## 2 Materials and Methods
### Spatial Multi-Dimensional Pulse Wave Signal Processing Method
Therefore, there are a total of N representative points. As shown in Equation (5), the spatial coordinates \((p,q)\) of the maximum value and the corresponding maximum value are recorded by comparing the values of \(N\) representative points sequentially. In one acquisition cycle, the one-dimensional pulse wave signal \(S_{p,q}\) of the sensor array is formed by N points with coordinates \((p,q)\) in the pulse waveform \(S_{n,x,y}\), as in Equation (6). Algorithm III The information carried by a single sensor pulse wave is limited and is susceptible to the influence of the sensor array's position relative to the radial artery test area. Linear synthesis of multiple sensors can reduce the influence of a single sensor and increase the pulse wave acquisition system's gain. However, due to the area covered by the sensor array, which exceeds the test area, some of the sensors can only collect ambient noise and interference. Suppose the data from sensors are added to the data set. In that case, the pulse's characteristics will be affected, and the reliability of the diagnosis will be reduced. Therefore, it is necessary to identify the effective pulse waveform before synthesizing the signal. Valid and invalid signals have many different characteristics in the time domain, as shown in

Figure 3: (**a**) Schematic diagram of the pulse wave signal processing flow; (**b**) block diagram of the Algorithm I process; (**c**) schematic diagram of spatial reconstruction of arrayed pulse wave signals; (**d**) block diagram of the Algorithm II process; (**e**) block diagram of the Algorithm III process. Figure 4a,c. The former has periodic peaks and troughs, and the time interval between adjacent peaks is within a specific range. Considering the human heart rate range of 55-160 beats/min, the lower limit of the time interval between adjacent peaks is 0.38 s and the upper limit is 1.09 s [34]. As shown in Figure 4b,d, the valid pulse wave signal's spectral distribution is quite different from the invalid signal is. The spectral energy of the invalid signal is concentrated near 0 Hz. The energy of the effective signal is distributed in the range of 0.5 Hz to 25 Hz and is concentrated at a few specific frequency points. The signals are examined in the time and frequency domains, respectively, as in Equations (7) and (8). where \(T\) is the time interval between adjacent wave peaks, \(f\) is the frequency, and \(max\) is the frequency value at which the spectral energy is maximum. Only pulse wave signals that satisfy both conditions are valid. \[0.38\;s\leq T\leq 1.09\;s \tag{7}\]

\[max(f)\
eq 0 \tag{8}\]

In the time series signals analysis, the Dynamic Time Warping (DTW) algorithm is often used to calculate the similarity between two time-series signals [35; 36]. The data collected from the MEMS sensor is based on a time series, so it is natural to use the DTW algorithm to calculate and measure the similarity of the pulse wave signal. The length of the time series \(X\) is \(m\), and the length of the time series \(Y\) is \(n\). The similarity distance between the two time series is \(dist_{m,n}\). Equation (11) is the iterative formula of the DTW algorithm, in which \(dist_{i,j}\) is the DTW distance between a point \(i\) on the time series \(X\) and a point \(j\) on the time series \(Y\), and \(d\big{(}x_{i},y_{j}\big{)}\) is the Euclidean distance between these two points. \[X=\{x_{1},x_{2},x_{3},\ldots,x_{m}\} \tag{9}\]

\[Y=\{y_{1},y_{2},y_{3},\ldots,y_{m}\} \tag{10}\]

Figure 4: Signals and their spectra: (**a**) time domain diagram of valid pulse wave signal; (**b**) frequency domain diagram of valid pulse wave signal; (**c**) time domain diagram of noise signal; (**d**) frequency domain diagram of noise signal. \[dist_{i,j}=\left\{ \begin{array}{ll}0,&m=n=0\\ \infty,&m=0|n=0\\ d\Big{(}x_{i},y_{j}\Big{)}+min\left\{\begin{array}{ll}dist_{i-1,j}\\ dist_{i,j-1}\\ dist_{i-1,j-1}\end{array}\right.&\mbox{other}\\ \end{array} \right.