# De-Noising Process in Room Impulse Response with Generalized Spectral Subtraction
## 4 Results Analysis and Discussion
### Performance of the GBSS Algorithm Factors  
The varying \(\beta\) decided by the SNR ranged from 0.1 to 0.001, with a fixed \(\alpha_{0}\), controlling the remaining noise levels, and the musical noise effects on the noisy RIR are given in Figure 2. Observing the EDCs given in Figure 2a, the EDC obtained using a value larger than 0.1 has a particular impact on the reverberation decay part of the EDC, which offers a significant dynamic range improvement of approximately 7 dB, and the noise floor reduction was about 5.6 dB. With \(\beta=0.05\), the obtained dynamic range of the EDC was 1.5 dB larger than that of the de-noising effects using \(\beta\) 0.1. A decrease in \(\beta\) to 0.001 yielded the best de-noising results, providing a dynamic range improvement of up to 10.15 dB. In this case, the reverberation decay range for the RT estimation was extended to \(-15\) dB, and the noise level reduction was approximately 9 dB. On the other hand, the late part of the EDC was not as smooth as the EDC of \(\beta=0.5\), which can be seen from the decay range from \(-35\) dB to \(-40\) dB. Compared to \(\beta=0.001\), the narrowband spectral peaks of the original RIR were converted to broadband noise using a larger \(\beta\), as can be seen from the spectrum using the FFT in Figure 2b. In this case, the musical noise was not perceptible, but the remaining noise levels were higher (Figure 2c). On the other hand, when \(\beta>0.05\), there was an increase in the other artifacts of residual noise levels, which did not belong  
Figure 1: Dynamic range improvement of the EDC between cross-point A at a noisy RIR and cross-point B at RIR after the GBSS. to the original RIR. Musical noise leads to high fluctuations in the remaining noise parts of the RIR using \(\beta=0.001\) (Figure 2d), contributing to the roughness of the EDCs, which is only prominent in the noise segments, but has less impact on the reverberation decay part. Furthermore, the noise attenuation effects were remarkable with a small \(\beta\), and the musical noise effects could be decreased using a larger \(\alpha\)[28]. Consequently, the GBSS algorithm with \(\alpha_{0}>3\) provided similar noise attenuation rules and musical noise effects in de-noising processing. Regarding the best dynamic range improvement of the EDCs, as well as the noise levels reduction effects on the RIRs with different noise types and levels filtered in the octave bands, the experimental results showed that varying \(\alpha\) worked wells when \(\beta=0.05\) for SNR \(<0\) dB, while \(\beta=0.001\) works best for SNR \(\geq 0\) dB. It is well-known that, with a fixed value, \(\alpha_{0}\), more noise attenuation increases with a decreasing value of \(\beta\). On the other hand, with a fixed \(\beta\) (suggested above), a change in the \(\alpha_{0}\) values also significantly impact the noise reduction effects and the dynamic range improvement. For example, the over-subtraction factor \(\alpha_{0}=3\) with a fixed \(\beta\) leads to an approximately 10.15 dB dynamic range improvement. In contrast, the best de-noising results mentioned above are achieved when the \(\alpha_{0}=4\). Therefore, determining the optimal sets of the two factors will improve EDC dynamic range more, which is essential for de-noising RIRs, particularly when the noise levels are high. Figure 2: Comparison of the noisy RIRs and de-noised RIR at 1 kHz by varying the noise spectral floor \(\beta\) for a fixed value of \(\alpha_{0}\). (**a**) The EDCs of the RIRs. (**b**) Power spectrum of the RIRs obtained using the FFT. (**c,d**) RIRs in the time domain. Figure 3 shows the noise attenuation effects of different values of \(\alpha_{0}\) with a fixed \(\beta\) value of 0.001. The remaining noise levels decreased with larger \(\alpha_{0}\) values, causing the later parts of the EDCs to decrease. The GBSS with \(\alpha_{0}=1\) produced a slight improvement in the EDC dynamic range (e.g., up to 3 dB), while \(\alpha_{0}=2\) provided a similar result of approximately 4 dB to the EDCs.