When base stations (BSs) are deployed with multiple antennas, they need to have downlink (DL) channel state information (CSI) to optimize downlink transmissions by beamforming. The DL CSI is usually measured at mobile stations (MSs) through DL training and fed back to the BS in frequency division duplexing (FDD). The DL training and uplink (UL) feedback might become infeasible due to insufficient coherence time interval when the channel rapidly changes due to high speed of MSs. Without the feedback from MSs, it may be possible for the BS to directly obtain the DL CSI using the inherent relation of UL and DL channels even in FDD, which is called DL extrapolation. Although the exact relation would be highly nonlinear, previous studies have shown that a neural network (NN) can be used to estimate the DL CSI from the UL CSI at the BS. Most of previous works on this line of research trained the NN using full dimensional UL and DL channels; however, the NN training complexity becomes severe as the number of antennas at the BS increases. To reduce the training complexity and improve DL CSI estimation quality, this paper proposes a novel DL extrapolation technique using simplified input and output of the NN. It is shown through many measurement campaigns that the UL and DL channels still share common components like path delays and angles in FDD. The proposed technique first extracts these common coefficients from the UL and DL channels and trains the NN only using the path gains, which depend on frequency bands, with reduced dimension compared to the full UL and DL channels. Extensive simulation results show that the proposed technique outperforms the conventional approach, which relies on the full UL and DL channels to train the NN, regardless of the speed of MSs.