# Optimization of Parametric Equalizer Filters in In-Vehicle Audio Systems with a Genetic Algorithm
## 5 Conclusions  
This study aimed to automate the process of optimizing the full-range speaker in the audio system of an SUV according to the equal-loudness principle. First, the frequency responses of the speaker and the input sound were transferred to the Matlab environment. Using the filter parameter values defined in the standards for \(1/1\) octave bands, ten parametric equalizers were modeled, and the speaker output was obtained using the convolution technique. The same filter settings were applied to the vehicle multimedia system, and the experimental results were obtained. These experimental results were validated by comparing them with the simulations. To achieve optimal acoustic performance, the center frequency, gain, and Q factor of each parametric equalizer were determined using a genetic algorithm. These filter parameters were iteratively optimized to closely match the ideal equal-loudness contour. After the optimization process, the calculated parameters were applied to the vehicle's multimedia system, and the obtained experimental results were compared with the simulation results in the Matlab environment using correlation and root mean square error (RMSE) analyses. This allowed for a detailed examination of the effectiveness of the modeling, simulation, and applied optimization strategy. First, the parametric equalizer filter parameters defined according to standard equal-loudness contour were applied to our modeling software, and the speaker output was calculated. Then, the same filter parameters were applied to the test setup, and the speaker output was measured. The simulation and experimental results were analyzed, yielding a Pearson correlation coefficient of 0.9295 and an RMSE value of 2.29. These findings indicate a high degree of similarity between the simulation and experimental results, demonstrating that the simulation model is consistent with the experimental data and performs successfully. The components not included in the model and attenuations from the test setup affected the correlation coefficient and the RMSE calculations. Subsequently, the results were compared with the ideal contour defined by the equal-loudness principle. The Pearson correlation coefficients for the simulation and experimental results were found to be 0.6341 and 0.6715, respectively, with RMSE values of 4.88 and 2.57. As understood from the results, despite using the ideal filter values, there was a low level of similarity with the equal-loudness contour. The used speaker was more sensitive to certain frequencies, causing deviations in amplitudes, which affected the overall system performance and reduced the similarity to the ideal contour. Following the relevant analyses and tests, the parameters of the ten parametric equalizer filters were calculated using a genetic algorithm-based optimization software. The genetic algorithm was executed thirteen times to ensure the robustness and reliability of the results. Each run involved evaluating the best, worst, and average fitness values to comprehensively assess the optimization process. The calculated parameters were applied to both the modeling software and the test setup for computation and measurement. The results of the genetic algorithm runs demonstrated the consistency and effectiveness of the algorithm in optimizing the filter parameters. Notably, the ninth run yielded the best overall performance, with a best fitness value of 2.2826, a worst fitness value of 3.8436, and an average fitness value of 3.0773. A high correlation and low RMSE values further validated the optimal performance achieved in this run. Specifically, the Pearsoncorrelation coefficient between the simulation results and the ideal contour was 0.9692, with an RMSE of 1.17. The experimental results showed a Pearson correlation coefficient of 0.9675 and an RMSE of 1.34 when compared to the ideal contour. Additionally, the correlation between the simulation and the experimental results was 0.9864, with an RMSE of 1.00.