## 4 Experiments
### Singing Voice-Separation Experiment
#### 4.1.3 Separation Results  
The experiment was conducted in 8 steps. The first architecture (\"A1\") is MDenseNet, which is the baseline. The 2 nd architecture (\"A2\") is MMDenseNet [15]. The 3 rd architecture (\"A3\") is MMDenseLSTM [20]. The 4 th architecture (\"A4\") adds a multi-band block to A1. The 5 th architecture (\"A5\") replaces the dense block with a dilated dense block containing TDConv and standard convolution. The 6 th architecture (\"A6\") replaces the TDConv of the A5 with FDConv. The 7 th architecture (\"A7\") replaces the TDConv of the A5 with 2 DConv. The 8 th architecture (\"A8\") is the proposed architecture which includes both TDConv and FDConv (T-FDConv). We programmed MDenseNet (\"A1\"), MMDenseNet (\"A2\"), and MMDenseLSTM (\"A3\") by ourselves to operate on monophonic signals. A1, A2, and A3 was to compare the performance in the same environment as the proposed architecture (\"A8\"). Table 1 shows the experimental results. Results were measured for _vocals_ and _accompaniment_ by signal-to-distortion ratio (SDR), signal-to-interference ratio (SIR), and signal-to-artifacts ratio (SAR) [32]. We used median as statistics. A4 performs better than A1 in _vocals_ and _accompaniment_, respectively. A5 yielded higher SDR than A4, A6, and A7 in _vocals_, while A7 produced higher SDR than A4, A5, and A6 in _accompaniment_. This shows that _vocals_ signals have a variety of patterns along the time axis rather than the frequency axis in the spectrogram, and _accompaniment_ signals have a variety of patterns simultaneously along the time and the frequency axes in the spectrogram. After we performed several combinations of experiments with TDConv, FDConv, and 2 DConv, we found that the proposed architecture, including TDConv and FDConv, produces the best results. In _vocals_, A8 showed significantly higher SDR than A1\(-\)A7. In _accompaniment_, A8 showed significantly higher SDR than A1, A2, A4\(-\)A7, and had the same SDR as A3. As a result, A8 improved 0.12 dB SDR over A3 (MMDenseLSTM) in _vocals_. The proposed architecture outperforms MMDenseLSTM in _vocals_. We compared the proposed architecture with the previous methods: Deep non-negative matrix factorization (DeepNMF), FNN, BLSTM, 4-stacked hourglass network (SH-4 stack), MMDenseNet, and MMDenseLSTM. For DeepNMF [9], FNN [8], SH-4 stack [14], and the proposed architecture, monophonic signals were used for evaluation. On the other hand, stereo signals were used to evaluate BSLTM [12], MMDenseNet [15], and MMDenseLSTM [20] with data augmentation and multi-channel Wiener filter (MWF). The performance of MMDenseNet [15] and MMDenseLSTM [20] presented in Table 2 differs from our experimental results A2 and A3 in Table 1. This difference is because our experiment used monophonic signals and did not use data augmentation and MWF. To obtain the results of our method in Table 2, we also applied data augmentation techniques to the A8 architecture for comparing performance with the previous methods. Here, we augmented training data by using three times the original data. The proposed method has higher SDR than BLSTM, therefore we can see that CNN-based architectures outperform BLSTM. The proposed method using DenseNet, which improves information flow between layers or blocks, outperforms a typical CNN-based SH-4 stack. The proposed method is better than MMDenseNet by effectively expanding the receptive field. The proposed method shows lower performance than MMDenseLSTM, but it does not use the Wiener filter and has the advantage of network configuration with very few parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Number of Parameters (\(\times 10^{6}\))** & **Vocals** & **Accompaniment** \\ \hline DeepNMF [9] & - & 2.75 & 8.90 \\ FNN [8] & - & 4.47 & 11.12 \\ BLSTM [12] & 30.03 & 4.86 & 11.26 \\ SH-4 stack [14] & 34.18 & 5.45 & 12.14 \\ MMDenseNet [15] & 0.33 & 6.00 & 12.10 \\ MMDenseLSTM [20] & 1.22 & **6.31** & **12.73** \\ Our method & 0.48 & 6.25 & 12.58 \\ \hline \hline \end{tabular}
\end{table}