# 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  
Because the most promising factors of the GBSS applied to RIRs with different noise levels are changed, and the dynamic range obtained was varied, it was essential to find the rule to choose the factors for different situations. Hence, the three measured RIRs with low noise levels, mentioned in Section 3.1, filtered in octave bands, convoluted with white noise and pink noise, with noise levels ranging from \(-\)65 dB to \(-\)40 dB,  
Figure 4: De-noising effects at the knee with various factors of \(\alpha_{0}\). (**a**) Comparison of the dynamic range at the cross point. (**b–d**) Comparison of the de-noised RIRs to the reference RIRs at the knee: factor of (**b**) 3, (**c**) 4.25, and (**d**) 6 applied. were used to determine the optimal factors. Based on the study above, removing the noise levels around the knee estimated from RIR contributed to the largest dynamic range improvement. In this case, the factors set in the GBSS were the most promising. The acoustic parameters calculated from the EDCs of the filtered RIRs in the octave bands were used to verify the results and guarantee the accuracy of the applied optimal factors, leading to no distortion of the EDCs during the noise subtraction process using the GBSS. Considering the optimal factors determined using the knees obtained with the compensation method, the corresponding RTs were compared with the reference RTs. The RTs calculated at the critical point positioned on the de-noised EDCs were compared with the values of the compensation method and the reference results to ensure that the achieved decay levels at the critical points were the best. At the same time, EDT, T15, and T20 were used to verify the GBSS algorithm and it was compared with the reference results, as listed in Table 2.  
The EDCs generated from the RIRs of the meeting room filtered in the octave bands with noise levels of \(-60\) dB are presented in Figure 5; the noise level estimated from the RIRs in each frequency band for the convoluted white noise remained the same as the noise levels of the pink noise. In this case, the knees located at the EDCs obtained using the S-T-C method were similar in each frequency band. In addition, the largest difference of the knee estimated at the EDCs for the pink noise and the white noise was 0.02 s in the octave band at 2000 Hz, causing an approximately 1.5 dB difference in the dynamic EDC ranges. However, the EDCs have a slight, but visible, deviation from the reference EDCs at the knees, and the maximum difference of the decay level was 2 dB. Figure 6 illustrates a comparison of the GBSS with the reference and compensation methods for RT estimation at critical points of white and pink noise. Compared to the reference results, the maximum deviation of the RTs for the GBSS algorithm was 0.13 s at 2000 Hz, and the dynamic range improvement of white noise compared to pink noise was about 2 dB. The compensation method generally produced similar results to the GBSS algorithm. This is why the knee can be used as the endpoint for the EDCs obtained using the compensation method, but is not adopted as the endpoint for EDCs with the GBSS algorithm. On the other hand, the EDCs are coincidental with the reference EDCs above the critical points positioned above the knees. At the same time, there was no apparent deviation of the three EDCs at the critical points.