# Active Noise Control Using Modified FsLMS and Hybrid PSOFF Algorithm
## 6 Result and Discussion
Case 2: The following noise signal is considered to be generated at the cancelling point, and it is a third order polynomial model expressed by  
\[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]7  
Figure 6, shows the Gaussian noise signal. In this noise signal, the expression for \(g(n)\) is considered as the convolution of \(x(n)\) and the impulse response of the transfer function \(B(z)=z^{-3}-0.3z^{-4}+0.2z^{-5}\), denoted as \(b(n)\). \(x(n)\) is the reference signal defined as in Case 1. For the comparison of the performance,  
\[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]8 Noise removed signal. (**a**) Proposed method; (**b**) Existing method. \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]9 Number of iterations versus normalized mean square error. (**a**) Proposed method; (**b**) Existing method. the existing method FsLMS and the proposed modified technique are considered. The results are plotted with the comparison of iteration and the normalized mean square error. The parameters for Case 2 were taken as in Case 1. Figure 7a,b provide the noise-removed signal obtained by the proposed and existing techniques, respectively. This is the reduced noise signal from the Gaussian noise signal. It represents the significance of the proposed technique in noise removal. The normalized mean square error is used for the comparison of defined work with the existing FsLMS algorithm. The mean square error (reduced in the proposed case), and existing works are shown in Figure 8a,b. From the result, it is evident that the MFsLMS algorithm dictates the ultimate noise removal in the signal. The minimum value of NMSE in the proposed case is **0.265 dB** and for the existing case is **0.425 dB**. \[x(n+1)=\eta\;x(n)\;[1-x(n)]. \tag{10}\]0 Gaussian noise. \[x(n+1)=\eta\;x(n)\;[1-x(n)]. \tag{10}\]1 Noise removed signal. (**a**) Proposed method; (**b**) Existing method (FsLMS). Table 2 shows the comparison of the proposed method with hybrid PSO-ABC (Particle Swarm Optimization-Artificial Bee Colony) and hybrid PSO-GA (Particle Swarm Optimization-Genetic Algorithm). The enhanced performance of the proposed method, along with other two as mentioned above, is shown in Figure 9 (as a comparison chart). The NMSE value (in dB) has been reduced by **0.187 dB** with the time consumption of about **0.385 s**; in the proposed method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S.no** & **Method** & **NMSE (dB)** & **Computational Time (s)** \\ \hline
1 & Proposed Method & 0.187 & 0.385 \\
2 & Hybrid PSO—ABC & 0.300 & 0.524 \\
3 & Hybrid PSO—GA & 0.428 & 0.628 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the proposed method with other hybrid algorithms. Figure 8: Number of iterations versus normalized mean square error (**a**) Proposed method; (**b**) Existing method (FsLMS). Figure 9: Performance evaluation of the proposed method. Figure 10a,b shows the performance of the proposed MFsLMS algorithm with the existing FxLMS and FsLMS algorithms regarding the NMSE (in dB) for Case 1 and Case 2 respectively. In summary, this work explains the noise removal in multichannel active noise control system via the MFsLMS and HPSOFF algorithm. From the resulting discussion, it has been proved that the proposed work eliminates the noise well when compared to the existing techniques. The capability of noise removal has been achieved with a minimum computational time and reduced complexity. Thus, the system poses a higher efficiency, so the proposed method is better for noise removal from the multichannel ANC. The stability of the proposed system has been evaluated through the HPSOFF algorithm. Figure 10: Performance evaluation of proposed method in terms of NMSE (**a**) Case 1; (**b**) Case 2.