# De-Noising Process in Room Impulse Response with Generalized Spectral Subtraction
## 4 Results Analysis and Discussion
### Performance of the Optimal Factors  
Based on the above, the de-noised results showed the possibility of achieving the largest dynamic range improvement when reducing the noises in the RIR up to the truncation time (the knee). The knee is the time point where the reverberation decay of the impulse response intersects with the noise levels, which can be detected by the nonlinear model [13]. At the same time, the decay level of the knee located at the truncated EDCs, calculated from the original RIR implemented by the subtraction-truncation-correction method, was also for the noiseless EDCs. In the process, the estimated noise level was subtracted from the RIR before backward integration, where the correction term for the truncation was calculated using the parameters obtained from the nonlinear model. Therefore, the noise levels convoluting the RIRs used in Section 4.1 were increased to \(-45\) dB to better observe the remaining noise levels around the knee and verify the method validity as applied for severe background noise levels. The EDCs of the de-noised RIRs with different values, \(\alpha_{0}\), compared to the EDCs of the noisy RIRs and the reference RIRs in the time domain, are given in Figure 4. Observing the RIRs in the time domain, the noises were remarkably reduced for the applied GBSS algorithm with \(\alpha_{0}\) higher than 3. The higher the \(\alpha_{0}\), the lower the remaining noise level. However, compared with the reference RIRs, the three values gave different performances in terms of the energy levels around the knee (about 0.28 s), leading to the variable performance to the generated EDCs. Observing the EDCs presented in Figure 4a, compared to the other two values, a value of 3 resulted in the worst dynamic range improvement. The amplitudes of the de-noised RIRs presented in Figure 4b were higher than the reference RIR at the knee. In such cases, much of the noise was removed, but not completely. Further increasing the \(\alpha_{0}\) value to 4.25 resulted in a decrease in the amplitudes at the knee until the energy levels were almost equal to the reference RIR around the knee (seen Figure 4c), yielding the largest dynamic range improvement (about \(-13\) dB). At the same time, the EDC was overlapped with the reference before a cross point at the decay level \(-15\) dB. In this regard, the cross point was called the critical point for the largest dynamic range obtained using the optimal over-subtraction factor \(\alpha_{0}\). For a higher value of 6, though the noise levels were obviously reduced, the amplitudes around the knee decreased significantly, as shown in Figure 4d. Relative energy loss occurred at the original noisy signal around the knee, causing the corresponding EDC to be divided from the reference EDC to drop below the decay curve in the range of \(-15\) dB to \(-24\) dB. As a result, the estimated decay level at the corresponding cross point is smaller than the reference results. Most important is that the reverberation decay rate was degraded more severely than the reference one. It was observed that the processing of RIR de-noising showed a strong dependence on the over-subtraction factors of \(\alpha_{0}\) of the GBSS algorithm. The performance showed that changing \(\alpha_{0}\) led to different cross points with the reference EDCs, and de-noised EDCs had a tremendous relationship with the reduced noise levels in noisy RIRs. On the other hand, the cross point located at the de-noise EDCs did not extend to the critical point until the noise levels around the knee were removed. On the other hand, the reverberation decay part of the signal would be lost using an \(\alpha_{0}\) value higher than the optimum, leading to a decay rate distortion at the knee and causing more significant deviations of the EDCs relative to the reference EDCs. Furthermore, the optimal factors providing the best results regarding the dynamic range improvements were variable for different noise levels.