# De-Noising Process in Room Impulse Response with Generalized Spectral Subtraction
## 4 Results Analysis and Discussion
### Over-Subtraction Factor for the Octave Band RIRs and Different Noises
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Octave** \\ **Band** \\ \end{tabular} } & \multirow{2}{*}{**Reverberation**} & \multirow{2}{*}{**Reference**} & \multicolumn{3}{c}{**Noise Level (\(-60\) dB)**} & \multicolumn{3}{c}{**Noise Level (\(-50\) dB)**} \\ \cline{4-7}  & & & **Pink** & **White** & **Pink** & **White** \\  & & & **Noise** & **Noise** & **Noise** & **Noise** \\ \hline \multirow{4}{*}{125 Hz} & EDT(s) & 0.728 & 0.73 & 0.727 & 0.73 & 0.722 \\  & T15(s) & 0.727 & 0.73 & 0.727 & 0.73 & 0.72 \\  & T20(s) & 0.727 & 0.73 & 0.727 & & \\  & EDT(s) & 0.677 & 0.677 & 0.676 & 0.676 & 0.676 \\
250 Hz & T15(s) & 0.739 & 0.739 & 0.738 & 0.74 & 0.74 \\  & T20(s) & 0.672 & 0.673 & 0.672 & & \\  & EDT(s) & 0.691 & 0.691 & 0.69 & 0.69 & 0.69 \\
500 Hz & T15(s) & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 \\  & T20(s) & 0.626 & 0.627 & 0.624 & & \\  & EDT(s) & 0.609 & 0.61 & 0.61 & 0.61 & 0.61 \\
1000 Hz & T15(s) & 0.704 & 0.7 & 0.7 & 0.7 & 0.7 \\  & T20(s) & 0.717 & 0.71 & 0.71 & & \\  & EDT(s) & 0.529 & 0.53 & 0.53 & 0.53 & 0.53 \\
2000 Hz & T15(s) & 0.611 & 0.61 & 0.61 & 0.61 & 0.61 \\  & T20(s) & 0.707 & 0.7 & 0.7 & & \\  & EDT(s) & 0.436 & 0.434 & 0.436 & 0.437 & 0.437 \\
4000 Hz & T15(s) & 0.535 & 0.533 & 0.534 & 0.535 & 0.533 \\  & T20(s) & 0.614 & 0.61 & 0.613 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of RTs and EDT between the de-noised RIRs and the reference RIRs. Figure 5: De-noising effects using the optimal set factors of the GBSS on the RIRs of the meeting room with different added noises filtered at the octave bands. The red dotted line is the EDCs with the pink noise. The green dotted line is the EDCs with white noise. Figure 6: Comparison of the RTs of the filtered RIRs at octave bands with pink noise and white noise with noise levels of \(-60\) dB. The ranges from \(-5\) dB to the decay levels estimated at the critical points were used to estimate the RTs presented in Table 2. T20 was considered for comparison at a noise level of \(-60\) dB because the decay levels estimated at the critical points from the EDCs with two noises were independently in the range of \(-26\) dB to \(-35\) dB. In contrast, T15 was used when the noise level was \(-50\) dB. The maximum differences of EDT and T20 was \(0.006\) s and \(0.007\) s, respectively. The deviation between the de-noised EDCs and the reference EDCs was approximately \(0.01\) dB. The critical points depended strictly on the over-subtraction factor to decide the improved decay levels of the dynamic range, and the accuracy of the produced reverberation decay rates. Over-subtraction factor \(\alpha\) for the segment SNR achieved the best dynamic range improvement with the best \(\alpha_{0}\) value, connecting the estimated SNR at the filtered RIRs with the octave band, as shown in Figure 7a,b. The estimated SNRs and the optimal factors applied to the situation presented in Table 2 gave the same results. The values were \(3.75\) for frequency bands lower than \(500\) Hz when the estimated SNRs were higher than \(30\) and \(4\) for the frequency band higher than \(500\) Hz when the estimated SNRs were higher than \(25\). Consequently, the similar results of the two noises showed that the GBSS algorithm does not depend on the noise type. In applying optimal factors, the processing of the noise subtraction to achieve the best dynamic range, leading to no or minimal degradation of the reverberation decay, is reliable for implementing the RIRs. Figure 7: Results of the optimal \(\alpha_{0}\) for different SNRs of three filtered RIRs in octave bands with two types of noise and various noise levels (\(-65\) dB to \(-40\) dB estimated in broadband RIRs). (**a**,**b**) Optimal \(\alpha_{0}\) for RIRs with noise levels \(-60\) dB and corresponding SNRs. (**c**) Relationship of the optimal \(\alpha_{0}\) and SNR. (**d**) Dynamic range improvement.