## 4 Results and Discussion
### Results of the Active Control for White Noise  
Hereinafter, a completely random noise signal filtered up to 1000 Hz is used as a disturbance. However, all the successive conclusions are valid both for completely random \begin{table}
\begin{tabular}{l|c c|c c|c c|c c} \hline \hline
**Pseudo-Random** & \multicolumn{2}{c}{**FF_FXLMS**} & \multicolumn{2}{c}{**FB_FXLMS**} & \multicolumn{2}{c}{**FF_FURLMS**} & \multicolumn{2}{c}{**FF_FXNLMS**} \\ \hline Side & Left & Right & Left & Right & Left & Right & Left & Right \\ Reduction [dB] & 2.5 & 2.4 & 3.2 & 2.9 & 2.5 & 2.3 & 2.5 & 2.6 \\ Reduction [dB(A)] & 2.3 & 1.6 & 3.5 & 2.7 & 2.1 & 1.4 & 2.2 & 2.9 \\ Convergence [dB/s] & 0.7 & 0.6 & 0.8 & 0.7 & 0.6 & 0.6 & 0.1 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Attenuation and speed of convergence for internal reference microphone for the tested pseudo-random noise. Figure 12: Time history of the left error signal amplitude for a pseudo-random noise signal filtered up to 1000 Hz and with period T = 0.10 s, for external and internal reference microphone. \begin{table}
\begin{tabular}{l|c c|c c|c c|c c} \hline \hline
**Pseudo-Random** & \multicolumn{2}{c}{**FF_FXLMS**} & \multicolumn{2}{c}{**FB_FXLMS**} & \multicolumn{2}{c}{**FF_FURLMS**} & \multicolumn{2}{c}{**FF_FXNLMS**} \\ \hline Side & Left & Right & Left & Right & Left & Right & Left & Right \\ Reduction [dB] & 5.4 & 4.5 & 1.2 & 1.0 & 6.4 & 5.6 & 2.6 & 1.9 \\ Reduction [dB(A)] & 13.9 & 9.5 & 1.0 & 0.5 & 14.2 & 9.8 & 7.2 & 3.5 \\ Convergence [dB/s] & 2.5 & 1.9 & 0.1 & 0.1 & 2.3 & 1.8 & 0.5 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Attenuation and speed of convergence for external reference microphone for the tested pseudo-random noise. noise and pseudo-random noise signals, in which the period is greater than the duration modeled by the filters. For this kind of broadband noise, the achievement of a high level of reduction with an adaptive algorithm in a short time becomes difficult with respect to a periodic signal, as can be observed by comparing the results of the pseudo-random noise signal, given in Tables 5 and 6, with the results obtained for white noise and reported in Tables 7 and 8. In this latter case, the speed of convergence is not specified due to the high variability of the sound pressure level in time (fluctuations of \(\pm\)3 dB). The reduction in the performance for all the algorithms can be related to the LMS procedure: since the updating of the adaptive filters occurs in an iterative way, the lack of periodicity does not allow the coefficients to converge quickly to an optimal value, reducing the capability of attenuation. As illustrated in Figure 13, the feedback system FB_FXLMS is completely ineffective due to its predictor nature and shows some instability effects with amplification above 500 Hz, where the feed-forward systems generally show a higher efficiency and a better performance. The main contribution to the reduction of the overall A-weighted sound level is related to the band of 800 Hz (up to 10.1 dB of attenuation for FF_FXLMS and FF_FURLMS and 6.5 dB for FF_FXNLMS) for the case of external reference microphone, while for the internal position, it is associated with the band of 630 Hz (1.8, 1.2, and 2.1 dB, respectively for FF_FXLMS, FF_FURLMS, and FF_FXNLMS). As for the pseudo-random noise signal, it should be pointed out that the convergence speed depends on the bandwidth of the disturbing signal, which acts directly on the complexity of the signal. To improve these results, pre-calculated and non-adaptive filters should be employed, for instance, based on the optimization of the H\({}_{\infty}\) norm [31; 32; 33]. pressure level at the position of the error microphones with respect to the case with the cabin, while the reference microphone has been brought nearer to the noise source, to guarantee a similar reference signal level.