## 2 Sound Simulation System Design Methods
### Sound Synthesis Method  
Sound Synthesis Algorithm Analysis  
Currently, the main use of sound synthesis algorithms can be usually divided into two categories: parameter analysis and synthesis and time domain waveform synthesis, usually used in the field of speech synthesis. Parametric analysis synthesis is mainly based on the relevant sound channel model and calculates the corresponding sound parameters and sound synthesis. This method can greatly reduce the storage space for soundand has relatively flexible control of sound parameters to realize multiple variations of sound. It has been widely used in the field of speech synthesis. However, the sound synthesized by this method is rather stiff and lacks a sense of naturalness. Time-domain waveform synthesis is the encoding and storage of sound sample waveforms. Alternatively, one can store the time domain waveform after editing the fragments according to the fundamental sound, and then synthesize the final speech after selecting and splicing the stored sound sample fragments and adjusting them according to external conditions. This method synthesizes speech based on the original sound fragments with more natural sound quality but requires more storage space for the sound fragment samples. The number of primitives in engine sound is greatly reduced compared with speech which can effectively save storage space to make the simulated engine acceleration sound natural and harmonious. In this paper, we analyze the time-domain waveform synthesis method to synthesize sound based on the idea of synchronous superposition algorithm of time-domain fundamental tones. In the process of implementing the time-domain fundamental sound synchronization superimposition algorithm for the engine acceleration sound, the sound signal needs to be framed to get a number of short time signals, with one primitive per frame as a sound sample. The period between primitives is then adjusted synchronously. Finally, we select the appropriate primitive fragment according to the external conditions to splice the synthesized sound [44; 45]. The principle is essentially to use short-time Fourier changes to reconstruct the signal. For signal A, the short-time Fourier transform is (10). \[X_{n}(e^{iw})=\sum_{m=-\infty}^{+\infty}x(m)w(n-m)e^{-i\omega m} \tag{10}\]  
In Equation (10), \(n\in Z\),\(Z\) is the set of integers, \(w(n)\) is a window of length \(n\), and \(X_{n}(e^{iw})\) is a two-dimensional time-frequency function of \(n\) and \(w\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Description Dimension** & **Related Semantics** \\ \hline \multirow{3}{*}{Auditory characteristics} & Thicker; a little roughness; low; full sound; clear; \\  & low-speed rumble; pure sound; intense sound; pitch \\  & undulation; pleasant \\ \cline{1-1}  & Pleasant; kinetic; powerful; exciting; exililarating; \\ \cline{1-1}  & interesting; restless; urgent; strong driving sensation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of motion-sensitive sounds. The implementation process of the algorithm is divided into the following steps:  
(1) Sound signal framing and fundamental frequency estimation. In-vehicle acceleration sound samples as time-varying non-stationary signals. The overall noise is mainly composed of each order of noise; the main order component of the four-cylinder engine is the 2 nd order and the energy of each other order gradually increases as the speed rises. At the time of frame splitting, set the original signal as \(x_{m}(n)=x(n)w_{m}(t_{m}-n),w(n)\) is the window function, and \(x_{m}(n)\) is the \(m\)th short time signal after framing. Then, the signal of segment m after adding the window \(x_{m}(n)\) can be expressed as (11):  
\[x_{m}(n)=x(n)w_{m}(t_{m}-n) \tag{11}\]  
In Equation (11), \(t_{m}\) is the center of the window function and consistent with the estimated marker position of the fundamental frequency. Then, the frequency of the main order of the sound signal needs to be analyzed; sound clip signals can be considered smooth in short periods of time.