This paper derives the channel estimation of a discrete cosine transform- (DCT-) based orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective multipath fading channel. Channel estimation has been proved to improve system throughput and performance by allowing for coherent demodulation. Pilot-aided methods are traditionally used to learn the channel response. Least square (LS) and mean square error estimators (MMSE) are investigated. We also study a compressed sensing (CS) based channel estimation, which takes the sparse property of wireless channel into account. Simulation results have shown that the CS based channel estimation is expected to have better performance than LS. However MMSE can achieve optimal performance because of prior knowledge of the channel statistic.