## 2 Materials and Methods
### Spatial Multi-Dimensional Pulse Wave Signal Processing Method
\tag{11}\]

\[P_{i}=\frac{1}{T_{0}}\int_{0}^{T_{0}}\Bigl{|}x_{i}(t)\Bigr{|}^{2}dt \tag{12}\]

\[y=\frac{P_{i}}{P_{j}}*x_{j}\;(j=L_{2}(k);\;i=P_{2}(k);\;k=\{1,2,\ldots\}) \tag{13}\]

\[y=\sum_{i=1}^{12}f(x_{i})*g(x_{i})*x_{i} \tag{14}\]

The similarity matrix \(R\) was calculated using the DTW algorithm based on the data from the valid waveform. The similarity is sorted from largest to smallest to obtain the ranking vector \(L_{1}\) of the waveform signal similarity and the ranking vector \(L_{2}\) of the corresponding subscript. A similar approach was sampled to deal with the average power of the pulse wave over a single acquisition period, a parameter that describes the pulse wave's energy per unit of time as in Equation (12). \(Q_{1}\) is the average power ranking vector of \(M\) sensors and \(Q_{2}\) is the ranking vector of the corresponding subscript. \(L_{2}\) and \(Q_{2}\) are not identical. The former is related to the array sensor's overall pulse waveform, while the latter is related to the amplitude of the pulse wave signal. To correct the mismatch between similarity and average power, a linear approach shown in Equation (13) was used. The linear coefficients are related to the similarity ranking vector \(L_{2}\) and the average power ranking vector \(Q_{2}\), where \(i\) and \(j\) are the values of the \(k\)-th element in \(Q_{2}\) and \(L_{2}\), respectively. \(P_{i}\) and \(P_{j}\) are the elements in the ordering vector \(Q_{1}\). For a signal with high similarity and low average power, the subscript of the average power sequence is necessarily more incredible than the subscript of the similarity sequence, so \(Q_{i}>Q_{j}\). The linear adjustment results in an increase in the average power of pulse waves with high similarity, a decrease in the average power of pulse wave signals with low similarity, and no change in the two's overall average power. The elements in \(L_{1}\) are traversed sequentially, adjusting the data for the effective waveform linearly until \(L_{2}\) and \(Q_{2}\) are identical. In summary, the entire processing of Algorithm III, as described in Equation (14). \(f(x)\) is a discriminant function of pulse wave signal validity, which results in only 0 or 1, \(g(x)\) is the linear adjustment factor calculated from the similarity ranking vector and the average power ranking vector, \(x_{i}\) is the pulse wave signal collected by PAWS. ## 3 Experimental Results

In order to assess the performance of the above methods, multiple repetitions of the test in different test areas are employed under certain standard conditions. The pulse waveform calculated by the pulse wave processing method is theoretically the same as the standard input waveform in two aspects. On the one hand, the method-processed waveform has the same trend as the standard input waveform, which means that the two waveforms are very similar. Consistent with the above, the DTW distance was used to assess the similarity of the two waveforms. On the other hand, the energy of both is identical. Define the gain of the algorithm as the ratio of the energy of the processed signal in a single acquisition cycle to the energy of the standard input signal, as shown in Equation (15), where \(x(t)\) is the standard input signal acquired by the ZM-300, \(y(t)\) is the processing results of the above method, and \(T_{0}\) is an acquisition cycle. The smaller the energy difference between the processed signal and the standard input signal, the closer the system's gain is to zero. Thus, the degree of energy change after processing by different algorithms can be assessed by gain. \[Gain=10*log(\frac{\int_{0}^{T_{0}}\abs{y(t)}^{2}dt}{\int_{0}^{T_{0}}\abs{x(t)}^{ 2}dt}) \tag{15}\]

An SPVG consisting of the ZM-300, periodically squeezing the PAWS' MEMS sensor array, is used to simulate the pulse wave signal input, as shown in Figure 5a. In Equation (16), the force tested by the sensor in ZM-300 is \(F_{ZM-300}\) and the force tested by the sensor array in PAWS is \(F_{PWAS}\).