## 4 Experimental Setup, Results, and Discussion
### Spectrogram Demonstration for Various SE Methods  
In addition to the objective evaluation metrics, here we use the spectrograms of a single utterance at various situations to examine the presented DWT-wise Conv-TasNet and DPTNet. First of all, Figure 14a-c depict the magnitude spectrograms of an utterance (a) without noise corruption, (b) with noise corruption (with bus noise at SNR 17.5 dB), and (c) corrupted as (b) and then enhanced by time feature-wise Conv-TasNet. Comparing Figure 14a,b, we see that noise causes a significant interference to the clean speech, while the original Conv-TasNet (with time-domain features) can bring noise alleviation, as shown in Figure 14c. The noise alleviation is especially significant in the region outlined by the red box. Next, the enhanced spectrograms with the Conv-TasNet variants with three versions of one-level DWT and three versions of two-level DWT are depicted in Figure 14d-i, and the spectrograms enhanced with various versions of DPTNet are depicted in Figure 15a-d. From these figures, we can find that the presented DWT-based Conv-TasNet and DPTNet frameworks are also helpful to reduce the noise distortion in the utterance sample, while it is somehow difficult to compare these methods in SE performance simply with these spectrogram demonstrations, and thus we just use the sample spectrograms for illustration purpose.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Feature Domains**} & \multirow{2}{*}{**Integration Manner**} & \multicolumn{3}{c}{**VoiceBank-QUT**} \\ \cline{3-5}  & & **PESQ** & **STOI** & **SI-SNR** \\ \hline \multicolumn{5}{c}{Unprocessed Baseline} & 1.247 & 0.784 & 3.876 \\ \hline Time & - & 1.804 & 0.845 & 12.802 \\ \hline Time and STFT [31] & - & 2.019 & 0.870 & 14.500 \\ \hline Time and & One BPF and & & & \\ one-level DWT & concatenation & 2.044 & 0.873 & 14.543 \\ \hline Time and & Two BPFs & 2.033 & 0.872 & 14.549 \\ \cline{2-5} two-level DWT & One MPF with & & & \\ (concatenation) & inter-channel softmax & 2.034 & 0.871 & 14.611 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The evaluation results of DPTNet using different domains of features for the test set in noise environment of “QUT-NOISE”.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Feature Domains**} & \multirow{2}{*}{**Integration Manner**} & \multicolumn{3}{c}{**VoiceBank-DEMAND**} \\ \cline{3-5}  & & \multicolumn{3}{c}{**Metric Scores**} \\ \cline{3-5}  & & **PESQ** & **STOI** & **SI-SNR** \\ \hline \multicolumn{5}{c}{Unprocessed baseline} & 1.970 & 0.921 & 8.445 \\ \hline Time & - & 2.549 & 0.935 & 19.080 \\ \hline Time and STFT [31] & - & 2.782 & 0.946 & 19.963 \\ \hline Time and & One BPF and & & & \\ one-level DWT & concatenation & 2.724 & 0.945 & 19.960 \\ \hline Time and & Two BPFs & 2.745 & 0.944 & 19.624 \\ \cline{2-5} two-level DWT & One MPF with & & & \\ (concatenation) & inter-channel softmax & 2.779 & 0.944 & 19.470 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The evaluation results of DPTNet using different domains of features for the test set in noise environment of “DEMAND”.  
Figure 14: Spectrogram of a sentence in various situations: (**a**) clean and noise-free, (**b**) noise-corrupted (with bus noise at 17.5 dB SNR), noise-corrupted and enhanced by (**c**) time-feature Conv-TasNet, noise-corrupted and enhanced by three one-level DWT-wise Conv-TasNet; (**d**) addition, (**e**) concatenation, (**f**) one BPF and concatenation, and noise-corrupted and enhanced by three two-level DWT-wise Conv-TasNet; (**g**) two BPFs, (**h**) MPF with intra-channel softmax, and (**i**) MPF with inter-channel softmax. The regions outlined by the red box help us compare different methods in denoising.