Reverberation and additive noise have detrimental effects on the performance of automatic speech recognition systems. In this paper we explore the ability of a DNN-based spectral feature mapping to remove the effects of reverberation and additive noise. Experiments with the CHiME-2 database show that this DNN can achieve an average reduction in WER of 4.5%, when compared to the baseline system, at SNRs equal to -6 dB, -3 dB, 0 dB and 3 dB, and just 0.8% at greater SNRs of 6 dB and 9 dB. These results suggest that this DNN is more effective in removing additive noise than reverberation. To improve the DNN performance, we combine it with the weighted prediction error (WPE) method that shows a complementary behavior. While this combination provided a reduction in WER of approximately 11% when compared with the baseline, the observed improvement is not as great as that obtained using WPE alone. However, modifications to the DNN training process were applied and an average reduction in WER equal to 18.3% was achieved when compared with the baseline system. Furthermore, the improved DNN combined with WPE achieves a reduction in WER of 7.9% when compared with WPE alone.