## 4 Results and Discussion
### Results of the Active Control for Pure Tones  
In this section, the results of the application of ANC to pure tones are described. It is well known that ANC for pure tones works very well, particularly for middle and low frequencies. However, this part is useful as an introduction to the practical problems in the studied configurations and as a reference for the successive more complex signals. Figure 10 illustrates a comparison between the ANC algorithms applied to a pure tone at 500 Hz. The results show that the feedback configuration is the slowest system to converge. Since the unique difference between the FB_FXLMS and FF_FXLMS algorithms consists of the way in which the reference signal is acquired, the slowness of the feedback system is attributed to its additional internal modeling of the reference signals. Moreover, some instability phenomena can be observed for the FB_FXLMS algorithm when the step-size parameter is increased, as shown on the right-hand side plot of Figure 10. The FF_FXLMS algorithm seems to exhibit a strong reduction in the speed of convergence when the reference microphone is moved inside the cabin. In reality, this behavior is not associated with the position of the reference microphone, but with the choice of the step size near the stability limit for the FF_FXLMS algorithm, making the convergence slower. On the other hand, FF_FURLMS is able to maintain a similar velocity thanks to its capability of considering the acoustic feedback coming from the control sources and corrupting the reference signal, while the FF_FNLMS algorithm is able to preserve a similar performance thanks to the convergence to a smaller value of step size with respect to FF_FXLMS. As shown in Figure 11, the normalized step size varies in time when the active noise control is turned on, starting from a high value due to the transitory phase and converging in a few seconds to a stable value, which is calculated by adapting to the power of the reference signal, which is different between outside and inside.  
The total attenuation within the first 15 s and the mean speed of convergence, expressed in dB/s and evaluated in the first second from the start of the active control, are summarized in Tables 3 and 4 for the conditions with external and internal reference microphone respectively. Considering the reference microphone outside the cabin, the FB_FXLMS exhibits the worst performance, both in terms of total attenuation and speed of convergence, for both the considered pure tones. When the reference microphone is inside the cabin, for a large wavelength (i.e., 100 Hz), the feed-forward algorithms, which do not consider possible acoustic feedback (i.e., FF_FXLMS and FF_FXNLMS), exhibit a decrease in their performance due to the influence of the sound generated by the control sources on the reference signal. On the other hand, as the frequency increases, the performance of the feed-forward algorithms increases, outperforming the FB_FXLMS approach. Finally, it should be pointed out that for disturbing tones with a small wavelength, the ANC becomes sensitive to the imperfections of the system, and a marked difference between the left ear and the right ear could be sensed.  
Figure 9: Amplitude of the frequency response function of the (**a**) direct and (**b**) cross secondary paths.