## 5 Simulations and Discussion
### Simulation Results and Discussion
\"ANCoff\" represents that the ANC was turned off, whereas \"ANCon\" represents that the ANC was turned on. Figure 6 depicts the power spectrum densities (PSDs) of noise attenuation in  
Figure 4: Converged filter weight coefficients of (**a**) feedforward control structures and (**b**) feedback control structures for different hybrid sound quality control systems. different structures when the ANC was off and on. The gain factor was equal to zero in Figures 5 and 6. It is shown that the two modified algorithms could not only offset the line-spectrum noise to achieve the control goal for sound quality, but they could also attenuate the Gaussian random noise. The total sound pressure levels between 10 Hz and 100 Hz were calculated as follows [30]:  
\[SPL=20\log_{10}(\frac{p}{p_{ref}}), \tag{25}\]  
where \(p\) denotes the sound pressure, \(p_{ref}=2\times 10^{-5}\)Pa is the reference sound pressure in the air, and \(SPL\) denotes the sound pressure level. \[T\_SPL=10\log_{10}(\sum_{i=i_{low}}^{i_{high}}10^{SPL_{i}/10}), \tag{26}\]  
where \(T\_SPL\) denotes the total sound pressure level. Figure 5: Spectra of noise attenuation in different structures (\(\beta=0\)): (**a**) traditional hybrid structure; (**b**) simplified hybrid structure using new leaky filtered-x least mean square (FxLMS) algorithm in the feedback controller; (**c**) modified hybrid structure; (**d**) simplified hybrid structure using leaky FxLMS algorithm in the feedback controller (\(\gamma=0.8\)). The total sound pressure levels of different structures are shown in Table 3. The SPL is defined as the sound pressure level. The total sound pressure level of the modified structure was 69.5 dB when that of the primary noise was 92.1 dB. The total sound pressure level of the traditional structure was close to that of the modified structure. The modified structure not only had a more stable iteration process, but it also had basically the same noise reduction as the traditional structure. This also validated that the beneficial influence of decoupling was balanced with computational complexity because the iteration process of the line-spectrum noise cancellation filter still occurred in practice. The total sound pressure levels of the simplified structures were slightly higher than those of the traditional structure, owing to the use of leaky class FxLMS algorithms in the feedback controllers. Although the computational complexities of the simplified structure using leaky class FxLMS algorithms were less increased, their iteration processes of control filters were more stable. Therefore, it can be obtained that the simplified structures had the approximate ability of noise reduction compared with the traditional structure, because the simplified structures had better performance in terms of stability. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **ANCoff** & **Tra Structure** & **Tsim Structure** & **Nsim** & **Mod Structure** \\  & & [10] & [19] & **Structure** & **Mod Structure** \\ \hline SPL (dB) & 92.1 & 69.4 & 70.1 & 70.0 & 69.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Noise reductions of the different structures (\(\beta=0\)). Figure 6: Power spectrum densities (PSDs) of noise attenuation in different structures (\(\beta=0\)): (**a**) traditional hybrid structure; (**b**) simplified hybrid structure using new leaky FxLMS algorithm in the feedback controller; (**c**) modified hybrid structure; (**d**) simplified hybrid structure using leaky FxLMS algorithm in the feedback controller (\(y=0.8\)). Furthermore, it can be noted that only the harmonic noise signal was utilized to validate the algorithm performance. The reference input signal with multiple frequencies could be controlled by configuring multiple feedforward sound quality controllers in parallel. The spectra of noise attenuation in different structures are shown in Figure 7 when the gain factor was 0.5. The noise reductions were measured when the ANC system was turned off and on.