# Acoustic Impulsive Noise Based on Non-Gaussian Models: An Experimental Evaluation
## 4 Experimental Results and Analysis
### Sample Number Analysis  
A crucial issue of signal estimation is the stationarity assumption [28]. If data is non-stationary, we can not affirm that the estimated parameters (e.g., mean, variance and autocorrelation) do not change over time. However, several researchers persist with stationarity assumption because the problems are mathematically easier to model. Initially, we present an investigation about the number of samples and the windowing strategy. In this section, we start the discussions about stationarity, and in the Section 4.5, we provide a more statistically rigorous hypothesis test to legitimate the estimated model for each scenario. First, we show in Figure 17 the variance of the \(\alpha\) values (from SaS model) estimated for the whole set of 240,000 samples. We split samples in time windows of fixed size and evaluate the variances of the estimated \(\alpha\) inside window sizes from 1000 to 30,000. Looking at the results for indoor and hall scenarios, we see that longer the window size is, the more stable is the estimation (the lower the variance). However, for the outdoor scenario, this behavior is only observed for more extended window sizes (longer than shown in the Figure 17, suppressed for better visualization of curves). Comparing the results for the three scenarios, we can choose a window length of 1500 samples for the parameter analysis. This window provides a trade-off of low variance (estimation stability) and the window size. From a system point of view, a long window size could reflect higher signaling cost or latency. Figure 16: Outdoor scenario: Comparison between the data distribution and the estimated Gaussian and SaS models. Secondly, only with illustrative purposes, we present the difference between overlapped and non-overlapped estimation in Figures 18 and 19. When we use a non-overlapped estimation, shown in Figure 18, the estimated parameters are much smoother than overlapped estimation, illustrated in Figure 19.  
In both cases, the window size is 10,000 samples, but we overlapped 1000 samples (10% of the window) for the estimation in Figure 19. The objective is to show that, due to the different number of snapshots (24 for the non-overlapped and 240 for the overlapped case), the overlapped estimation better captures the variations of the estimated parameters. Thus, we use the overlapped  
Figure 17: Variance of the estimated \(\alpha\) parameter versus the window length. Figure 18: Illustration of non-overlapped estimation. window technique to get better analysis, exploring the trade-off between low window length and high resolution estimation. Now, we analyze the estimation stability for the Gaussian (Figure 20), GMM (Figure 21) and SaS (Figure 22) models for all scenarios. We plot the estimated parameters of 1590 snapshots for a window size of 1500 with 10% of window overlapping (this is the total number of snapshots with 240,000 samples, window size of 1500 and 150 overlapped samples, calculated as \(\left(240,000-1500\right)/150\;=\;1590\) snapshots). We show the parameter estimation for the two Gaussians of GMM model (Figure 21). Analyzing all figures, while the indoor and hall scenarios present reasonable stability on parameter estimation, especially considering Gaussian and GMM models, the outdoor scenario presents an estimation with significant variance. Finally, looking at the parameters for \(\alpha\)-stable model (Figure 22), one can confirm that the outdoor scenario has a highly impulsive noise due to the \(\alpha\) values near to 1. We may conclude that \(\alpha\) values far from 2 indicate a poor fitting of Gaussian model and noise data. It suggests that the variance from Figure 20 is not enough to describe the noise data, especially from the outdoor scenario. As discussed previously discussed, from a system perspective, short window size produces less signaling cost and latency.