## 2 Materials and Methods
### Proposed Calculation Method
#### 2.3.2 High-Frequency Noise Components  
As shown in Section 2.2, the tractive force on the tires also has a significant influence on high-frequency components of the tire noise. To further investigate these high-frequency components under the influence of torque, the vehicle's interior measurements are filtered according to the bark scale. In this way, a high correlation between the human perception of sounds and the utilized masking model can be achieved. Figure 9 shows the mean values of the sound pressure ratios up to the power limit of the evaluated critical bandwidths for exemplary torque levels of the luxury vehicle. In accordance with the previous investigations, the reference value is the sound pressure at full throttle. High influence of torque can be seen in low-frequency ranges and around the 15 th critical band. The torque influence in the low-frequency range is assumed to be the influence of the first block harmonic and is therefore not considered further, as this issue was already addressed in the previous section. However, the 15 th bark corresponds to the frequency range that was detected in Section 2.2 and will be investigated in more detail. In this evaluation, a low sound pressure ratio signifies a high influence of torque on the respective critical band. In order to derive generalized results to describe the influence of torque, a similar approach is used as for the block harmonic. Figure 10 indicates the sound pressure ratios between 50 Nm and the torque at full throttle for the three investigated vehicles. To create a generalized regression model, a polynomial regression is performed on the data points around the 15 th critical band over the tractive force on the tire (see Figure 11). In accordance with the procedure in Section 2.3.1, a correction factor can be calculated with the regression model. Figure 9: SPL ratio for different torque levels according to the bark scale. In order to take the torque dependency of the high-frequency components into account, the masking threshold map can be adjusted according to the torque, as represented by the flow chart (see Figure 5). The correction factor given by the regression formula is applied to the masking threshold map with a rotational speed-dependent weighting function to consider the decreasing torque for rpms higher than the power limit. The weighting function represents the gradient of the torque over the rotational speed of the engine. A representative weighting function with a specified power limit at 4100 rpm (dashed line) is shown in Figure 12.  
The frequency range in which the high-frequency components are adjusted can be derived from Figure 9. As mentioned before, the highest sensitivity is at 15 barks and declines at higher and lower barks. To adjust the masking threshold, the declining curve is approximated using a cosine-tapered windowing function (Tukey window) [39]. This function adjusts the correction factor that is calculated by the regression formula. In this way, the high-frequency components can be adjusted as a function of the frequency and the rotational speed of the engine. Figure 11: Regression model of the spl ratio over the tractive force on the tires. Figure 10: Sound pressure ratios between 50 Nm and the torque at full throttle for the investigated vehicles. By combining the frequency and rpm-dependent correction factors of the first (correction factor C\({}_{\rm BH1}\)) and second block harmonic (correction factor C\({}_{\rm BH2}\)) and the high-frequency components (correction factor C\({}_{\rm HI}\)), a 2-dimensional correction map according to Equation (6) can be generated, which can be used to adjust the 2-dimensional masking threshold map (see Figure 5). \[\rm C_{total}(n,f)=C_{BH1}(n,f)+C_{BH2}(n,f)+C_{Hf}(n,f) \tag{6}\]  
The following Figure 13 exemplarily shows a correction factor map that converts the masking threshold map of the luxury vehicle from 200 Nm to 400 Nm. Figure 12: Rotational speed-dependent weighting function. Figure 13: Two-dimensional correction factor map (200 Nm to 400 Nm; luxury vehicle).