# Notes on a New Structure of Active Noise Control Systems
## 4 Simulation Case Studies  
The simulation case studies described below are arbitrarily designed to show some basic properties of the proposed new FeFxLMS active noise control structure. All simulations are done in Matlab according to the block diagrams are shown in Figures 3 and 4. Figure 4: The new filtered-reference filtered-error LMS (FeFxLMS) control system structure with the featured error signal measurement path and estimation of the signal at the error microphone embedded in simulation environment. Models of the reference signal measurement path, disturbance path, acoustical disturbance path, secondary path, secondary path control signal part, and error signal measurement path used in the first two simulation case studies are simplified to focus on properties of the presented new FeFxLMS control system structure. In the third simulation case study the corresponding models identified in the laboratory room are used. All models used in simulations are FIR filters with 100 coefficients. It is assumed in the presented below simulation case studies that: The active noise control systems operate with the constant sampling frequency equal to 500 Hz; an acoustic feedback between the control loudspeaker and the reference microphone is perfectly canceled; simulations started from the time instant 0 and adaptation is activated at the iteration number 1000; the number of FIR filter \(W(z^{-1})\) coefficients is equal to 50 and are tuned online using the LMS algorithm from initial values equal to 0; \(\mu\) parameter (convergence coefficient) is chosen individually for each simulation experiment, the same for both control system structures; the number of FIR filter \(F_{est}(z^{-1})\) coefficients is 100 and the value of parameter \(\Delta\) is equal to 50; and the same realizations of the noise to be attenuated are used to simulate the classical FxLMS and new FeFxLMS control system structures. Additionally, the same model is used to simulate the secondary path and as a model of secondary path. The dynamics of the error microphone present in the error signal measurement path as well as dynamics of the amplifier are omitted in the simulations: It is assumed that dynamics of the error signal measurement path is represented only by dynamics of the antialiasing filter. Such a simplification has no influence on general conclusions drawn. To run the new FeFxLMS control system structure with an estimation of signal values at the error microphone the coefficients of the filter \(F_{est}(z^{-1})\) are calculated with equalization methods. With given (offline identified) models of the disturbance, secondary and error signal measurement paths corresponding to the acoustical disturbance path and secondary path control signal part are calculated using model identification algorithms as well as the model of the error signal measurement path. All FIR models obtained in this way are truncated to 100 coefficients. Power spectral densities of the discrete-time signals presented in the paper are estimated by the averaging of periodograms calculated for non-overlapping data segments [33] taken from a single realization of the corresponding signal. They are obtained using 1500 consecutive data segments consisting each of 1024 signal samples. The calculation of each estimate starts after all transients implied by initial conditions and initial adaptation have decayed. The time plots of mean square values of signals presented in the paper are obtained by the averaging of curves obtained for 100 or 50 realizations of the noise to be attenuated. Single estimates of the mean square values of the corresponding signals at consecutive discrete-time instants \(i\) are obtained as a result of the filtration of squared values of these signals through the first-order discrete-time filter with a gain equal to 1 and an autoregressive parameter equal to 0.999 or 0.99 [34].