequency shifter (RFS). Theoretical and experimental analysis of the RFS is performed to study its effectiveness in extending OFDM bandwidth. In particular, the RFS produces a 320.6-GHz wide frequency comb from a single laser with superior flatness and tone-to-noise ratio (TNR). The 1-Tb/s CO-OFDM signal is consisted of 36 uncorrelated orthogonal bands achieved by adjusting the delay of the RFS to an integer number of OFDM symbol periods. The 1-Tb/s CO-OFDM signal with a spectral efficiency of 3.3 bit/s/Hz is successfully received after transmission over 600-km SSMF fiber without either Raman amplification or dispersion compensation.