## 2 Recommended Topology and Working Principles  
The function \(S_{id}(n)\) that presents the horn sound based on specified parameters, adhering to a defined frequency and amplitude profile is given in (1). This is crucial for delivering precise alerts to both drivers and other road users. \[S_{id}(n)=-\sum_{k=1,2,3,...}^{K}\frac{1}{k}\sin(2\pi\cdot f\cdot k\cdot\frac{ n}{f_{s}}) \tag{1}\]  
In the given equation, the variable \(k\) denotes the harmonic number, \(f\) denotes the sound frequency, \(f_{s}\) represents the sampling frequency, and \(n\) represents the octave. When generating the sound, the amplitude is modulated using a fundamental sine waveform [21]. Nevertheless, to achieve a natural and harmonically rich tone in the sound, additional harmonics are incorporated into this fundamental sine waveform. Here, the adjustment of amplitude is tailored based on the number of harmonics. In essence, the sound texture is enhanced by assigning distinct amplitude values to each of these harmonics. Each of the first 16 harmonics, commencing with the note C2, is accompanied by its nearest musical note as shown in Figure 1. Additionally, the disparity (measured in cents) between the frequency of a harmonic and the central frequency of the closest note is displayed at the top. In music theory [22], the concept of octaves holds significant relevance in the process of amplitude adjustment. In music, an octave signifies a doubling of the frequency. When modifying amplitudes in this program, harmonic frequencies rise proportionally across octaves. Specifically, the utilization of the 12-step octave structure aids in maintaining the coherence and consonance of the sound. Figure 2a presents the proposed block diagram for the horn sound generator system. Figure 2b displays the suggested corresponding Python code for the blocks in the diagram. Below is an explanation of the block diagram, the code functionality, and the definitions of the functions used. From here, the \"\(calculate_{pitch}(frequency)\)\" function within the software embodies a mathematical formula that translates frequency into a musical note value, as depicted in (2). \[note_{pitch}=69+(12\cdot log_{2}(\frac{frequency}{440})) \tag{2}\]  
The octave (notepitch) detection formula identifies the musical note corresponding to any frequency by measuring its deviation from the 440 Hz reference frequency. This method offers a straightforward interpretation of the frequency's placement within conventional musical notation. For instance, consider note A5 with a frequency of 880 Hz: note = 81 signifies that the frequency is positioned one octave higher than the reference frequency. The derived note factor is subsequently employed in the software through reverse engineering to ascertain the frequency values of both low and high-tone frequencies within each octave (Equation (2)). \[frequency=440\cdot 2^{\frac{nat_{pitch}-\theta}{12}} \tag{3}\]  
This computation serves as a fundamental tool for comprehending musical organization and ascertaining the relative placements of frequencies. By employing this formula, the note factors and fundamental frequency values for both the fundamental frequency and harmonics, which are instrumental in generating the horn sounds within the framework, are established. Figure 2a presents the schematic depiction of the proposed horn generator code, and Figure 2b illustrates the suggested Python code. As depicted in Figure 2, the \"\(limited\_horn\_sound\_thick\_thin\)\" function within the software facilitates the determination of the Limiterval value. This function enables the overall management of the amplitude level of the audio signal. Its primary objective is to prevent signal saturation by imposing a specific limit on the overall amplitude level. Notably, this section is entirely optional; if the frequency-based amplitude levels are meticulously designed to harmonize without reaching saturation, the inclusion of a limiter becomes unnecessary (refer to Figure 3). Figure 1: The harmonic series in musical notation. Figure 2: _Cont._  
1.