## 2 Materials and Methods
### Proposed Calculation Method
#### 2.3.1 Noise Components Within the Block Harmonic  
To further investigate the noise components within the block harmonic, the signal of the recorded vehicle interior noise is evaluated using a Butterworth filter with a bandwidth of % octave. This bandwidth is selected according to the mean value of the block harmonic bandwidth of one- to two-thirds as described in the literature [36]. For the investigation, loudness evaluations of the filtered block harmonic signal as per DIN 45631 [37] were conducted. In order to quantitatively compare the torque dependency of the block harmonic between the investigated vehicles, the ratio N\({}_{\text{ratio}}\) of the loudness at the investigated torque level N\({}_{\text{TL}}\) and the loudness at the torque level with full-throttle N\({}_{\text{FT}}\) was calculated as a function of the rotational speed of the engine according to Equation (3). By using the torque at full throttle as reference value, the reproducibility was ensured. Additionally, the highest noise excitation can be expected at full throttle and facilitates the comparison between different torque levels. \[\text{N}_{\text{ratio}}=\frac{\text{N}_{\text{TL}}}{\text{N}_{\text{FT}}} \tag{3}\]  
Figure 6 shows the loudness ratio of the individual torque levels with respect to the loudness at full throttle. It can be seen that, especially at low torque levels, the loudness ratio shows a similar characteristic, and the loudness ratio rises with higher torque levels due to the decreasing loudness differences between the denominated torque and the torque at full throttle. In the following, the loudness ratio will first be considered with respect to the tractive force on the tires only, where the tractive force (F\({}_{\text{tire}}\), [N]) is calculated from the torque of  
Figure 6: Loudness ratio of different torque levels as a function of the rotational speed of the engine. the electric machine (M\({}_{\text{EM}}\), [Nm]), the gear transmission ratio (i\({}_{\text{gear}}\)) and an estimate of the rolling circumference of the tire (r\({}_{\text{tire}}\), [m]) (see Equation (4)). \[\text{F}_{\text{tire}}=\frac{\text{M}_{\text{EM}}\times\text{i}_{\text{gear}}}{ \text{r}_{\text{tire}}\times 2} \tag{4}\]  
In order to establish a calculation method that provides generalized results that can be applied to a variety of different vehicle categories, the mean value of the loudness ratio is calculated for each torque level in the speed range up to the power limit (see Figure 1) for the three investigated vehicles. The results of the mean values of the investigated vehicles are shown in Figure 7 according to the tractive force acting on the tire for the respective torque levels/loudness ratio. When considering the loudness ratio of each vehicle individually, an approximately linear increase in the loudness ratio with increasing tractive force on the tire can be seen. For each individual vehicle, a linear regression was performed, which is indicated with the dashed lines. Due to the goal of a generalized method that can be easily implemented in existing evaluation tools, a linear regression method was chosen due to its simplicity and interpretability. It can be seen that the luxury vehicle shows the smallest gradient compared to the other vehicles, thus showing less sensitivity to the loudness of the first block harmonic with variation in the tractive force. To calculate a correction factor that adjusts the masking threshold level of the block harmonic according to the torque, Equation (5) is used to calculate the correction factor from the slope of the regression and the input and output tractive forces on the tire. The tractive force is calculated with the gear transmission ratio and the approximated rolling circumference of the tire.