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Recently, the advantages of the discrete cosine transform (DCT) based orthogonal frequency-division multiplexing (OFDM) have come to the light. We thus consider DCT- OFDM with non-circular transmission (our results cover circular transmission as well) and present two blind joint maximum- likelihood frequency offset and phase offset estimators. Both our theoretical analysis and numerical comparisons reveal new advantages of DCT-OFDM over the traditional discrete Fourier transform (DFT) based OFDM. These advantages, as well as those already uncovered in the early works on DCT-OFDM, support the belief that DCT-OFDM is a promising multi-carrier modulation scheme.