# 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
An extension analysis was applied to three broadband-measured RIRs with two types of added noise (pink and white noises) at noise levels ranging from \(-40\) dB to \(-65\) dB. Figure 7c shows that the optimal factors of \(\alpha_{0}\) in the range of 3.75 to 5 depended on the SNR estimated in the octave bands. The higher the SNR, the lower the over-subtraction factor of \(\alpha_{0}\). The optimal \(\alpha_{0}\) for an SNR higher than 30 was 3.75, 4 for an SNR higher than 24, and 4.25 for an SNR in the range from 10 to 24. Figure 7d shows the mean dynamic range improvements achieved in the octave bands by applying the most reliable optimal factor of \(\alpha_{0}\), ranging from 3.75 to 4.25 for an SNR higher than 10. The dynamic range improvement achieved for noise levels lower than \(-60\) dB was around 15 dB to 20 dB. The dynamic range decreased slightly with an increasing noise level, up to \(-40\) dB, contributing to about a 13 dB improvement in the mean dynamic range. In most cases, the reverberation decay range could be extended to \(-10\) dB. The deviation of the improvement was less than 2 dB, and the mean value and deviation of the noise level reduction were approximately 9 dB and 2.5 dB, respectively. When the SNR is lower than 10, the applied optimal factors of \(\alpha_{0}\) were higher than 4.5, and the noise levels estimated at the frequency bands were lower than 40 dB. In this case, the mean improved dynamic range of the EDC ranged from 3 dB to 8 dB, causing the decay range for calculating the RT to be less than 10 dB. When the noise levels were higher than \(-40\) dB, leading to similar poor results in the mean dynamic range improvement, approximately 5 dB, most of the SNRs estimated in the octave band were lower than 10. The application of the GBSS algorithm did not lead to a significant change in the dynamic range improvement when the SNRs in the octave bands were lower than 10. The application of the GBSS algorithm did not lead to a significant change in dynamic range improvement when the SNRs of the octave bands were lower than 10. The optimal factors do depend on the SNRs instead of on the steady noise types and levels. The recommended spectral flooring parameter and over-subtraction factor \(\alpha\) with different desired \(\alpha_{0}\) of the GBSS algorithm contributed to significant effects on both the dynamic range improvement and the noise floor reduction when the SNRs were estimated at frequency bands higher than 10. When de-noising the measured RIRs with real ambient noise, the \(\alpha_{0}\) used could be smaller than the optimal factor. A threshold of 0.25 is recommended for lowering the risk of signal over-subtraction regarding the difference in the dynamic range being smaller than 1 dB. Applying the GBSS algorithm assumes that noise affects the entire spectrum of the signal equally. Over-subtraction factor \(\alpha\) subtracts an overestimation of noise over the whole range. Although the noise affects the RIRs uniformly across the entire spectrum, the energy distribution in the frequency bands varies, leading to significantly different estimated SNRs of the RIRs filtered in the octave band. Thus, the factors of \(\alpha_{0}\) are significantly influenced by the SNRs in each frequency band and are estimated from the filtered noisy RIR. Hence, setting the optimal factors of the \(\alpha_{0}\) variable depends on the estimated SNR of the original RIR filtered in frequency bands instead of applying the same constant value of \(\alpha_{0}\) for every frequency band.