# De-Noising Process in Room Impulse Response with Generalized Spectral Subtraction
## 4 Results Analysis and Discussion
### GBSS Method in Measured RIRs with Natural Ambient Noise  
In the preceding sections, with the fixed spectral flooring parameter, the optimal factor \(\alpha_{0}\), leading to the best dynamic range improvement, depended on the estimated SNRs of the filtered RIRs in the frequency bands presented in Figure 7c. The optimal spectral flooring parameter, \(\beta\), depended on the averaged posterior SNR of the input signal [21; 24]. Extensive experiments at noise levels higher than \(-40\) dB were performed to set \(\beta\) = 0.001 at SNR \(>=0\) while \(\beta\) = 0.05 at SNR \(<0\). The best de-noising results were obtained using the optimal sets of factors that were conducted in two normal rooms with real ambient noise. In this part, the reference RIRs represent the measured RIRs with a noise level of \(-60\) dB, while the noisy RIRs mean the RIRs were noise levels of \(-40\) dB and \(-46\) dB, separately. A detailed comparison of the GBSS algorithm with the noise compensation method and reference RIRs in terms of the EDCs, EDT, and RTs of the measured RIRs filtered in the octave bands showed that the optimal factors could be valid for actual applications. The generated EDCs at 250 Hz and 2 kHz were taken as examples to compare the results of the EDCs given in Figure 8. The optimal factors of \(\alpha_{0}\) applied for the two rooms in the octave bands were different. The value used in room A was 4.25 because of the estimated SNRs of the filtered RIRs in octave bands ranged from 12 to 18, and a factor of was 4 was used for room B because the estimated SNRs of the filtered RIRs in the octave bands ranged from 24.5 to 28. The de-noised EDCs were almost identical to the reference EDCs and the compensated EDCs were above the critical point and are indicated by the dash-dotted vertical line. The reverberation decay ranges were obviously extended using the optimal factors. The mean dynamic range improvements for rooms A and B were 12 dB and 14.4 dB, respectively. The mean noise levels reductions for rooms A and B were approximately 7.8 dB and 8.5 dB, respectively. Table 3 lists the parameters of the EDT and RTs estimated at critical points using the optimal factors for the two rooms, compared with the reference results. The overall differences of the RTs estimated at the critical points, and the EDT of the frequency bands estimated at the de-noised EDCs, were small compared to the reference RIRs and the compensation method. The fluctuations caused by the GBSS algorithm had slight effects on the EDCs, leading to minor deviations in the early reverberation decays. The maximum relative errors of the EDTs for rooms A and B were 0.89% at an octave band of 500 Hz and 1.3% at an octave band of 1000 Hz, respectively. The corresponding time deviations were 0.011 s and 0.007 s, respectively. The maximum relative errors of the RT were 1.09% for  
Figure 8: Effects of the GBSS algorithm and compensation method of the measured RIRs filtered in octave bands (250 Hz and 2 kHz): (**a,b**) comparison results for room A; (**c,d**) comparison results for room B.  
room A at an octave band of 1000 Hz and 0.89% for room B at an octave band of 500 Hz. The corresponding time deviations were 0.015 s and 0.007 s, respectively. A comparison with the noise compensation method showed that the GBSS algorithm produced slightly better results when the optimal factors were applied. The mean relative errors of the EDT and RTs were 0.41% and 0.42% using the GBSS algorithm, respectively, whereas the corresponding values were 0.59% and 0.48% using the noise compensation method. The relative errors of the RTs and EDT presented in Figure 9 showed that the optimal factors of the GBSS algorithm had a significant impact on the RIR de-noising. Nevertheless, the EDT calculated from the de-noised EDCs in the same octave bands were smaller than the reference ones, which illustrated that the EDCs went below the reference EDCs, leading to minimal degradation of the reverberation decay. The value of the factor was acceptable because the decay rate was not degraded.