## 2 Materials and Methods  
The principle of the SMSG algorithm is mainly based on the painter's algorithm, also known as depth-sorting algorithm [14]. It is the same as when observing two objects, the frontal object obscures the back one. For example, there is a cuboid and a tetrahedron in Figure 1a, the cube being behind the tetrahedron. It can be seen from Figure 1b that the overlapped part of the two objects, especially a part of the cube is covered and is not visible. When drawing the graph, the HSR displaying was realized [15]. There are two commonly used projection methods--orthogonal projection and perspective projection. An orthogonal projection means that no matter how far away from the view point (eyes or a camera), the size of the projected object remains unchanged. Unlike 3D models, such as convex polyhedron and concave polyhedron, there is no need to produce a significant perspective effect in time-frequency spectrogram. Additionally, the computational cost of orthogonal projection is less than that of perspective projection. Therefore, the orthogonal projection has been used for generating 3D figures, in this paper. To draw 3D graphics on a computer, or an embedded device, more specifically, means to draw the projection figure of 3D objects on a certain plane, at a certain angle. The screen coordinates used in the LCD is shown in Figure 2, where the \(Z\)-axis is perpendicular to the LCD screen. Here, the \(XOY\)-plane was chosen as the projection plane. The viewpoint was located at the positive infinity of the \(Z\)-axis. The formula of the orthogonal projection is shown in Equation (1):  
\[\left[ \begin{array}{ccccc}x^{\prime}&y^{\prime}&z^{\prime}&1\end{array} \right]= \left[ \begin{array}{ccccc}x&y&z&1\end{array} \right].\left[ \begin{array}{ccccc} 1&0&0&0\\ 0&1&0&0\\ 0&0&0&0\\ 0&0&0&1\end{array} \right] \tag{1}\]  
\([x,y,z]\) was the homogeneous coordinate of a point in 3D space, and \([x^{{}^{\prime}},y^{{}^{\prime}},z^{{}^{\prime}}]\) was the orthogonal projection coordinate. According to Equation (1), the \(Z\)-axis value was omitted if orthogonal projection was performed directly. To produce a three-dimensional effect, it was necessary to rotate the coordinates around the \(X\)-axis and the \(Y\)-axis, by a certain angle. When a degree of \(\alpha\) was rotated around the \(X\)-axis, the transformation formula was as follows:  
\[\left[ \begin{array}{ccccc}x^{\prime}&y^{\prime}&z^{\prime}&1\end{array}  \right]=\left[ \begin{array}{ccccc}x&y&z&1\end{array} \right].\left[ \begin{array} []{ccccc}1&0&0&0\\ 0&\cos\alpha&\sin\alpha&0\\ 0&-\sin\alpha&\cos\alpha&0\\ 0&0&0&1\end{array} \right] \tag{2}\]  
When a degree of \(\beta\) was rotated around the \(Y\)-axis, the transformation formula was as follows:  
\[\left[ \begin{array}{ccccc}x^{\prime}&y^{\prime}&z^{\prime}&1\end{array}  \right]=\left[ \begin{array}{ccccc}x&y&z&1\end{array} \right].\left[ \begin{array} []{ccccc}\cos\beta&0&-\sin\beta&0\\ 0&1&0&0\\ \sin\beta&0&\cos\beta&0\\ 0&0&0&1\end{array} \right] \tag{3}\]  
Figure 1: Example of the principle of the painter’s algorithm: (**a**) 3D scene in observer’s visual area; (**b**) projection of the 3D scene. Figure 2: The screen coordinates. It is important to note that \(\alpha\) and \(\beta\) were positive rotation angles in the right-handed coordinate system. Given a point (\(x\), \(y\), \(z\)) in the three dimensions, when rotating \(\alpha\) degree around the \(X\)-axis, the coordinate changed to:  
\[\left\{ \begin{array}{c}x\prime=x\\ y\prime=y\cos\alpha-z\sin\alpha\\ z\prime=y\sin\alpha+z\cos\alpha\end{array} \right. \tag{4}\]  
If a degree of \(\beta\) was rotated around the \(Y\)-axis, then Equation (5) could be updated with Equation (4), from which Equation (6) could be obtained:  
\[\left\{ \begin{array}{c}x\prime=z\sin\beta+x\cos\beta\\ y\prime=y\\ z\prime=y\cos\beta-x\sin\beta\end{array} \right. \tag{5}\]  
\[\left\{