## 3 Simulation Results
Therefore, in this experiment, we use this number of filter coefficients and vary the number of particles to verify how the performance of the proposed PSO-based ANC system is affected. As can be observed from Figure 7, the number of particles is an important factor to be considered, especially when high level of noise reduction and fast convergence speed are required. Hence, the use of a large number of particles and high order filters guarantees good convergence properties at the cost of increasing the computational complexity. * _Comparison between the proposed PSO-based ANC system with switching filter selection and existing approaches._ In addition to previous simulations, we simulate the proposed PSO-based ANC system and existing approaches [23,24] to make a consistent comparison between them in terms of the MSE level. Table 2 shows the fixed parameters of the existing approaches, such as acceleration coefficients and inertia weights, which were selected to provide the best performance of these approaches. Here, the primary and secondary path of the proposed PSO-based ANC system and existing approaches were multiplied by \(-1\) at generation 750 to test their tracking behavior, as shown in Figures 8 and 9, respectively. As can be observed, the proposed PSO-based ANC system achieves a higher MSE level when compared with existing approaches. It should be noted that the most recent approach based on quantum-behaved (QPSO-based ANC system) [24] achieves a slight improvement of the MSE level compared with the PSO-based ANC system [23] at the cost of increasing its computational complexity, as shown in Table 3. As can be observed, the proposed PSO-based ANC system with switching filter selection reaches similar convergence speed compared with the QPSO-based ANC system. However, the proposed approach exhibits better MSE-level by expending lower computational cost. On the other hand, we include the FXLMS algorithm in the comparison. Obviously, the FXLMS algorithm exhibits lower computational cost compared with the existing bio-inspired approaches. Nonetheless, the FXLMS algorithm presents the lowest convergence speed. Figure 6: Learning curves of the proposed PSO-based ANC system for different filter lengths \(N\) using 100 particles. Figure 8: Comparison between approaches when a change in the primary path occurs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Approach** & **Algorithm** & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{\phi_{min}}\) & \(\mathbf{\phi_{max}}\) \\ \hline [PERSON] et al. [23] & PSO & \(1\) & \(1\) & \(0.0009\) & \(0.79\) \\ \hline [PERSON] et al. [24] & QPSO & \(1.5\) & \(1.5\) & \(0.5\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Acceleration coefficients and inertia weights of the PSO and QPSO algorithms  
Figure 7: Learning curves of the proposed PSO-based ANC system for different number of particles. \(P\) using 50 filter coefficients. * _Power Spectrum analysis._ Apart from previous results, we obtained the residual noise at the error microphone by using two different reference signals. Figure 10 depicts the residual noise and the power spectrum when a multi-tonal signal is used as undesired-noise. As can be observed from this figure, if the adaptation process occurs, the noise at the error microphone decreases. Figure 10: Residual noise and power spectrum of the error signal at error microphone by processing a multi-tone signal as reference signal. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Approach** & **Algorithm** & **Additions** & **Multiplications** & **Logarithms** \\ \hline Adapted from & & & & \\ [PERSON] et al. [35] & FXLMS & \(2N+M{-}1\) & \(N+M+1\) & 0 \\ \hline Adapted from & & & & \\ [PERSON] et al. [23] & PSO & \(5 NP+2\) & \(5 NP+2\) & 0 \\ \hline Adapted from & & & & \\ [PERSON] et al. [24] & QPSO & \(5 NP+2P+3\) & \(4 NP+3\) & \(N\) \\ \hline This work & PSO & \(5 NP+7\) & \(5 NP+5\) & 0 \\ \hline \hline \end{tabular}
\end{table}