# Optimization of Parametric Equalizer Filters in In-Vehicle Audio Systems with a Genetic Algorithm
## 4 Results  
First, the parametric equalizer filter parameters defined by the standards for equal loudness given in Table 1 were applied to the modeling software created to calculate the speaker output. The resulting speaker output contour is shown in Figure 7. Here, the blue line represents the simulation results, while the black line represents the ideal contour taken from the principle of equal loudness, with the effective frequency range of the speaker highlighted. Subsequently, the experimental setup shown in Figure 8 was established to create the test environment. This experimental setup was also intended to evaluate the degree of alignment between the modeling and simulation results with a real-world application and to measure the performance of the simulation model. In the test setup, the same filter parameters were loaded into the vehicle multimedia sound system, and the speaker output was measured. The simulation and experimental results are presented together in Figure 9 and compared with the ideal contour. Here, the blue line represents the simulation results, the red line represents the experimental results, and the black line represents the ideal contour. First, the experimental and simulation results were compared for the effective frequency range of the speaker to evaluate the performance of the simulation model. For this purpose, Pearson correlation analysis and root mean square error (RMSE) calculations were performed. The correlation coefficient between the experimental and simulation results was found to be 0.9295. This result indicates a high degree of similarity, and it demonstrates the success of the simulation model. Due to the unknown frequency responses of the cables, vehicle multimedia system, and audio analyzer, these factors were not included in the models, and this situation affected the similarity. The RMSE value was calculated as 2.29. Attenuations caused by the elements and cables of the experimental setup created differences in amplitude values, which impacted the root mean square error rate. Figure 7: Comparison of simulation results of speaker output, obtained with ideal filter parameters and the equal-loudness contour. Subsequently, the simulation results and experimental results were compared with the ideal contour. The Pearson correlation coefficient for the simulation and experimental results was found to be 0.6341 and 0.6715, respectively. The RMSE values were calculated as 4.88 and 2.57, respectively. As seen from the results, despite applying the ideal filter values, high similarity results were not achieved with the ideal contour. As shown in Figure 6, the speaker response is more sensitive to certain frequencies, causing deviations in amplitudes, which affected the overall system performance and reduced the similarity to the ideal contour. Following these processes, the parametric equalizer parameters were calculated using a genetic algorithm-based optimization algorithm. The genetic algorithm was executed  
Figure 8: Test setup in a laboratory environment (real-world scenario). Figure 9: Comparison of simulation, experimental, and equal-loudness contour for speaker output obtained with ideal filter parameters. 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 results of the genetic algorithm runs are summarized in Table 4, which shows the best, worst, and average fitness values for each run. These values demonstrate the consistency and effectiveness of the genetic algorithm in optimizing the filter parameters. The results indicate that the genetic algorithm effectively optimized the filter parameters, as seen in the range of best, worst, and average fitness values across the thirteen runs. The best fitness value of 2.2826 was achieved in run 9, demonstrating the algorithm's ability to find highly optimized solutions.