## 3 Dynamic Sampling Rate Adjustment Method  
In this section, we introduce our dynamic sampling rate adjustment method, designed to improve the performance of sign language recognition in mobile environments by adjusting the sampling rate based on the number of frames extracted in real time during sign language utterances. Mobile environments typically have less computational power compared to server environments, resulting in greater variability in the number of frames that can be captured in real time during sign language utterances. The method suggested in previous research [17] does not account for these variations, potentially leading to suboptimal recognition accuracy in mobile environments. Our proposed dynamic sampling rate adjustment method addresses this issue by dynamically adjusting the sampling rate according to the actual frame rate obtained during sign language utterances. Table 3 provides a comprehensive list of symbols and their descriptions to explain our proposed method. In the previous research of [17], the start and end points of sign language utterances were detected based on the amount of change in the movement of each keypoint. \(SR_{server}\) is the sampling rate for counting and measuring keypoint coordinates. The keypoint coordinates are counted and measured every \(SR_{server}\) frames of the data frame. In the experiment, \(SR_{server}\) was set to 5, and \(N_{change}\) represents the total number of keypoint position changes. Therefore, \(N_{change}\) can be calculated using Equation (1). The counted and measured keypoint information data are structured as \((x,y)\) coordinates. \(C_{i}\) is the \(i\)-th keypoint change information, counted and measured by \(SR_{server}\). \(C_{i}\) can be calculated using Equation (2). \[N_{change}=\lfloor\frac{F_{total}}{S_{r}}\rfloor \tag{1}\]  
\[C_{i}=\sum_{k=1}^{K_{max}}\sqrt{(x_{i}^{k_{idx}}-x_{i-1}^{k_{idx}})^{2}+(y_{ i}^{k_{idx}}-y_{i-1}^{k_{idx}})^{2}} \tag{2}\]In Equation (2), \(k_{idx}\) represents the index of the counted and measured keypoint, and the maximum index is \(K_{max}\). The maximum value of \(K_{max}\) varies depending on the keypoints used at the start and end of the hand. \(x_{i}^{k_{idx}}\) is the \(x\) coordinate of the keypoint with index \(k_{idx}\) in the \(i\)-th keypoint extraction frame. Similarly, \(y_{i}^{k_{idx}}\) is the \(y\) coordinate of the keypoint with index \(k_{idx}\) in the \(i\)-th keypoint extraction frame. \(C_{Total}\) is the sum of the position changes of each keypoint and can be calculated using Equation (3). As shown in Equation (3), \(C_{Total}\) is calculated as the sum of all \(C_{i}\). \[C_{total}=\sum_{i=1}^{N_{change}}C_{i} \tag{3}\]  
\(C_{avg}\) is the average value of the position changes of each keypoint and can be calculated using Equation (4). \(C_{avg}\) is used as the threshold for determining the start and end of hand motion. \[C_{avg}=\frac{C_{total}}{N_{change}} \tag{4}\]  
Finally, in the detection algorithm, the start and end of hand motion are determined by Equations (5) and (6). For the start of hand motion, the frame with the smallest index \(i\) among the frames larger than \(C_{avg}\) becomes the start of hand motion. Conversely, for the