## 2 Background
### Psychoacoustics  
Psychoacoustics is the study of the relationship between the physical quantity of sound and subjective auditory emotion [11]. To demonstrate this relationship, physical parameters such as loudness, sharpness, roughness, SPL, and frequency are used. Loudness is a measure of acoustic intensity using size estimation in relation to human auditory perception [33]. This is a dominant feature in sound quality assessment, and loudness is the most important parameter in the preference test of vehicle design [34]. The sound pressure level (SPL) is defined as \"the SPL of a 1 kHz tone in a plane wave and frontal incident that is as loud as the sound; its unit is phone, and the unit is phone\" [35]. The critical band is a specific range of audio frequencies in 24 bands of Bark, and the intensity of a specific sound is the calculated volume of each important band. The mathematical equation of the loudness is shown in Equation (1).  
\[N=\int_{0}^{24 Bark}N^{\prime}dz \tag{1}\]  
where \(N\) is the overall loudness and \(N^{\prime}\) is the specific loudness. The variable \(z\) represents the critical band.  
Sharpness is related to auditory perception, which is a measure of tone and is used to measure the sound at high frequencies that play an important role in sound quality evaluation [36]. The sharpness can be estimated relatively easily by calculating the weighted area of loudness [35]. The sharpness is due to the narrowband noise corresponding to one critical bandwidth at the center frequency of 1 kHz at a level of 60 dB, where the unit is defined as 1 acum. [PERSON] modified the Bismarck model to reflect the effect of loudness on the sharpness [37]. The mathematical expression of the sharpness calculation is shown in Equation (2).  
\[S=0.11\frac{\int_{0}^{24 Bark}N^{\prime}g^{\prime}(z)zdz}{\int_{0}^{24 Bark}N^{ \prime}dz} \tag{2}\]  
where is \(N^{\prime}\) is the specific loudness, \(z\) is critical band rate and \(g^{\prime}(z)\) is if \(z<14\), then \(g^{\prime}(z)=1\), and if \(z>14\), then \(g^{\prime}(z)=0.00012z^{4}\)\(-0.0056z^{3}+0.1z^{2}-0.81z+3.51\).  
Roughness has been considered as one of the important psychoacoustic parameters for its significant influence on the reduction of pleasantness [35; 38], which leads to a negative effect of sound quality. The roughness is a subjective perception evoked from rapid (15-300 Hz) amplitude modulation of a sound, and [PERSON] [38] introduced a calculation model of roughness for sound. The unit of roughness is asper and the equation of the roughness is shown in Equation (3).  
\[R=0.3\frac{f_{\rm mod}}{kHz}\int_{0}^{24 Bark}\frac{\Delta L(z)\cdot dz}{dB/Bark} \tag{3}\]  
where \(f_{\rm mod}\) is the frequency of modulation, and \(\Delta L(z)\) is the perceived masking depth.  
Tonality is a measure of the ratio of tonal elements in a spectrum of complex signals. [PERSON] and [PERSON] proposed a method of calculating tonality [39; 40]. According to their study, the measurement unit of tonality is tu, and 1 tu is the sine tone of 60 dB, 1 kHz. [PERSON] [39] proposed a calculation method of tonality considering the influence of frequency, bandwidth, level, and noise of all tone components.