# Notes on a New Structure of Active Noise Control Systems
## 4 Simulation Case Studies
### Case Study 3
The corresponding noise attenuation obtained with the classical FxLMS algorithm was reduced to 2.2 dB in comparison with the result from Table 3. A similar improvement was observed in the results of the simulation experiments repeated for the Gaussian white noise variance equal to 2 and parameter \(\mu\) equal to \(5\times 10^{-8}\). The noise reduction values obtained were 1.79 dB for the classical FxLMS control system structure and 2.78 dB for the new FeFxLMS control system structure. In the last simulation experiments, the influence of the equalization filter precision was addressed. A new filter \(F_{est1}(z^{-1})\) was applied to estimate values of signal at the error microphone. It was designed to estimate signal values at the error microphone precisely for a wider band of frequencies than it was possible with the filter \(F_{est}(z^{-1})\). Amplitude frequency responses of the two compared filters are shown in Figure 19. The corresponding simulation results are summarized in Figures 20 and 21. The noise to be attenuated is the continuous spectrum wide-sense stationary Gaussian random noise defined by the power spectral density plotted with a red line in Figure 21. Simulation experiments were repeated for its 50 realizations of \(10^{6}\) samples. The parameter \(\mu\) was equal to \(5\times 10^{-7}\). In Figure 20, the estimated (with autoregressive parameter equal to 0.999) mean square values of the discrete-time signals \(e_{0}(i)\) are presented for the two discussed active noise control system structures. It follows from the presented time plots that the signal at the error microphone converged faster in the new FeFxLMS control system structures than in the classical FxLMS control system structure and the new structure with the filter \(F_{est1}(z^{-1})\) gave the highest noise reduction. The corresponding averaged noise reduction was the following: 2.77 dB in the classical FxLMS structure, 3.82 dB in the new FeFxLMS structure with the filter \(F_{est}(z^{-1})\), and 5.25 dB in the new FeFxLMS structure with the filter \(F_{est1}(z^{-1})\). Figure 18: Estimated mean square value of the discrete-time signals \(d(i)\) and \(e_{0}(i)\) at the error microphone—the classical FxLMS and new FeFxLMS control system structure, \(\mu=5\times 10^{-8}\). In Figure 21, the estimated power spectral densities of the signals at the error microphone in the new FeFxLMS control system structure with old \(F_{est}(z^{-1})\) and newly designed filter \(F_{est1}(z^{-1})\) and the classical FxLMS control system structure are presented. They were obtained for a single realization of the noise to be attenuated after convergence of the adaptation process. It is worth noting that the frequency domain properties of the filter applied to estimate values of the signal at the error microphone influence on a comfort of the active noise control system users. The new FeFxLMS control system structure with the filter \(F_{est1}(z^{-1})\), that estimates signal values at the error microphone precisely for a wider band of frequencies than it was possible with the filter \(F_{est}(z^{-1})\), gives the greatest noise  
Figure 19: Amplitude frequency responses of antialiasing, \(F_{est}(z^{-1})\) and \(F_{est1}(z^{-1})\) filters. Figure 20: Estimated mean square value of the discrete-time signals \(d(i)\) and \(e_{0}(i)\) at the error microphone—the classical FxLMS and new FeFxLMS control system structures with \(F_{est}(z^{-1})\) and \(F_{est1}(z^{-1})\). reduction but also amplifies noise at frequencies around 200 Hz more than the remaining active noise control systems considered.