## 3 Auditory Perception Study of Sound Field in Closed Spaces with Different Structural Parameters
### Experiment Details
#### 3.1.2 Binaural Signal Simulation  
In this experiment, three kinds of musical sounds are selected for spatial auditory perception research, i.e., flute (wind instrument), violin (stringed instrument), and symphony (multiple instruments). The flute music used in the listening test is published by Sony Music, the violin, and symphony music are published by China National Symphony Orchestra. All three signals are without any auxiliary effect, so they are proper original signals.  
In view of the influence of closed space volume on auditory perception, three cuboid space models with volumes of 24 m\({}^{3}\), 96 m\({}^{3}\), and 192 m\({}^{3}\) (see Table 3 for specific dimensions) and thick pit sand mortar polished brick walls are established, which are denoted as a, b, and c. The positions of sound source and receiving points in each space are shown in Table 4. The room sizes are selected randomly with referring the sizes of real rooms in Section 2.  
In view of the influence of inner surface absorption coefficient on auditory perception, four cuboid spatial models of thick pit sand mortar polished brick wall surface (the absorption coefficient of the wall is a function of frequency), \(\alpha=0.00\) (total reflection), \(\alpha=0.50\), and \(\alpha=1.00\) (total sound absorption) with a volume of 192 m\({}^{3}\) are constructed, which are denoted as c, d, e, and f. The positions of sound source and receiving points in each space are the same as model c in Table 4.  
Considering the influence of space shapes on auditory perception, cuboid, semicylinder, and semisphere closed-space models are established and denoted as b, g, and h, respectively (see Table 5 for specific dimensions). Assume the space volume is 96 m\({}^{3}\) and the wall surfaces are all thick pit sand  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Space Model** & **a** & **b** & **c** \\ \hline
**Coordinates of sound source** & \((2,0,1.4)\) & \((3,0,2)\) & \((4,0,2)\) \\ \hline  & \(1\) & \((1,0,1)\) & \((1.5,0,1)\) & \((2,0,1)\) \\ Coordinates of receiving & \(2\) & \((3,0,2)\) & \((4.5,0,3)\) & \((6,0,3)\) \\ points & \(3\) & \((2,0.5,1)\) & \((3,1,1)\) & \((4,1.5,1)\) \\  & \(4\) & \((2,-0.5,2)\) & \((3,-1,3)\) & \((4,-1.5,3)\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The positions of sound source and receiving points in closed-space models.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Space Model** & **L/m** & **W/m** & **H/m** & **S/m\({}^{2}\)** & **V/m\({}^{3}\)** \\ \hline a & \(4\) & \(2\) & \(3\) & \(52\) & \(24\) \\ b & \(6\) & \(4\) & \(4\) & \(128\) & \(96\) \\ c & \(8\) & \(6\) & \(4\) & \(208\) & \(192\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The dimensions of closed-space models with different volumes.  
mortar polished brick. The positions of sound source and receiving points in each space are shown in Table 6.  
To sum up, current research has established a total of eight closed-space models with different volumes, inner surface absorption coefficients, and space shapes. After determining the above experiment parameters, select the research type calculation level, set the number of sound lines to be 5000 (maximum number of sound lines, more accurate calculation result), and take 1000 ms as the response time of the binaural impulse. Then, the indoor binaural impulse responses of the above eight closed-space models are calculated. Next, the three original signals (flute, violin, and symphony with length of 10 s) are convolved with those binaural impulse responses to synthesize the binaural signals at different positions within different closed spaces, i.e., 8 (closed space) \(\times\)4 (receiving point) \(\times\)3 (original signal) = 96.