## 3 Dynamic Sampling Rate Adjustment Method
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Descriptions** \\ \hline \(F_{total}\) & Total number of frames in a sign language utterance \\ \hline \(k_{idx}\) & Index of a keypoint \\ \hline \(K_{max}\) & Maximum index for keypoints \\ \hline \(S_{r}\) & Sampling rate \\ \hline \(N_{change}\) & Total number of keypoint position change records (\(N_{change}=\left\lfloor\frac{F_{total}}{S_{r}}\right\rfloor\)) \\ \hline \(C_{i}\) & Change record of the \(i\)-th keypoint position \\ \hline \(x_{i}^{k_{idx}}\) & \(x\)-coordinate of keypoint at index \(k_{idx}\) in the \(i\)-th frame \\ \hline \(y_{i}^{k_{idx}}\) & \(y\)-coordinate of keypoint at index \(k_{idx}\) in the \(i\)-th frame \\ \hline \(K_{info}\) & The \(x\) and \(y\) coordinate information of keypoints for all frames \\ \hline \(C_{total}\) & Sum of all keypoint position change records (\(\sum_{i=1}^{N_{change}}C_{i}\)) \\ \hline \(C_{avg}\) & Average of all keypoint position change records (Threshold value) \\ \hline \(S_{start}\) & Detected start frame of the sign language utterance \\ \hline \(S_{end}\) & Detected end frame of the sign language utterance \\ \hline \(T_{utterance}\) & Duration of the sign language utterance in mobile environments \\ \hline \(N_{frames}\) & Total number of frames captured during \(T_{utterance}\) \\ \hline \(fps_{server}\) & Frame rate in server environments \\ \hline \(fps_{mobile}\) & Frame rate in mobile environments \\ \hline \(SR_{server}\) & Optimal fixed sampling rate in server environments \\ \hline \(SR_{mobile}\) & Dynamic sampling rate in mobile environments \\ \hline \(R_{fps}\) & Ratio of \(fps_{mobile}\) to \(fps_{server}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Symbols and descriptions. end of hand motion, the frame with the largest index \(i\) among the frames larger than \(C_{agg}\) becomes the end of hand motion. \[S_{start}=\min(\forall i,\text{where}(C_{agg}\leq C_{i})) \tag{5}\]  
\[S_{end}=\max(\forall i,\text{where}(C_{agg}\leq C_{i})) \tag{6}\]  
The key parameter is the sampling rate, \(SR_{server}\). If \(SR_{server}\) is too small, many frames need to be counted and measured to detect the start and end points of the sign language utterance. Conversely, if it is too large, fewer frames are counted and measured. In short, this parameter determines the frequency at which keypoint changes are observed. Applying this fixed sampling algorithm directly to mobile environments presents challenges due to mobile devices having lower computing power compared to servers. As a result, typical mobile devices, such as smartphones, extract fewer frames per unit of time, making the use of a server-optimized fixed sampling rate impractical. For example, in the case of a server, it is possible to obtain more than 30 fps (frames per second) during sign language utterances, whereas mobile devices, such as smartphones, may obtain less than 30 fps depending on their computing performance. Therefore, in mobile environments, it is necessary to dynamically adjust the sampling rate based on the obtained frames to detect the start and end points of sign language utterances. As we explained, in mobile environments, frames are extracted in real time during sign language utterances, leading to variations in the number of frames extracted over the same period compared to servers, where all frames can be extracted from a video. This variation necessitates adjusting the sampling rate dynamically based on each mobile device's frame extraction rate. By doing so, the accuracy of detecting the start and end points of sign language utterances can be improved, ultimately leading to an improvement in the overall accuracy of the sign language recognition model. This dynamic method is crucial in resource-constrained environments like mobile devices to provide sign language recognition-based services.