## 2 Materials and Methods
### Spatial Multi-Dimensional Pulse Wave Signal Processing Method  
The processing of a spatial multi-dimensional pulse wave signal is divided into two main modules, as shown in Figure 3a. The first module focuses on removing noise and interference from the 12 dynamic pulse wave signals collected by PAWS using two sets of filters. The other module extracts the one-dimensional pulse wave signal from the filtered array signal using various pulse wave processing algorithms, as described in Figure 3b,d,e. Pulse wave noise and interference consist of three main components: random noise, baseline drift, and 50 Hz power line interference. Random noise, distributed over the entire frequency range, is also present in the frequency band where pulse waves occur. Therefore, it is difficult to eliminate the noise using frequency-based filtering. The Sym8 wavelet function is chosen as the wavelet base to decompose the original signal into four layers. Hard threshold filtering is applied to each layer to reduce the random noise energy effectively. During the test results, the baseline drifts partly from the slow release of the sensor's additional pressure during cuff pressurization and partly from the testers' breathing. The former is below 0.1 Hz, while the latter is distributed in the range of 0.2 to 0.4 Hz. A zero-phase shift bandpass filter with a bandwidth of 0.5 Hz to 40 Hz can remove baseline drift and 50 Hz-frequency interference and avoid the relative shift of signal phase during filter processing. The following part is a detailed description of Algorithm I, Algorithm II, and Algorithm III. ```
1:Input: \(\mathbf{x}_{1},\mathbf{x}_{2},\ldots,\mathbf{x}_{12}\), \(\mathbf{x}_{1},\ldots,\mathbf{x}_{12}\),



_MAX_ the latter is \(m\), as in Equation (1). The pulse wave signal collected by the \(m\)-th sensor during the current acquisition cycle is used as the pulse waveform graph as shown in Equation (2). \[MAX=\underset{i\in M}{max}\{r_{i}\}=\underset{i\in M}{max}\{\underset{j\in N}{ max}(x_{i,j})\} \tag{1}\]

\[y=x_{m} \tag{2}\]

Algorithm II Before Algorithm II processing, the \(M\)-channel pulse wave signal needs to be reconstructed according to the spatial location of the acquisition sensor to facilitate interpolation fitting. As shown in Figure 3c, the spatial coordinates of sensor 1 are (1,1); along the positive \(X\)-axis, the spatial coordinates of sensor 4 are (4,1); and along the positive \(Y\)-axis, the spatial coordinates of sensor 9 are (1,3). There is a total of \(M\times N\) sampling points in an acquisition cycle, where \(M\) is the number of sensors, and \(N\) is the number of sampling points of a single sensor in the cycle. Figure 3: _Cont._

\[f(x,y)=\sum_{i=0}^{3}\sum_{j=0}^{3}f\Big{(}x_{i},y_{j}\Big{)}W(x-x_{i})W\Big{(}y-y _{j}\Big{)} \tag{3}\]

\[W(x)=\left\{ \begin{array}{ll}(a+2)|x|^{3}-(a+3)|x|^{2}+1&|x|\leq 1\\ a|x|^{3}-5a|x|^{2}+8a|x|-4a&1<|x|<2\\ 0&otherwise\end{array} \right. \tag{4}\]

\[MAX=s_{p,q}=\underset{n\in N}{max}\{\underset{x\in E,y\in F}{max}S_{n,x,y}\} \tag{5}\]

\[y=S_{p,q} \tag{6}\]

The Bicubic Interpolation Algorithm [33] is implemented using a convolutional operation as in Equation (3) to compute the point \(f(x,y)\) to be interpolated, where \(f\Big{(}x_{i},y_{j}\Big{)}\) is the 16 neighborhood points in the vicinity of \(f(x,y)\). \(W(x)\) in Equation (4) implements the convolutional kernel in Equation (3), and \(a\) is typically \(-0.5\). For each acquisition moment, \(E\) points are interpolated in the x-direction and \(F\) points are interpolated in the y-direction, producing a total number of \(E\times F\) interpolation points, which are then fitted to the 3D pulse wave signal \(S_{x,y}\). \(x\) and \(y\) are the horizontal and vertical coordinates of the interpolation point \(S_{x,y}\), with \(x\in E\) and \(y\in F\), respectively. \(N\) samples can be interpolated to get \(N\) 3D pulse waveforms \(S_{n,x,y},n\in N\). Like Algorithm I, the point s with the highest amplitude value in each pulse waveform graph is used as the representative point.