## 4 Experiment Results and Analysis
### Control Performance Analysis of the Pure ASP Algorithm
#### 4.1.2 Tracking Performance for Sound Enhancing  
For comparison of the tracking performance of the C3, C6, and C9, the tracking error \(L_{TE}(f)\) can be defined as the difference between the SPL of the measured error signal \(L_{E}(f)\) and the target SPL \(L_{target}(f)\), and can be given as  
\[L_{TE}(f)=L_{E}(f)-L_{target}(f) \tag{11}\]  
\(L_{TE}(f)\) indicates how closely the error signal tracks the target sound, so the closer it is to zero, the higher tracking performance is. The positive value of \(L_{TE}(f)\) means the measured SPL of the error signal is larger than the target SPL, and the negative value implies the opposite. This can be expressed in root mean square (RMS) over the engine speed range of 1000-5500 r/min for each engine order as \(L_{TE,\text{RMS}}\) and those of the C3, C6, and C9 before and after controls summarized in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Averaged Noise Reduction (dBA): \(L_{NR,\text{Avg}}\)**} \\ \hline Order & C2 & C4 & C8 \\ \hline Before control & 0 & 0 & 0 \\ \hline After the pure ASP control & \(-8.0\) & \(-6.8\) & \(-6.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of the noise reduction performance of the C2, C4, and C8 for canceling order noise using the pure ASP algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**RMS of Tracking Error (dBA): \(L_{TE,\text{RMS}}\)**} \\ \hline
**Order** & **C3** & **C6** & **C9** \\ \hline Before control & 13.2 & 11.0 & 14.4 \\ \hline After the pure ASP control & 2.9 & 1.4 & 7.5 \\ \hline After the additive ASP control & 1.8 & 1.3 & 1.7 \\ (Proposed) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the tracking performances of the pure and additive algorithms for the C3, C6, and C9 orders. Figure 8 shows the comparisons of the tracking performances at the C3, C6, and C9 orders before control (dotted lines) and after the pure ASP control (thin solid lines) with the target profile (dashed lines). Figure 8a,b displays the SPLs of the C3 order before and after controls and the tracking error \(L_{TE}(f)\), respectively. Figure 8c,d show those of the C6 order, and Figure 8e,f denote those of the C9 order. In each figure, the leakage term for each order is included at the upper side. Figure 7: Comparisons of the measured SPL of each order before and after the pure ASP control, and noise reductions. (**a**) SPL of the C2 order. (**b**) Noise reduction of the C2 order. (**c**) SPL of the C4 order. (**d**) Noise reduction of the C4 order. (**e**) SPL of the C8 order. (**f**) Noise reduction of the C8 order. In the case of the C3 order, as illustrated in Figure 8a,b, the SPLs in particular above 2200 r/min after control were dramatically enhanced to track the target profile. Thus, \(L_{TE}(f)\) was obtained by \(-10\) to 3 dBA over the entire engine speed range, whereas \(L_{TE}(f)\) before control was varied from \(-25\) to 1 dBA. It is noteworthy that there was a sharp drop in \(L_{TE}(f)\) of \(-10\) dBA at 4300 r/min (215 Hz). This was because the control signal was  
Figure 8: Comparisons of the measured SPL of each order before and after the pure ASP control, and the tracking errors between the measured SPLs and the target profiles. (**a**) SPL of the C3 order. (**b**) Tracking error of the C3 order. (**c**) SPL of the C6 order. (**d**) Tracking error of the C6 order. (**e**) SPL of the C9 order. (**f**) Tracking error of the C9 order. suppressed by the leakage term, which was given as 0.98 due to insufficient coherence at this frequency. Nevertheless, \(L_{TE,\text{RMS}}\) after control was greatly improved by 2.9 dBA, which was 10.3 dBA less than that before control as shown in Table 3.  
In the case of the C6 order, as can be seen from Figure 8c,d, the ASP control was activated at almost the entire engine speed range except for 215 Hz. The SPLs after control were followed the target profile very closely with \(L_{TE}(f)\) of \(-4\) to 3 dBA compared with that of \(-26\) to 6 dBA before control.