## 4 Results and Discussion
### Results of the Active Control for Pseudo-Random Noise  
The tests with pseudo-random signals are reported in Figure 12. This noise is composed of a broadband signal filtered up to 1000 Hz, repeated with a periodicity of 0.10 s. The period has been chosen in order to be lower than the duration modeled by the filters (computed as the number of elements of a filter divided by the sampling frequency) so that  
\begin{table}
\begin{tabular}{l|c c|c c|c c|c c} \hline \hline \multicolumn{2}{c}{**100 Hz**} & \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] & 4.7 & 3.4 & 12.1 & 10.7 & 24.5 & 25.1 & 2.5 & 2.4 \\ Convergence [dB/s] & 2.4 & 1.8 & 5.0 & 4.3 & 9.2 & 6.3 & 1.4 & 1.5 \\ \hline
**500 Hz** & **FF\_FXLMS** & **FB\_FXLMS** & **FF\_FURLMS** & **FF\_FXNLMS** \\ \hline Side & Left & Right & Left & Right & Left & Right & Left & Right \\ Reduction [dB] & 37.2 & 37.8 & 14.0 & 12.8 & 37.6 & 37.4 & 37.1 & 34.9 \\ Convergence [dB/s] & 6.1 & 7.0 & 4.9 & 4.6 & 15.2 & 20.9 & 18.9 & 13.7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Attenuation and speed of convergence for internal reference microphone for the pure tones.  
Figure 11: Example of time history of the step-size parameter for the FF_FXNLMS algorithm when active noise control is turned on and comparison with the fixed value.  
\begin{table}
\begin{tabular}{l|c c|c c|c c|c c} \hline \hline \multicolumn{2}{c}{**100 Hz**} & \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] & 45.0 & 45.4 & 7.0 & 6.1 & 42.5 & 42.3 & 44.0 & 32.6 \\ Convergence [dB/s] & 15.5 & 13.4 & 1.5 & 1.3 & 23.5 & 22.1 & 19.8 & 15.5 \\ \hline
**500 Hz** & **FF\_FXLMS** & **FB\_FXLMS** & **FF\_FURLMS** & **FF\_FXNLMS** \\ \hline Side & Left & Right & Left & Right & Left & Right & Left & Right \\ Reduction [dB] & 38.0 & 37.4 & 9.0 & 8.7 & 37.7 & 36.4 & 37.5 & 27.4 \\ Convergence [dB/s] & 23.8 & 23.0 & 2.4 & 2.8 & 29.4 & 28.0 & 14.1 & 8.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Attenuation and speed of convergence for external reference microphone for the pure tones.  
Figure 10: Time history of the left error signal amplitude for a pure tone at 500 Hz for external and internal reference microphone.  
the pseudo-random signal can be considered as an intermediate case study between the pure tone and the completely random noise. Furthermore, it should be pointed out that the results described in the following depend on the chosen bandwidth of the disturbing signal, since the convergence becomes slower with the increment of the bandwidth due to the higher complexity of the signals; moreover, by exceeding the limit of a quarter of the sampling frequency in the disturbance source, the instability of the system occurs. In this case, a low-pass filter directly applied to the reference signal to remove high frequencies would be beneficial to guarantee stability.  
For the case of the external reference microphone, the feed-forward systems with fixed step size (i.e., FF_FXLMS and FF_FURLMS) produce the best performance in terms of reduction and speed of convergence. Also in this case, the feedback system FB_FXLMS shows a slow convergence with the same step size of the feed-forward algorithms. When the reference microphone is inside the cabin, the performance exhibited by the different configurations becomes similar in terms of reduction and convergence velocity. The global results are presented in Tables 5 and 6. We can observe that the performance of all the feed-forward algorithms is reduced when the reference microphone is moved inside the cabin, while the feedback system FB_FXLMS increases its performance both in terms of total attenuation and speed of convergence, thanks to the increment of step size.