## 4 The Evaluation Results and Discussions
### Experimental Results and Discussions for the Proposed Method with Data Augmentation  
In this subsection, we provide the experimental results of a variant of our presented method, which further adopted the data augmentation technique [40]. To realize it, the DNN-HMM acoustic models were retrained with the original FBANKs and MSPP-enhanced FBANKs in the multi-condition training set (the original acoustic models were trained with the original FBANKs only). In particular, the training set here was arranged such that 50% of the utterances were converted to plain FBANKs while the remaining 50% corresponded to MSPP-enhanced FBANKs. The resulting acoustic models were evaluated on MSPP-enhanced FBANKs in the noisy test set to see how the recognition accuracy would be influenced. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Signal-To-Noise Ratio (SNR)**} \\ \hline  & & \(-\)**6 dB** & \(-\)**3 dB** & **0 dB** & **3 dB** & **6 dB** & **12 dB** \\ \hline  & baseline & 0.973 & 0.959 & 0.938 & 0.909 & 0.870 & 0.790 \\ \cline{2-8}  & MSPP & 0.967 & 0.948 & 0.919 & 0.881 & 0.832 & 0.732 \\ \cline{2-8}  & FMSE & 0.966 & 0.946 & 0.919 & 0.882 & 0.832 & 0.734 \\ \cline{2-8}  & MMSE & 0.977 \({}^{*}\) & 0.965 \({}^{*}\) & 0.947 \({}^{*}\) & 0.917 \({}^{*}\) & 0.882 \({}^{*}\) & 0.799 \({}^{*}\) \\ \cline{2-8}  & IRM & 0.974 \({}^{*}\) & 0.958 & 0.937 & 0.906 & 0.870 & 0.786 \\ \hline  & baseline & 67.3 & 64.7 & 61.1 & 56.3 & 50.4 & 39.4 \\ \cline{2-8}  & MSPP & 64.4 & 60.9 & 55.2 & 49.8 & 43.8 & 34.7 \\ \cline{2-8}  & FMSE & 69.9 \({}^{*}\) & 65.5 \({}^{*}\) & 59.7 & 52.3 & 46.8 & 36.6 \\ \cline{2-8}  & MMSE & 69.1 \({}^{*}\) & 65.9 \({}^{*}\) & 62.5 \({}^{*}\) & 57.3 \({}^{*}\) & 52.1 \({}^{*}\) & 40.7 \({}^{*}\) \\ \cline{2-8}  & IRM & 66.8 & 65.1 \({}^{*}\) & 60.6 & 55.7 & 49.7 & 39.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The state error rate and WER (%) of the baseline, MSPP, FMSE, MMSE, and IRM with clean-condition training for the test set in noise environment “**engine**”. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Signal-To-Noise Ratio (SNR)**} \\ \hline  & & \(-\)**6 dB** & \(-\)**3 dB** & **0 dB** & **3 dB** & **6 dB** & **12 dB** \\ \hline  & baseline & 0.739 & 0.701 & 0.677 & 0.638 & 0.612 & 0.576 \\ \cline{2-6}  & MSPP & 0.720 & 0.682 & 0.653 & 0.625 & 0.606 & 0.583 \({}^{*}\) \\ \cline{2-6}  & FMSE & 0.733 & 0.692 & 0.660 & 0.633 & 0.614 \({}^{*}\) & 0.587 \({}^{*}\) \\ \cline{2-6}  & MMSE & 0.746 \({}^{*}\) & 0.710 \({}^{*}\) & 0.676 & 0.645 \({}^{*}\) & 0.621 \({}^{*}\) & 0.585 \({}^{*}\) \\ \cline{2-6}  & IRM & 0.728 & 0.692 & 0.660 & 0.631 & 0.610 & 0.575 \\ \hline  & baseline & 35.3 & 31.5 & 28.5 & 26.7 & 24.9 & 23.1 \\ \cline{2-6}  & MSPP & 33.8 & 30.6 & 28.7 \({}^{*}\) & 27.0 \({}^{*}\) & 26.3 \({}^{*}\) & 24.9 \({}^{*}\) \\ \cline{2-6}  & FMSE & 35.0 & 32.2 \({}^{*}\) & 29.7 \({}^{*}\) & 28.1 \({}^{*}\) & 27.0 \({}^{*}\) & 25.4 \({}^{*}\) \\ \cline{2-6}  & MMSE & 36.5 \({}^{*}\) & 32.8 \({}^{*}\) & 29.6 \({}^{*}\) & 27.7 \({}^{*}\) & 25.3 \({}^{*}\) & 23.7 \({}^{*}\) \\ \cline{2-6}  & IRM & 34.8 & 31.8 \({}^{*}\) & 28.8 \({}^{*}\) & 26.6 & 24.9 & 23.3 \({}^{*}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The state error rate and WER (%) of the baseline, MSPP, FMSE, MMSE, and IRM with clean-condition training for the test set in noise environment “**jackhammer**”. In Tables 10-12, we present the state error rates and WER (%) under the multi-condition training scenario with respect to the aforementioned two acoustic model configurations. Here, the configuration using data augmentation is termed \"MSPP-Aug\". From the three tables, we see that with data augmentation, the resulting acoustic models can further reduce the WERs and the state error rates for the MSPP-enhanced test set compared with the original FBANK-wise acoustic models. The WER reduction can be as high as 1% for some SNR cases for the noise types \"white\" and \"engine\".