# Optimization of Parametric Equalizer Filters in In-Vehicle Audio Systems with a Genetic Algorithm
## 3 Materials and Methods
### Parametric Equalizer Filters  
The parametric equalizer filter is a tool commonly used in audio processing and music production and has become a standard component in automotive multimedia systems. This filter adjusts the audio signal by targeting specific frequency ranges, thereby facilitating the adjustment of the sound's tonal balance. The parametric equalizer is adjusted based on three primary parameters: center frequency (\(f_{0}\)), bandwidth (or \(Q\) factor), and gain (\(G\)). The gain modifies the intensity of the sound signal by increasing or decreasing the amplitude within the selected frequency band. The bandwidth determines the range of frequencies where the filter is effective, and it is usually expressed in octaves. The \(Q\) factor is defined as the inverse of the ratio of the bandwidth to the center frequency and indicates the sharpness of the filter. A high \(Q\) factor means a narrower bandwidth and a sharper filter response. These parameters allow users to finely tune how narrowly or broadly they want to affect a specific frequency, thereby precisely achieving the desired sound characteristics. The parametric equalizer is a crucial tool in audio processing, primarily incorporating various filter types such as peaking (bell), shelving, and notch filters. In vehicle multimedia systems, the peaking filter is particularly favored. This filter facilitates the adjustment of in-vehicle sound systems in, accordance with the principle of equal loudness, through its  
Figure 4: B-frequency response of the weighting filter. advantages, such as frequency adjustment flexibility, tone control, and focused frequency intervention. The peaking filter is designed to either emphasize or attenuate signals within a specific frequency band and plays a critical role in sound processing and equalization [15]. The mathematical model of the peaking filter is represented by a transfer function \(H(f)\) that describes its effect on the frequency domain of the signal. This transfer function defines the relationship between the input and output of the signal as a function of frequency and is commonly formulated as (1)  
\[H(f)=1+\frac{GQ\Big{(}\frac{f}{f_{0}}-\frac{f_{0}}{f}\Big{)}}{1+Q\Big{(}\frac {f}{f_{0}}-\frac{f_{0}}{f}\Big{)}} \tag{1}\]  
Here, \(f\) represents the frequency under study, \(f_{0}\) is the center frequency (the frequency to be emphasized or attenuated), \(G\) denotes the gain (in amplitude level, measured in dB), and \(Q\) represents the quality factor (which inversely defines the bandwidth of the filter) [5]. According to the principle of equal loudness, the precise regulation of different frequency bands is necessary. Therefore, multiple parametric equalizer filters are generally used. The ISO 226:2003 standard [12] defines the characteristics of parametric filters required to achieve an ideal equal-loudness contour. Adjusted according to this standard, ten parametric filters were designed to provide optimal sound correction with corresponding gain and Q factor values at the specified frequencies. Each of these filters is set according to the frequency, gain, and Q factor values detailed in Table 1.  
In this study, ten parametric equalizer filters have been utilized to ensure an ideal sound experience in vehicle multimedia systems. A filter order of 12 was chosen, which is aligned with the order of existing filters in in-vehicle multimedia sound systems. The filters were created using the fdesign.parameq function, which is available in the DSP System Toolbox library of Matlab R2021b (9.11.0.1769968 version) software, and allows users to design a parametric equalizer filter with specified parameters. 1. Amplifier  
Amplifiers serve as fundamental power-boosting devices in sound systems. In vehicle multimedia systems, amplifiers increase the amplitude of the received audio signal, enabling speakers to produce sound at higher volumes and with higher quality. This improves the signal-to-noise ratio (SNR), enhancing the clarity and detail of the sound while minimizing distortions.