# Active Noise Control Using Modified FsLMS and Hybrid PSOFF Algorithm
## 6 Result and Discussion  
The multichannel ANC system, with L reference microphones, M loudspeakers and N error microphones, have been analyzed. By modifying the original algorithm with a Maclaurin series part. The computational complexity of the proposed system has been reduced. The functional expansion used in every previously defined algorithm was the trigonometric expansion. However, in this work, the functional expansion is given by the simple computation of the Maclaurin series. When comparing \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & \multicolumn{2}{c}{**FsLMS**} & \multicolumn{2}{c}{**MFsLMS**} \\ \hline
**Length of Secondary Path (V)** & **Multiplication** & **Addition** & **Multiplication** & **Addition** \\ \hline
2 & 852 & 634 & 316 & 154 \\
4 & 950 & 781 & 332 & 202 \\
6 & 1024 & 948 & 348 & 250 \\
8 & 1095 & 1012 & 364 & 298 \\ \hline \end{tabular}
\end{table} 
Table 1: Computational complexity. with the FsLMS algorithm, the functioning of the MFsLMS algorithm is verified. The computer simulations are used to analyze the strength of the defined work with two different noise signals. The normalized mean square error value is plotted with the number of iterations for the performance evaluation. The successive relations are used for evaluating the values of the normalized mean square error  
\[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]  
where \(\sigma_{d}{}^{2}\) is the variance of the primary noise (at cancellation point) and \(e^{2}(n)\) is the square value of the error function. Case 1: A logistic chaotic primary noise signal [20] is created by using a recursive equation  
\[x(n+1)=\eta\;x(n)\;[1-x(n)]. \tag{10}\]  
Figure 3 denotes the noise signal for the considered logistic chaotic noise. In the above noise signal, \(\eta=0.01\) and \(x(0)=0.9\). The non-linear noise is normalized to a signal value of one. The primary and secondary path transfer functions used in the simulation are  
\[H_{(1,1)}(z)=z^{-5}-0.3z^{-6}+0.2z^{-7},\] \[H_{(1,2)}(z)=z^{-5}-0.2z^{-6}+0.1z^{-7},\] \[H_{(1,3)}(z)=z^{-5}-0.3z^{-6}+0.1z^{-7},\] \[H_{(1,4)}(z)=z^{-5}-0.2z^{-6}+0.2z^{-7},\] \[A_{(1,4)}(z)=z^{-5}-0.2z^{-6}+0.2z^{-7},\] \[A_{(1,4)}(z)=z^{-2}-1.5z^{-3}+0.2z^{-4},\] \[A_{(1,2)}(z)=z^{-2}-1.7z^{-3}-z^{-4},\] \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]0 \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]1 \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]2 \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]3 \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]4 \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]5  
Figure 4a,b are the expected outcome of the noise-cancelled signal. It is evident that a better noise cancellation is provided through the defined work, as compared to the existing method. The noise cancellation performance yields a reduced normalized mean square error value. \[NMSE=10\log_{10}\left(\frac{E(e^{2}(n))}{\sigma_{d}{}^{2}}\right) \tag{9}\]6 Logistic chaotic noise. The parameters chosen for the simulation are L = 1; M = 2; N = 4 and, the memory size, m = 10. The step size or learning rate used for FsLMS is \(\mu=0.1\) and, for FsLMS, \(\mu\) is 0.000097. Figure 5a,b is the representation of the error cancellation performance of the proposed and existing methodology. The minimum value of the normalized mean square error, for the proposed work, is **0.187 dB**. When it is compared with conventional noise reduction techniques, the proposed work provides significant noise reduction. The minimum value of the normalized mean square error, of the existing technique, is **0.257 dB**. The reduction of the normalized mean square error enhances the performance of the ANC system, without the addition of any of the specialized noise control devices. The optimal outputs with the reduced computational time is obtained through the proposed algorithm.