# Acoustic Impulsive Noise Based on Non-Gaussian Models: An Experimental Evaluation
## 4 Experimental Results and Analysis
### PDF Fitting  
Table 1 presents the estimation of the distribution's parameters using 240,000 samples for each scenario without an audio source (only noise). From the estimation point of view, the mean of the Gaussian model is always zero, and the standard deviation is the parameter to be analyzed. Among the tested scenarios, the outdoor presents the highest Gaussian variance, indicating a lower SNR. As previously presented, the \(\mathsf{S}\alpha\)S model is characterized by \(\alpha\) and \(\gamma\) parameters. The lowest values of such parameters are estimated for the outdoor scenario, evidencing a high impulsiveness level and a lower dispersion, respectively. The \(\alpha\) value of about 1.27 of outdoor scenario indicates a non-Gaussian noise with frequent impulsiveness characteristics. We assume two Gaussian distributions for GMM model. In the indoor scenario, the GMM does not have zero mean. In this case, the two Gaussians are not enough to fit the data. In the outdoor scenario, variances of two Gaussians are very different, capturing the impulsiveness characteristic of the noise. For illustrative purposes, we build the Figures 12 and 13 for 1500 samples of outdoor scenario in a time window with severe impulsiveness (a lower \(\mathsf{S}\alpha\)S's \(\alpha\) value). Figure 12 presents a comparison of the Gaussian and GMM PDFs with the estimated parameters as well as the two Gaussians' PDF of GMM. As the GMM is the linear combination of two Gaussians weighted by \(c_{1}\) and \(c_{2}\), each Gaussian has its different variances \(\sigma_{1}\) and \(\sigma_{2}\) that can be associated to different sources of noise. Although the \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Gaussian**} & \multicolumn{2}{c}{\(\mathsf{S}\alpha\mathsf{S}\)} & \multicolumn{6}{c}{**GMM**} \\ \hline Scenario & \(\sigma\) & \(\alpha\) & \(\gamma\) & \(c_{1}\) & \(\mu_{1}\) & \(\sigma_{1}\) & \(c_{2}\) & \(\mu_{2}\) & \(c_{2}\) \\ \hline
**Indoor** & 0.003793 & 1.9817 & 0.3390 & 0.5934 & \(-0.0009358\) & 0.003618 & 0.4066 & 0.001466 & 0.003584 \\ \hline
**Hall** & 0.002837 & 1.9764 & 0.3513 & 0.6165 & 0 & 0.002402 & 0.3835 & 0 & 0.003422 \\ \hline
**Outdoor** & 0.04743 & 1.2669 & 0.005058 & 0.7043 & 0 & 0.01809 & 0.2957 & 0 & 0.08264 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters estimated for Gaussian, Gaussian mixture model, and \(\alpha\)-stable models. Figure 11: Power Spectrum Density of measured data in all scenarios (tone of 1 kHz of audio source). individual Gaussians of GMM has a poor fit due to heavy tails of the data, the GMM may reach a better fit using its two Gaussian components. Figure 13 shows a similar plot including the S\(\mathfrak{a}\)S fitting. The PDF is computed using the direct integration method, as described in [25]. We also visualize the significant error from the Gaussian model fitting. However, it is very hard to precise if GMM is better than the S\(\mathfrak{a}\)S model. This behavior is also observed when we draw similar plots for indoor and hall scenarios, Figures 14 and 15, respectively. In the indoor scenario, no difference is noticed among the models. The low impulsiveness causes a better fit from the Gaussian model as shown in Figure 14. The two components from the GMM model have similar behaviors; probably they are modeling the same class of noise. The \(\alpha\) from S\(\mathfrak{a}\)S model has the value close to 2, indicating that the model is similar to a  
Figure 12: Illustration of Gaussian mixture model fitting with two Gaussians (data from the outdoor scenario in a time window with severe impulsiveness). Figure 13: Illustration of PDF fitting for all models (data from the outdoor scenario in a time window with severe impulsiveness). Gaussian model. In the hall scenario, all models also have similar performance, as shown in Figure 15. However, compared to the indoor case, the \(\alpha\) can reach slightly lower values, indicating a higher impulsiveness condition.