# Two-Stage Single-Channel Speech Enhancement with Multi-Frame Filtering
## 5 Results and Discussion
### Effect of the Framework on System Performance  
The framework shown in Figure 1 can integrate MFMVDR information into DNN\({}_{2}\), but incorporating two neural networks in the framework results in a relatively large number of parameters for the model. A possible modification could be to use a single neural network instead, reducing the total number of parameters in the entire system by 50%; the framework is shown in Figure 4. It is worth noting that we have depicted two neural networks in Figure 4 to better illustrate the training process; however, both of these networks are, in fact, identical.  
The training of this framework still adopts a two-stage strategy. In the first stage, the noisy spectrum \(Y\) are concatenated with two zero matrices of the same shape and fed to the DNN to estimate the clean spectrum. In the second stage, two iterations are required to produce the final output. In the first iteration, similar to the first stage, \(Y\), concatenated with two all-zero matrices, is fed into the DNN, and the initial estimate of the clean spectrum, \(\hat{X}^{(1)}\), is obtained. \(\hat{X}^{(1)}\) and \(Y\) are used to calculate the filtered spectrum \(\hat{X}^{(F)}\). In the second iteration, the noisy spectrum \(Y\), the result of the previous iteration \(\hat{X}^{(1)}\), and the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Filter** & **\# Frames** & **PESQ-NB** & **STOI** & **SI-SNR (dB)** & **SDR (dB)** \\ \hline noisy & - & 1.63 & 0.77 & \(-\)2.76 & \(-\)2.67 \\ DNN\({}_{1}\) & - & 2.79 & 0.94 & 13.24 & 13.69 \\ \hline \multirow{3}{*}{MFMVDR} & \(2\times 2+1\) & 2.10 & 0.86 & 3.86 & 3.94 \\  & \(2\times 4+1\) & 2.34 & 0.89 & 7.19 & 7.37 \\  & \(2\times 6+1\) & 2.39 & 0.90 & 9.20 & 9.60 \\ \hline \multirow{3}{*}{MFWF} & \(2\times 2+1\) & 2.35 & 0.90 & 10.62 & 10.98 \\  & \(2\times 4+1\) & 2.47 & 0.91 & 11.15 & 11.63 \\ \cline{1-1}  & \(2\times 6+1\) & 2.46 & 0.91 & 11.35 & 12.04 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The effect of the number of frames on different filters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Filtering Module** & **PESQ-NB** & **STOI** & **SI-SNR (dB)** & **SDR (dB)** & **WER (\%)** \\ \hline MFMVDR & 2.84 & 0.94 & 13.50 & 13.92 & 19.60 \\ MFWF & 2.83 & 0.94 & 13.49 & 13.92 & 20.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The performance of the proposed system with different filtering modules.  
filtered spectrum \(\hat{X}^{(F)}\) are concatenated and fed into the neural network to obtain the final output \(\hat{X}^{(2)}\).  
Table 4 displays the performance of systems utilizing the two different frameworks on the WHAM! test set. The results indicate that the framework using two DNNs outperforms the one using only one DNN. We hypothesize that there are two possible reasons for this observation. Firstly, it may be challenging for a single neural network to learn both noise reduction and the utilization of MFMVDR results to reduce distortion in the final output. Secondly, it is more probable that when using only a single neural network, the network parameters keep changing, which cannot ensure the accuracy of the input provided to the filter module. In contrast, a dual neural network-based framework can ensure the accuracy of the input provided to the filter module, resulting in superior filtered results and ultimately improving the overall performance.  
Given the results shown in Tables 3 and 4, the system proposed in this study is based on the framework utilizing two neural networks and employs MFMVDR as the filter module.